ABSTRACT Title of Document: AIRSIDE PASSIVE HEAT TRANSFER ENHANCEMENT, USING MULTI-SCALE ANALYSIS AND SHAPE OPTIMIZATION, FOR COMPACT HEAT EXCHANGERS WITH SMALL CHARACTERISTIC LENGTHS Daniel Fernandes Bacellar, Doctor of Philosophy, 2016 Directed By: Reinhard Radermacher, Professor Department of Mechanical Engineering The study of compact heat exchangers (HX) is a very common, although broad topic that draws interest from many engineering applications. Most technologies contain at least one HX serving as a fundamental component for the proper system functioning. The rapid worldwide population growth, increasing demand for energy resources, widespread environmental concerns, space exploration efforts and economy are all good reasons for developing smaller, lighter and more efficient HX’s. This research sheds the light on the next generation of heat exchangers, with a focus on air- to-fluid applications. For incompressible flows and low-pressure applications, the HX’s airside thermal resistance is the major limitation to overall thermal conductance. On conventional surfaces fins are required, but bring many drawbacks. Among these include being prone to fouling/frosting, reduced heat transfer coefficient, higher friction resistance, and more material consumption. Tubes by nature provide more valuable heat transfer than do fins; there is little focus on tubes in the literature. The first objective of this work is to discuss the fundamental aspects of primary (tubes) and secondary (fins) surfaces, with the aid of numerical analyses. The latter demonstrates how the reduction of characteristic length and novel shapes impact surface performance and compactness of finless and finned tubes. A further discussion is presented arguing that conventional fin concepts are not always beneficial. The second objective of this work entails developing a comprehensive multi- scale analysis with topology and shape optimization methodology leveraging automated CFD simulations and approximation assisted optimization. Novel finless air-to-fluid HX concepts were developed, for single-phase and two-phase applications, and achieved more than 20% reduction in size, 20% better performance and 20% less material than state-of-the-art HX’s including microchannel HX’s. Two prototypes (one manufactured in metal 3D printing) were tested in an in-house wind tunnel. The numerical predictions agree with the experimental results in less than 5% deviation for total capacity, 10% for airside heat transfer coefficient and 20% for air pressure drop. Finally, the last objective is to present the development of robust and computationally inexpensive tools that can accurately predict CFD simulation responses for conventional tube and fin surfaces using small diameter tubes (<5.0mm). AIRSIDE PASSIVE HEAT TRANSFER ENHANCEMENT, USING MULTI- SCALE ANALYSIS AND SHAPE OPTIMIZATION, FOR COMPACT HEAT EXCHANGERS WITH SMALL CHARACTERISTIC LENGTHS By Daniel Fernandes Bacellar Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2016 Advisory Committee: Professor Reinhard Radermacher, Chair Professor James Baeder (Dean’s Representative) Professor Jungho Kim Professor Bao Yang Professor Marino diMarzo Dr. Vikrant Aute © Copyright by Daniel Fernandes Bacellar 2016 ii Dedication To Heather and Julia. iii Acknowledgements First and foremost, I would like to express my lifetime gratitude to Professor Reinhard Radermacher who believed in my potential when few did. It was a privilege being part of this world class research team, thank you Professor! I would like to thank Dr. Vikrant Aute who was to me an advisor, a mentor and a role model. This research could have never happened without his assistance. I probably haven’t shown enough appreciation for everything he has done. I would also like to thank all of my professors during my PhD, in particular the members of this committee: Dr. Jungho Kim, Dr. Bao Yang, Dr. James Baeder and Dr. Marino di Marzo. I want to thank Dr. Jiazhen Ling for his help with numerical analysis and for having a broad knowledge of engineering faculties that have helped me in many ways; Mr. Jan Muehlbauer for his unmatched experience in the lab and contributions to the novel heat exchanger designs; Zhiwei Huang for all of her effort in testing the heat exchangers and providing the data that successfully validated my work; and Mr. Yoram Shabtay for his relentless effort in finding manufacturing solutions to the novel heat exchangers. I want to acknowledge my predecessors in the quest for the next generation of heat exchangers: Dr. Khaled Saleh and Dr. Omar Abdelaziz who, not only provided the baseline framework for this research, but also gave me invaluable advices on CFD modeling and optimization. I hold in high regards Dr. Hongtao Qiao and Dr. Long Huang - whom I also had the privilege of collaborating with – for sharing their knowledge and expertise that were iv fundamental for my growth as a researcher. I would also like to mention a few colleagues and friends who also had an influence on my graduate life experience, either directly or indirectly to my research: Dr. Sahil Popli, Dr. Mohamed Beshr, Ms. Radia Eldeeb, Dr. Moon Soo Lee, Ms. Camli Badrya, Dr. Ayan Moitra, Mr. Viren Bhanot and Zhenning Li. I would also like to thank Mary Baugher and Tanya Pringle; their administrative and paper editing support are amongst the key reasons for the center’s and students’ successful achievements. I am very grateful for all of their support throughout these years. I grew up in an environment where I had great role models of academic excellence and high standards; I attribute my pursuit for this degree in great part to my mother, Dr. Flora Fernandes, and step-father, Dr. Sergio Matioli. I’d like to thank my father, Flavio Bacellar, for always encouraging me not to be step away from challenges and seeking what is best for me. I must also acknowledge the endless support from my grandparents Marialba Bacellar, Mariano Bacellar and Adhemar Fernandes. Last (but definitely not the least!), I’d like to thank my wife, Heather Sutton, for her patience and emotional support during this long and winding road. This work was supported by the United States Department of Energy Grant Number DE-EE0006114 and the Modeling and Optimization Consortium of the Center for Environmental Energy Engineering at the University of Maryland. v Table of Contents Chapter 1: Introduction ................................................................................................. 1 1.1 Motivation ................................................................................................1 1.2 Literature Review.....................................................................................3 1.2.1 Airside Heat Transfer ....................................................................... 3 1.2.2 Computational Fluid Dynamics (CFD) ............................................ 7 1.2.3 Numerical Optimization................................................................. 10 1.2.4 Performance Evaluation Criteria (PEC) ......................................... 12 1.2.5 Airside Heat Transfer and Friction Characterization in Crossflow 19 1.2.6 Fabrication of Heat Exchangers with Complex Surfaces .............. 25 1.2.7 Literature Gaps............................................................................... 26 Chapter 2: Research Objectives .................................................................................. 29 2.1 Summary ................................................................................................29 2.2 Dissertation Organization ......................................................................30 Chapter 3: Theoretical Background ............................................................................ 34 3.1 Airside Modeling ...................................................................................34 3.1.1 CFD Modeling and Simulation ...................................................... 34 3.1.2 CFD Data Reduction ...................................................................... 39 3.1.3 CFD Grid Uncertainty Analysis..................................................... 41 3.1.4 Non-Uniform Rational B-Splines (NURBS) ................................. 44 3.2 Heat Exchanger Modeling .....................................................................46 3.3 Numerical Optimization.........................................................................48 vi 3.3.1 Design of Experiments ................................................................... 50 3.3.2 Kriging Metamodeling ................................................................... 50 3.3.3 Multi-Objective Optimization ........................................................ 51 Chapter 4: First & Second Order Analyses................................................................. 52 4.1 First Order Analysis ...............................................................................52 4.2 Second Order Analysis ..........................................................................53 4.2.1 Surface Level Analysis .................................................................. 54 Chapter 5: Multi-Scale Analysis and Shape Optimization ......................................... 62 5.1 Design Framework .................................................................................62 5.2 Concept Surfaces ...................................................................................62 5.2.1 Round Tube Heat Exchangers (RTHX & FTHX) ......................... 63 5.2.2 NURBS Tube Heat Exchangers (NTHX) ...................................... 71 5.2.3 Webbed-NURBS Tube Heat Exchangers (WTHX) ...................... 74 5.2.4 Airfoil-Shaped Tube Heat Exchangers (AFHX)............................ 76 5.3 Design Problems (DP) ...........................................................................78 5.3.1 DP I: 1.0kW Single-Phase Heat Exchangers ................................. 78 5.3.2 DPII: 10.0kW Single-Phase Heat Exchangers ............................... 98 5.3.3 DP III: Two-Phase Heat Exchangers ........................................... 101 Chapter 6: CFD-Based Correlation Development .................................................... 106 6.1 Round Finless Tubes ............................................................................107 6.1.1 Data Reduction............................................................................. 108 6.1.2 Correlations .................................................................................. 108 6.1.3 Verification .................................................................................. 113 vii 6.2 Plain Fin-and-Tubes .............................................................................114 6.2.1 Data Reduction............................................................................. 115 6.2.2 Correlation ................................................................................... 115 6.3 Wavy Fin-and-Tubes ...........................................................................117 6.3.1 CFD model ................................................................................... 118 6.3.2 Correlation ................................................................................... 121 Chapter 7: Surface Optimization Study .................................................................... 124 7.1 Optimization Results ............................................................................126 7.1.1 Discussion .................................................................................... 130 Chapter 8: Conclusions ............................................................................................. 134 8.1 Summary of Contributions ...................................................................134 8.2 List of Publications ..............................................................................139 8.3 Recommendations for Future Work.....................................................143 Appendices ................................................................................................................ 148 Appendix A – Non-Uniform Rational B-Spline C# code ..........................148 Appendix B – NTHX-001 Stress Analysis ................................................150 Appendix C – Optimum HX Designs ........................................................154 RTHX .................................................................................................... 154 FTHX .................................................................................................... 183 NTHX ................................................................................................... 189 WTHX................................................................................................... 194 AFHX .................................................................................................... 198 Appendix D – Experimental Materials, Methods and Data .......................203 viii Appendix E – Correlation Data..................................................................210 Wavy Fin Correlation Coefficients Matrices ........................................ 210 Appendix F – Optimum Heat Transfer Surfaces .......................................214 Surface Optimization Study Results ..................................................... 214 Appendix G - Performance Evaluation Criteria Analysis..........................245 Introduction ........................................................................................... 245 HX Evaluation Criteria ......................................................................... 249 HX Design ............................................................................................ 252 ix List of Tables Table 1. Summary of HX optimization methods (adapted from Huang et al. [85]) ... 10 Table 2. PEC for single-phase HX (adapted from Webb and Kim [90]) .................... 14 Table 3. Selected correlations for finless tube bundle. ............................................... 22 Table 4. Most relevant fin-and-tube airside correlations in the literature. .................. 23 Table 5. Design variable types. ................................................................................... 63 Table 6. RTHX and FTHX Design space. .................................................................. 65 Table 7. NTHX Design space. .................................................................................... 72 Table 8. WTHX Design space. ................................................................................... 75 Table 9. AFHX Design space. .................................................................................... 77 Table 10. 1.0kW Baseline MCHX. ............................................................................. 78 Table 11. NTHX-001 Numerical results compared to the baseline MCHX. .............. 81 Table 12. RTHX-001 Numerical results compared to the baseline MCHX. .............. 83 Table 13. Baseline cycle verification. ....................................................................... 101 Table 14. Two-Phase HX’s operating conditions. .................................................... 102 Table 15. Finless tubes correlations design space. ................................................... 109 Table 16. Correlations I coefficients. ........................................................................ 110 Table 17. Correlations II coefficients. ...................................................................... 110 Table 18. Correlations III coefficients. ..................................................................... 111 Table 19. Round finless tubes correlations fitness. ................................................... 112 Table 20. Flat fin and tube correlations design space. .............................................. 115 Table 21. Fin-and-tube correlations coefficients. ..................................................... 116 Table 22. Flat fin-and-tube correlations fitness. ....................................................... 117 x Table 23. Wavy fin-and-tube correlation design space. ........................................... 118 Table 24. Air thermophysical properties for wavy fin correlations. ......................... 122 Table 25. Wavy fins correlations fitness. .................................................................. 122 Table 26. Parametric Variables. ................................................................................ 125 Table 27. Surface Optimization Study Computational Cost. .................................... 125 Table 28. Material yield strength (SolidWorks® database). .................................... 153 Table 29. NTHX-001 Stress analysis results. ........................................................... 153 Table 30. Optimum RTHX dimensions. ................................................................... 154 Table 31. Optimum RTHX performance and operating conditions. ........................ 169 Table 32. FTHX optimum designs dimensions. ....................................................... 184 Table 33. Optimum FTHX performance and operating conditions. ......................... 186 Table 34. NTHX dimensions. ................................................................................... 189 Table 35. NTHX performances and operating conditions. ....................................... 191 Table 36. WTHX dimensions. .................................................................................. 194 Table 37. WTHX performance and operating conditions. ........................................ 196 Table 38. AFHX dimensions. ................................................................................... 199 Table 39. AFHX performance and operating conditions. ......................................... 201 Table 40 – Specifications of test facility. .................................................................. 203 Table 41 - Accuracy of every sensor of airside. ....................................................... 206 Table 42 - Uncertainty calculation of airside (courtesy from Zhiwei Huang). ......... 206 Table 43. RTHX-001 Test data. ................................................................................ 207 Table 44. NTHX-001 Test data. ............................................................................... 207 Table 45. RTHX-468 Test data. ................................................................................ 208 xi Table 46. Herringbone correlation: parameters power matrices. .............................. 210 Table 47. Herringbone correlation: coefficients arrays. ........................................... 211 Table 48. Smooth correlation: parameters power matrices. ..................................... 212 Table 49: Smooth correlation: coefficients arrays. ................................................... 213 Table 50. WFTS Optimum designs dimensions. ...................................................... 219 Table 51. WFTS optimum designs performance. ..................................................... 228 Table 52. RFTS Optimum designs dimensions. ....................................................... 237 Table 53. RFTS optimum designs performance. ...................................................... 241 Table 54: Optimization Problem. .............................................................................. 252 xii List of Figures Figure 1. Local heat transfer coefficient. ...................................................................... 4 Figure 2. Boundary layer disruption – attachment sites on various fin surfaces: a) Plain; b) Louver; c) Slit; d) Perforated. ................................................................................... 5 Figure 3. Streamwise periodic flow computational domain: a) 2-Dimension; b) 3- Dimension. .................................................................................................................... 9 Figure 4. Dissertation organization workflow. ........................................................... 33 Figure 5. Typical CFD 2-D computational domain. ................................................... 36 Figure 6. Two-dimensional computational domain mesh schemes: a) triangle; b) quadrilateral. ............................................................................................................... 37 Figure 7. Three-dimensional computational domain. ................................................. 37 Figure 8. Dry air properties as function of temperature. ............................................. 39 Figure 9. Sequentially increasing grid resolutions. ..................................................... 42 Figure 10. 3rd degree NURBS curve and base functions example from Piegl and Tiller [157]. ........................................................................................................................... 44 Figure 11. Tube shape parameterization. .................................................................... 46 Figure 12. Air-to-fluid cross flow HX’s. .................................................................... 46 Figure 13. HX Temperature profile illustration. ......................................................... 47 Figure 14. Numerical optimization framework. ......................................................... 49 Figure 15. Parallel Parameterized CFD (PPCFD) framework. ................................... 49 Figure 16. Space sampling example: a) biased; b) unbiased (LHS). .......................... 50 Figure 17. First order analyses I: compactness, material utilization and internal volume. ..................................................................................................................................... 53 xiii Figure 18. First order analyses II: fin-to-tube surface ratio. ....................................... 53 Figure 19. Second order analysis I: thermal-hydraulic characteristics. ...................... 54 Figure 20. Thermal characteristics for same Reynolds and different diameters. ........ 55 Figure 21. Hydraulic characteristics for same Reynolds and different diameters ...... 55 Figure 22. Thermal characteristics for same velocities and different diameters. ....... 55 Figure 23. Hydraulic characteristics for same velocities and different diameters. ..... 56 Figure 24. Momentum boundary layer over different tube diameters and air velocities. ..................................................................................................................................... 57 Figure 25. Normalized temperature and velocity profiles within the boundary layer at 25% of the tube surface for same velocity. ................................................................. 57 Figure 26. Surface temperature gradient over different tube diameters and air velocities. ..................................................................................................................................... 58 Figure 27. Surface velocity gradient over different tube diameters and air velocities. ..................................................................................................................................... 58 Figure 28. Momentum boundary layer over different tube diameters and Reynolds. 58 Figure 29. Normalized temperature and velocity profiles within the boundary layer at 25% of the tube surface for same Reynolds number. ................................................. 59 Figure 30. Surface temperature gradient over different tube diameters and Reynolds. ..................................................................................................................................... 59 Figure 31. Surface velocity gradient over different tube diameters and Reynolds. .... 59 Figure 32. Tube shapes: a) Round; b) Ellipse; c) Eye; d) Airfoil leading edge; e) Airfoil trailing edge. ............................................................................................................... 60 Figure 33. Thermal-hydraulic characteristics of airflow over different shapes. ......... 61 xiv Figure 34. Heat exchanger design framework. .......................................................... 64 Figure 35. Round finless tubes (RTHX): a) In-line; b) Staggered. ............................. 65 Figure 36. Flat fin and tube HX (FTHX) .................................................................... 65 Figure 37. RTHX computational domain and mesh: a) staggered; b) in-line. ............ 66 Figure 38. CFD GCI Analysis for BTHX in staggered and in-line arrangements. ..... 66 Figure 39. FTHX Computational domain and mesh. .................................................. 67 Figure 40. CFD GCI Analysis for FTHX. .................................................................. 67 Figure 41. Example of contour plots on different grid resolutions for the FTHX. ..... 67 Figure 42. Heat transfer coefficient metamodel verification for RTHX in staggered and in-line arrangements for 50 random samples. ............................................................. 68 Figure 43. Pressure drop metamodel verification for RTHX in staggered and in-line arrangements for 50 random samples. ........................................................................ 68 Figure 44. Metamodel verification for FTHX for 50 random samples....................... 69 Figure 45. Equivalent round tube arrangements. ........................................................ 69 Figure 46. In-line vs. Staggered. ................................................................................. 70 Figure 47. Contours of velocity angle......................................................................... 71 Figure 48. Local heat transfer coefficient and skin friction coefficient at the tube wall. ..................................................................................................................................... 71 Figure 49. NTHX surface concept. ............................................................................. 72 Figure 50. NTHX Profile parameterization. ............................................................... 72 Figure 51. NTHX Computational domain. ................................................................. 73 Figure 52. NTHX GCI Analysis. ................................................................................ 73 Figure 53. NTHX Metamodel verification against 961 random samples. .................. 74 xv Figure 54. WTHX Surface concept. ........................................................................... 74 Figure 55. WTHX Profile parameterization. .............................................................. 75 Figure 56. WTHX Computational domain. ................................................................ 75 Figure 57. WTHX Metamodel verification. ............................................................... 76 Figure 58. AFHX Concept. ......................................................................................... 77 Figure 59. AFHX Computational domain. ................................................................. 77 Figure 60. AFHX Metamodel verification.................................................................. 78 Figure 61. CFD Results for the NTHX-001: a) velocity; b) pressure; c) temperature. ..................................................................................................................................... 80 Figure 62. Proof-of-concept NTHX-001 dimensions. ................................................ 80 Figure 63. DP I: RTHX & FTHX Optimization results. ............................................. 82 Figure 64. RTHX-001 CFD verification contour plots: a) velocity; b) pressure; c) temperature. ................................................................................................................ 83 Figure 65. DP I: NTHX Optimization results I........................................................... 84 Figure 66. DP I: NTHX Optimization results II. ........................................................ 85 Figure 67. DP I: NTHX Metamodel verification for the optimum designs. ............... 85 Figure 68. DP I: WTHX & AFHX Optimization results. ........................................... 86 Figure 69. DP I HX Optimization map I..................................................................... 87 Figure 70. DP I Optimization map II. ......................................................................... 88 Figure 71. Velocity magnitude and angle contour plots for selected designs for DP I: a) RTHX-001; b) NTHX-001; c) NTHX-030; d) WTHX-011; e) AFHX-001............... 89 Figure 72. Static pressure and temperature contour plots for selected designs for DP I: a) RTHX-001; b) NTHX-001; c) NTHX-030; d) WTHX-011; e) AFHX-001. ......... 90 xvi Figure 73. DP I: Airside performance parametric analysis. ........................................ 92 Figure 74. RTHX-001 Prototype drawing. ................................................................. 94 Figure 75. Stainless steel RTHX-001 sample images. ................................................ 94 Figure 76. NTHX-001 Prototype drawing. ................................................................. 95 Figure 77. NTHX-001 sample images. ....................................................................... 95 Figure 78. Experimental validation: energy balance and overall capacity. ................ 96 Figure 79. Experimental validation: airside heat transfer coefficient and pressure drop. ..................................................................................................................................... 97 Figure 80. NTHX-001 CFD Validation: contour plots. .............................................. 97 Figure 81. DP II: Optimization results. ....................................................................... 99 Figure 82. RTHX-468 Prototype. ............................................................................... 99 Figure 83. RTHX-468 Experimental capacity results. .............................................. 100 Figure 84. Thermal imaging on RTHX-468 prototype. ............................................ 100 Figure 85. System level study for COP improvement. ............................................. 102 Figure 86. HX Pass configurations. .......................................................................... 103 Figure 87. DP III: Optimization results. ................................................................... 104 Figure 88. DP III: System level analysis. ................................................................. 105 Figure 89. CFD-Based correlation development. ..................................................... 106 Figure 90. Correlations I, II and III verification against source data. ....................... 112 Figure 91. Correlations I and III verification against random samples. ................... 112 Figure 92. Correlations I verification against experimental data. ............................. 113 Figure 93. Flat fin. .................................................................................................... 114 Figure 94. Flat fin and tube contour plots: a) velocity; b) temperature; c) pressure. 114 xvii Figure 95. Flat fin correlations verification against source data. .............................. 116 Figure 96. Wavy fin-and-tube surface: a) Herringbone; b) Smooth (Sinusoidal). ... 117 Figure 97. Wavy fin computational domain and mesh. ............................................ 119 Figure 98. Equivalent wavy fins: a) Herringbone; b) Smooth. ................................. 119 Figure 99. Sample velocity contour plots: a) Herringbone and b) smooth wavy fins. ................................................................................................................................... 120 Figure 100. Sample temperature contour plots: a) Herringbone and b) smooth wavy fins............................................................................................................................. 120 Figure 101. Sample pressure contour plots: a) Herringbone and b) smooth wavy fins. ................................................................................................................................... 120 Figure 102. Grid resolution uncertainty for wavy fins: a) fine; b) base; c) coarse meshes. ................................................................................................................................... 121 Figure 103. Wavy fin correlations verification against source data. ........................ 122 Figure 104. Herringbone correlations verification against 120 random samples. .... 123 Figure 105. Herringbone correlation comparison. .................................................... 123 Figure 106. Finless tubes surface optimization results I: tube diameter. .................. 126 Figure 107. Finless tubes surface optimization results II: tube diameter. ................ 126 Figure 108. Finless tubes surface optimization results I: hydraulic diameter........... 127 Figure 109. Finless tubes surface optimization results II: hydraulic diameter. ........ 127 Figure 110. Finless tubes surface optimization results I & II: pitch ratio................. 128 Figure 111. Wavy fin surface optimization results I: tube diameter. ........................ 128 Figure 112. Wavy fin surface optimization results II: tube diameter. ...................... 129 Figure 113. Wavy fin surface optimization results I: hydraulic diameter. ............... 129 xviii Figure 114. Wavy fin surface optimization results II: hydraulic diameter. .............. 130 Figure 115. Wavy fin surface optimization results I and II: pitch ratio. ................... 130 Figure 116. Selected surface optimization case. ....................................................... 132 Figure 117. Equivalent surfaces (same Dh) under wide range of Reynolds numbers. ................................................................................................................................... 133 Figure 118. Winglets on high-performance tube shape. ........................................... 144 Figure 119. High-performance tube and extended surface shapes. .......................... 145 Figure 120. Extension of the multi-scale analysis and shape optimization methodology. ................................................................................................................................... 145 Figure 121. Fan-coil single unit concept [169]. ........................................................ 146 Figure 122. Stress analysis problem setup. ............................................................... 150 Figure 123. Isotropic stress components and stress-strain engineering curve. ......... 151 Figure 124. NTHX-001 Cut views............................................................................ 151 Figure 125. NTHX-001 Header and tubes cross sections. ........................................ 152 Figure 126. NTHX-001 Header and tube meshes. .................................................... 152 Figure 127. VonMises stress contour plots for the NTHX-001 tube. ....................... 152 Figure 128. Deformation contour plots for the NTHX-001 tube. ............................. 153 Figure 129. Round finless tubes (BTHX): a) in-line; b) staggered........................... 154 Figure 130. Flat fin and tube HX (FTHX). ............................................................... 183 Figure 131. NTHX surface concept. ......................................................................... 189 Figure 132. WTHX concept. ..................................................................................... 194 Figure 133. AFHX Concept. ..................................................................................... 198 Figure 134 - Schematic diagram of air-side test facility. .......................................... 203 xix Figure 135 - Schematic of cold water loop (top), glycol water loop (middle), hot water loop (bottom) (courtesy from Zhiwei Huang). ......................................................... 204 Figure 136 - Schematic diagram of water/brines system loop. ................................. 204 Figure 137 - Schematic diagram of refrigerant system with oil loop. ...................... 205 Figure 138 - Schematic diagram of refrigerant system without oil loop (courtesy from Zhiwei Huang). ......................................................................................................... 205 Figure 139. Surface optimization results (Dh=0.5mm). ............................................ 214 Figure 140. Surface optimization results (Dh=1.0mm). ............................................ 215 Figure 141. Surface optimization results (Dh=1.5mm). ............................................ 216 Figure 142. Surface optimization results (Dh=2.5mm). ............................................ 217 Figure 143. Surface optimization results (Dh=3.0mm). ............................................ 218 Figure 144. Wavy fin surface segment. .................................................................... 219 Figure 145. RFTS Segment....................................................................................... 237 Figure 146: HX surface types: a) RTHX; b) WTHX. ............................................... 252 Figure 147: HX Design results: a) RTHX; b) WTHX. ............................................. 253 Figure 148: Entropy Generation: a)RTHX; b) WTHX. ............................................ 254 xx Nomenclature Acs Cross section area m² Ac Minimum free flow area (σAfr) m² Afin Fin surface area m² Afr Frontal face area m² Ao Total surface area m² At Tube surface area m² C Heat capacitance rate W/K Cf Skin friction coefficient - cp Specific heat J/kg.K d Depth mm Dh Tube hydraulic diameter m Dhin In-tube hydraulic diameter mm Dhs Surface hydraulic diameter mm Do Outer diameter mm e Absolute relative difference - f Friction factor - FPI Fins Per Inch 1/in Fs Grid factor of safety - GCI Grid Convergence Index - h Heat transfer coefficient W/m².K ht Tube height mm xxi hx Local heat transfer coefficient W/m².K k Thermal conductivity W/m.K k Turbulent kinetic energy m²/s L Tube length mm Lc Characteristic length mm ṁ Mas flow rate g/s Nr Number of tube rows (transverse) - Nt Number of tube rows (longitudinal) - Nu Nusselt number - p Spatial order of accuracy - p* Observed order of accuracy - p** Effective order of accuracy - P Pressure Pa P Curve length (tube perimeter) mm Pl Tube longitudinal pitch mm Pr Prandtl Number - Pt Tube transverse pitch mm Q Heat transfer rate W r Grid refinement ratio - Re Reynolds Number - rPl Longitudinal pitch ratio (Pl/Do) - rPt Transverse pitch ratio (Pt/Do) - xxii T Temperature K u Velocity m/s UA Thermal conductance W/K uc Mean velocity at minimum free flow area m/s uoo Uniform velocity m/s Ẇ" Friction power per unit area W/m² wt Tube width mm xcp x coordinate Control point mm ycp y coordinate Control point mm ΔP Pressure drop Pa j Colburn j factor - f Darcy friction factor - NTU Number of Transfer Units - B Exergy flow rate W s Specific entropy J/kg.K S Entropy flow rate W/K Ns Number of entropy generation units - Fp Fin pitch mm ΔTlm Logarithmic Mean Temperature Difference K V Volume cm³ COP Coefficient of Performance - xxiii Greek Letters δt Tube thickness mm δf Fin thickness mm εM Eddy diffusivity m²/s μ Dynamic viscosity Pa.s ρ Density kg/m³ σ Contraction ratio (u/umax) - α Thermal diffusivity m²/s Acronyms AAO Approximation Assisted Optimization AFHX Airfoil Heat Exchanger CFD Computational Fluid Dynamics FTHX Flat Fin and Tube Heat Exchanger HX Heat Exchanger MCHX Microchannel Heat Exchanger NTHX NURBS Finless Tube Heat Exchanger PPCFD Parallel Parameterized CFD RFTS Round Finless Tube Surface RTHX Round Finless Tube Heat Exchanger WFTS Wavy Fin Tube Surface WTHX Webbed Tube Heat Exchanger 1 Chapter 1: Introduction 1.1 Motivation According to the United States Energy Information Administration (EIA) the US end-use energy consumption in both commercial and residential sectors totaled 39.2 quadrillion BTU (quad) in 2013 [1]. This number is projected to increase by 6.7% by 2040 [1]. Although the residential energy consumption for space heating and cooling have decreased, they still account for 47% (in 2009) energy use in the nation. Nevertheless, the biggest consumers by some extent are those transferring heat, and thus need to use Heat eXchangers (HX). Westphalen et al. [2] suggested that potential of annual energy savings by heat transfer enhancement of air-cooled HX’s could reduce as much as 7 quads, and between 0.7 to 1.1 quads in air-conditioning and refrigeration systems, respectively. These amounts correspond to 20% of the energy consumed by commercial and residential sectors. One must maximize the overall HX conductance (UA) by Approach Temperature reduction in air-to-fluid HX’s to achieve energy conservation. A common way of increasing UA is by increasing surface area; however, such method entails more material consumption and increase of the HX size. This often results in the HX becoming over-sized. There are many consequences of having over-sized HX’s in HVAC&R (Heating, Ventilation, Air-Conditioning and Refrigeration) applications including: a) operate in cycling mode more often (i.e. part-load), thus reducing the COP for 2 being out of the design operating condition; b) installation site may have size limitations; c) extra refrigerant charge is required; d) may have higher costs associated with the extra material needed. From an environmental perspective resource consumption is a negative impact, thus should be limited as much as possible. Additionally, the additional refrigerant charge poses serious environmental threats (leakage and disposal) due to Global Warming Potential (GWP) and Ozone Depletion Potential (ODP). Therefore, there is an increasing need for reducing the use of such refrigerants, which can be translated in charge reduction in the HX. The use of compact heat exchangers with high-performance surfaces is a very common (although broad) research topic that draws interests from many engineering applications, and are not exclusive to the HVAC&R industry. Most technologies contain at least one heat exchanger serving as a fundamental component for proper system functioning. The world’s rapid population growth, never ending demand for energy resources, dire environmental concerns, expanded space exploration, and goals for increased economic growth are all good motivators for developing smaller, lighter and more efficient HX’s. As computer power and manufacturing technologies (e.g. additive manufacturing) evolve, paradigm shifting is inevitable. A next generation of heat transfer surfaces in smaller scales and complex shapes are starting to take place over conventional HX geometries in order to address the above discussion. This research entails shedding the light on the next generation of heat exchangers, with focus on air-to-fluid applications. 3 1.2 Literature Review 1.2.1 Airside Heat Transfer The passive HTE aims more compact surfaces (hydraulic diameters smaller than 6.0mm [3]) and higher thermal-hydraulic ratio [4, 5] without the assistance of any external power. A well-known way of reaching out to these goals is using extended secondary heat transfer surfaces (fins) which, in spite the benefits, bring many drawbacks. Fins will naturally provide additional viscous resistance and have a lower heat transfer potential due to temperature gradient. Furthermore, on the gas side, the fins reduce the mixing and the actual heat transfer coefficient on fins are smaller than the tubes; the resulting overall heat transfer coefficient can be as low as 40% [5] than finless surfaces. Such impact on the thermal resistance is compensated by the additional surface area the fins provide. Fins are also susceptible to performance degradation under fouling or frosting conditions, in particular for enhanced surface fins [6]. Lastly, fins inevitably require additional material consumption, resulting in heavier HX’s, and higher manufacturing costs. The reason fins are necessary in conventional gas-to-fluid HX’s (tube diameter >5.0mm) is that the primary surfaces cannot provide a minimum thermal resistance that allow the HX to deliver the required capacity within practical dimensions. The idea of a compact high-performance surface [7, 8, 4, 5] is usually associated to the fins, hence, researchers are heavily investing on fins and less on tubes. The principle of passive HTE is to leverage the developing boundary layer. For simplicity, the reader should follow this discussion assuming a Prandtl number 4 of 1.0 to avoid qualifications as to which boundary layer is being referred to. According to the thermal transport within the boundary layer we know that the local heat transfer coefficient is proportional to the temperature gradient at the surface (equation 1). The thickness of a developing boundary layer is smaller thus resulting in a higher temperature gradient (Figure 1), i.e. higher heat transfer coefficient.  x w w T h T T k y         (1) Figure 1. Local heat transfer coefficient. Typically for on fins, this mechanism is usually exploited with discontinuous surfaces (Figure 2) resulting in a significant improvement over plain flat (Figure 2a) or even wavy fins. Louvered fins (Figure 2b) have been exhaustively investigated, numerically and experimentally, and they are one of the most common types [9, 10, 11, 12, 13, 14, 15, 16, 17, 18] [19]. Slit fins (Figure 2c) [7, 12, 20, 21, 8, 22] are basically fins with offset strips that, unlike louvers, are not rotated thus not redirecting the flow. Perforated fins (Figure 2d) [7, 8, 23, 24] differ from slits and louvers on two matters; on the one hand, it has reduced surface area due to material removal from perforation, on the other hand, there are much less stagnation points resulting in reduced friction resistance [7]. ,u T  wT T T ( )dblT y T ( )fdblT y Fully developed ( )fdblT y( )dblT y y fdbldbl dTdT dy dy  y x h x 5 Figure 2. Boundary layer disruption – attachment sites on various fin surfaces: a) Plain; b) Louver; c) Slit; d) Perforated. In contrast, wavy fins [25, 4, 26, 27] are not a discontinuous surface, but they provide additional surface area for the same volume and can promote chaotic flow [28, 29] which result in enhanced heat transfer. Although wavy fins have lower performance than the discontinuous fin types, they are preferred in some applications where frosting may occur since they are less prone to performance degradation [30, 31]. More recently fins have been improved by addition of winglets, or vortex generators [8, 32, 33, 34, 35, 36, 27, 37], which result in induced turbulence within the boundary layer (or even its disruption), thus enhancing the thermal performance. The small diameter bare tubes result in high-performance surfaces with sufficiently low thermal resistance that can outperform conventional finned heat exchangers. There are many studies [38, 39, 40, 41, 42, 43] investigating the use of small round finless tubes for HX design, and they have demonstrated great potential for performance enhancement. A major shortcoming of round tubes, however, is the friction resistance, which is also increased with the reduction of the tube size. The consequence is that in order to satisfy a minimum of pressure losses, such surface requires low velocity and relatively short depth. For constant airflow rate this means larger face area [41], which is in many cases, undesirable or prohibitive. Attachment AttachmentDisruption Disruption ,u T  Attachment May or may not occur disruption Attachment Disruption Attachment Disruption a) b) c) d),u T  ,u T  ,u T  6 The limitation on friction resistance for round tubes can be addressed by employing alternate shapes. Min and Webb [44] presented a numerical analysis on different tube shapes namely round, oval and flat and the impact on thermal- hydraulic performance of a wavy fin and tube surface, with tube diameters above 6.0mm. Their analyses showed that the flat and oval can have as low as 50% of the pressure drop compared to round tube, while reducing 10-20% the thermal performance. Such reduction in pressure drop is leveraged when combining these alternate tubes with enhanced fins [27, 14, 45, 36]. In fact, flat, multi-port tube and fin heat exchangers have become a high-performance and state-of-the-art. They are commonly called microchannel heat exchangers (MCHX). This type of HX not only has good airside performance, but has mostly, excellent refrigerant side performance. Tuckerman and Pease [46] obtained a factor of 10 in the heat dissipation of integrated chips using a MCHX and have since then, changed the electronics, automotive and aerospace industries [47]. On HVAC&R applications, Kandlikar [48] showed that is a potential of reducing the refrigerant thermal resistance by a factor of 10 with same order reduction in the port size, in addition to significant reduction in refrigerant charge. Huang et al. [49] developed a variable geometry MCHX to address flow mal-distributions and optimizing material usage and localized thermal-hydraulic performance. Although these HX’s still require fins, their performance and compactness — but most importantly their low cost and relative ease of manufacturing — are yet to be outdone. Other relevant studies on alternate tube shapes in crossflow include polymer tubes with three different teardrop shapes [50], and cam-shaped tubes [51, 52, 53]. 7 Another significant branch of research is the shape optimization, which has many applications in various engineering problems. Perhaps the most common application is wings and airfoil design within aerospace field. The shape parametrization and optimization for such applications are comprehensively presented in the literature [54, 55], and they can be useful on heat transfer applications as well. High-performing aerodynamic airfoil profiles have been studied on gas-engines [56] and intercooled gas turbines [57]. Other shape optimization studies include convective periodic channels [58, 59, 60, 61], internally enhanced tubes [62, 63, 64, 65] and, most relevant to this work, the periodic crossflow over a tube bundle from Hilbert et al. [66] and Ranut et al. [67]. Their work was limited to the shape optimization while fixing scale and topology parameters. The results are mostly an exercise of their optimization tools and methods but have little use to actual HX design. 1.2.2 Computational Fluid Dynamics (CFD) Numerical modeling is a fundamental piece to the design and optimization of high-performance HX’s. The advances in numerical software have opened new opportunities to researchers worldwide [68]. Computational Fluid Dynamics (CFD), in particular, has become a powerful and reliable tool for HX design and performance prediction. Some still regard CFD with skepticism [68], and understandably so due to its intrinsic numerical uncertainty, which could possibly lead to significant under or over prediction. There are comprehensive methods that can reliably quantify the uncertainty associated to the model discretization. One standard approach is the 8 five-step Grid Convergence Index (GCI)) method [69, 70, 71], which quantifies the uncertainty of a metric of interest (φ) associated with the grid resolution for at least three mesh sizes. One can perform educated metric modification to the models as the uncertainty is substantially reduced, ensuring that reliable models and consistent simulations. Furthermore, the ultimate verification relies on a model accuracy assessment with experimental data, with which many have claimed to have found good agreements between their CFD simulations and the tested prototypes. Abdelaziz et al. [72] and Xioping et al. [73] verified their CFD models within 10% from experimental data, while Taler and Oclon [74] obtained at most a deviation of 4%. In summary, CFD simulations are a common practice in HX design and optimization and, in spite the uncertainties associated, successful results have been achieved thus shall be continuously used and improved. 1.2.2.1Airside HX Modeling For HX airside modeling the streamwise periodic flow numerical approach introduced by Pantakar [75] is extensively used in CFD due to the reduction of the computational cost by adequately reducing the HX into a small segment for a computational domain without losing the physical meaning. Typically, the end- effects can be neglected and the thermal-hydraulic characteristics of a surface can be determined by a segment of the HX, where the lower, upper and longitudinal boundaries can be assumed periodic or symmetric. In the literature, the numerical analysis on finless surfaces commonly employ two-dimensional (Figure 3a) computational domains [38, 41, 44, 66, 67], which makes the simulations much lighter and the results are very reliable. On the other hand, if the HX has a 9 discontinuous surface (fins) on the transverse direction then a three-dimensional (Figure 3b) computational domain types [10, 14, 16, 17] are often necessary. Figure 3. Streamwise periodic flow computational domain: a) 2-Dimension; b) 3- Dimension. 1.2.2.2Automation Although CFD provides new opportunities in HX design it also entails high costs in engineering time. The traditional manual procedure in building a CFD model is, in many times, a cumbersome task that consumes time which can become prohibitive if one wants to use CFD to perform optimization. Commercial CFD software allows high level parametrization limited to scaling variables only. Topology and shape change often requires new CFD models and cannot easily be done with available tools. One way to address that issue is to use CFD automation methods. The structure behind is a low-level programming language code that can assess every step including: geometry and mesh generation, CFD simulations (including all the settings for governing equations and boundary conditions), to, finally, post-processing the metrics of interest. The model and simulation can take placed either in a commercial software environment, or within a tailored CFD code. y x z Symmetry boundaries Periodic/Symmetric boundaries Periodic/Symmetric boundaries Symmetry boundaries Periodic/Symmetric boundaries a) b) 10 The ANSYS® platform is commonly used due to its journaling and scripting access from the user that allows the automation to happen. Although obsolete, Gambit® is a very robust tool for this kind of application. As for the CFD simulation environment, Fluent® is traditionally an excellent tool, but others can be equally good. Hilbert et al. [66] first presented this approach using a C code that was later used by Ranut et al. [67] for a similar study. Abdelaziz et al. [76, 77] called this method Parallel Parameterized CFD (PPCFD), which was many times used later by their colleagues [40, 78, 79]. These automation techniques potentially save in more than 90% of engineering time compared to conventional CFD modeling [76]. 1.2.3 Numerical Optimization Numerical optimization of HX’s has become quite common with the rapid evolution of computational power and numerical methods. Hedderich et al. [80] presented what is most likely the first numerical optimization tool for fin-and-tube air-cooled HX optimization using traditional deterministic methods such as Feasible Directions [81], and the Augmented Lagrangian Multiplier (ALM) [82]. The traditional methods, however, they are not efficient in handling discrete variables; and cannot be used in parallel computing [83]. The Heuristic methods like Genetic Algorithms (GA’s) [83] have proven to be more robust and are computationally less expensive (Table 1) than the traditional methods. Furthermore, GA’s have the ability of finding even better designs. Between 2005 and 2007 the average number of publications on heat transfer problems using GA had increased by a factor of five compared to the previous decade [84]. Table 1. Summary of HX optimization methods (adapted from Huang et al. [85]) 11 Approach Expertise Relative Computational Cost Exhaustive Search Low 100,000 Random Search Low 10,000 Parametric Analysis Low 1,000 Gradient-Based Methods Medium 100 Heuristic Methods (GA, MOGA) Med.-High 1-10 Many studies are leveraging the computational power to couple numerical solvers such as CFD to GA’s [86, 62, 59, 58] in order to investigate an otherwise impossible variety of new concepts. Queipo et al. [86] investigated electronic cooling devices; Fabbri [62, 63, 87] used FEM and GA for longitudinal fin shape design; Hilbert et al. [66] and Ranut et al. [67] optimized tube shape, using Non- Rational B-Splines (NURBS) method in a cross flow HX integrating CFD and GA; Nobile et al. [58] also used NURBS for periodic (longitudinal direction) flow channels; Foli et al. [59] used CFD and GA to optimize the channel shape of a gas- to-gas HX. The cost of coupling, however, can be extremely high depending on the complex of the geometry. More recently some researchers have employed approximation assisted optimization (AAO) techniques, [66, 67, 72] which reduces the number of numerical simulations required, thus saving significant computer time. Metamodeling is a robust approximation method commonly used in several different applications. A metamodel is a simplified version of an actual physical model, such as CFD, which with reasonable accuracy can predict the outcomes of a CFD simulation at a much lower computational cost. Amongst the metamodeling methods, Kriging [88] is a very effective and robust one and is recommended for design spaces with less than 50 design variables [89]. 12 1.2.4 Performance Evaluation Criteria (PEC) HX Performance Evaluation Criteria (PEC) comprises of quantifying the “goodness” of a heat transfer surface in terms of compactness and performance [90]. There are two main approaches to assess the HX PEC: a) energy-based (first law of thermodynamics); b) entropy-based (second law of thermodynamics) [91]. 1.2.4.1Energy-based PEC Cowell (1990) [92] summarized the energy-based PEC into four categories. The first, known as “area goodness” factor, is a typical way of evaluating surfaces and HX’s, and is simply defined as the ratio of j and f factors (equation 2). The main advantage of such metric is the non-dimensional nature, which allows one to compare surfaces regardless the geometrical scale, particularly the surface hydraulic diameter (equation 4). 2 2/3 2/3 2 2 1 Pr2 Pr , 2 c c p o c c j NTU mA Ph K K u c A uf A P                  (2) 1, 1.0; ,0.0 1.0; m nc c c cP u m h u n A u        (3) 4 chs o A D d A  (4) Although it well represents the surface characteristics, it leads to potential skewed evaluation of the HX. The simplified form shows the dependency to the thermal conductance and the inverse of the pressure drop and the square of the minimum free flow area. In other words, this metric can only have some meaning either if the thermal hydraulic ratio is fixed or if the minimum free flow area is fixed, otherwise an infinite combination of the two can result in the same factor. 13 Furthermore, the general knowledge is that this factor is inversely proportional to the Reynolds number, in which having a relatively low number is undesirable. The reason for this is that the pressure drop and face area (assuming constant flow rate) terms are more sensitive to the variation in velocity than for the thermal conductance (equation 3). If one uses this metric as an optimization objective there is a possibility that the optimizer will search for either low-pressure drop, and/or small face area designs, in detriment of lower thermal resistance. The second category is the “volume goodness”, also described by London (1964), but discussed in other relevant papers including Kays and London (1984), Webb and Kim (2005) and Shah (1978). This category evaluates the dimensioned heat transfer coefficient and pressure drop (in the form of pumping power per surface area as shown in equation 5). The common observation with regards to these metrics is their dependency to the hydraulic diameter, thus in order for one to make a fair comparison between two or more designs they must have the same hydraulic diameters [90, 92, 93, 94]. Additionally, the reduction in pressure drop is usually simpler to obtain instead of improving the heat transfer coefficient, thus normally resulting in large face area designs. 2 23 3 2/3 2 3 2 2/3 2" 2Re Re Pr 2 Pr Re/ p p hs hs hso c j c Dh h j f D D fW P V A                     (5) The third category is used for a direct comparison between a smooth surface type and an enhanced version of it. There are several relevant publications regarding this category including Bergles et al. [95, 96] , Webb et al. [90, 97]. They define 12 scenarios from a combination of the four HX design objectives and three 14 geometry constraint criteria. The three constraint criteria are: a) fixed geometry (FG) which comprises of fixing the frontal area and aspect ratio; b) fixed flow area (FN) which considers fixed frontal area but variable aspect ratio; and c) variable geometry (VG) which entails having fixed flow rates. All these assume fixed hydraulic diameter; the first two require this constraint given the nature of the criteria; the last one falls into the same issues of the “volume goodness” method. This category is summarized in Table 2. The last category accounts for all methods that are either of diffusive interpretation, or very particular and by any means extendable to a more general method [92]. A comprehensive summary of all metrics variations for the previous evaluation categories has been described by Shah [98]. Table 2. PEC for single-phase HX (adapted from Webb and Kim [90]) Case Fixed Parameters Objective Dh Nt L Afr ṁ Ẇ Q ΔTi FG-1a x x x x x x max Q FG-1b x x x x x x min ΔTi FG-2a x x x x x x max Q FG-2b x x x x x x min ΔTi FG-3 x x x x x x min Ẇ FN-1 x x x x x x min L FN-2 x x x x x min L FN-3 x x x x x min Ẇ VG-1 x x x x x min Nt*L VG-2a x x* x* x x x max Q VG-2b x x* x* x x x min ΔTi VG-3 x x* x* x x x min Ẇ * Product (Nt * L) constant Cowell [92] proposed a collection of methods that overcome some of the shortcomings of the previous methods by offering quantitative criteria that allows, amongst other things, varying the hydraulic diameter. The assumptions for the method consist of negligible resistance on the other fluid side, negligible fin 15 efficiencies and constant fluid properties throughout the HX (single-phase flow applications only). Although sometimes criticized [93], the assumptions fit quite well on air-to-fluid HX using small hydraulic diameters. 1.2.4.2Entropy-based PEC The second PEC approach entails a more fundamental perspective by employing the second law of thermodynamics to determine the most, and least, energy degrader surfaces. The entropy generation (irreversibility) is an elegant way of combining both the finite temperature difference and friction dissipation, which ultimately will determine the heat transfer augmentation and the associated costs to it. Shah [68] states that the thermodynamic approach to HX design is important for two reasons: a) bring light to the important factors affecting qualitatively and quantitatively the HX performance; and b) use the availability B (or exergy) perspective to design the HX within a bigger context such as part of a system. in out ref genB B T S  (6) In 1951 McClintock [99] introduced the concept of irreversibility to HX design, which was later formalized by Bejan [100] where he defined the concept of Number of Entropy Generation Units (NS) as an evaluation metric. His work culminated in the idealization of the Entropy Generation Minimization (EGM) method for broad applications of finite-size systems and finite-time processes [101, 102, 103]. min gen S S N C  (7) 16 The tradeoff between energy-based and entropy-based approaches comprises of balancing out the HX size and production costs directly for savings in energy degradation (irreversibilities) [100] further down the process. A larger and “more expensive” HX is more thermodynamically efficient [100], and better heat transfer performance does not lead to minimum entropy generation [100, 104, 105]. The previous statements are only true is one does not change the surface type and size, i.e. if there are no other ways to enhance a certain surface, the only way to achieve thermodynamic efficiency is by adding surface area, which consequently increases the HX size. Another parameter used in this approach is the ratio between the entropy generated due to friction loss and finite temperature difference (irreversibility distribution ratio [104, 106]), which indicates how much degradation is due to either mechanisms. This metric is, however, not useful as a design objective provided the expectations are to minimize both types. Lastly there is the entropy generation augmentation number (NS,a), that directly compares the ratio between total entropy generation from an enhanced surface to a baseline, i.e. it is similar to the Bergles et al. [95, 96] method, but using entropy as a parameter. If NS,a < 1 the design leads to exergy savings [104] (i.e. minimum entropy generation). , , , gen a S a gen ref S N S  (8) , , gen P gen T S S     (9) 17 Zimparov and Vulchanov [91] proposed additional equations derived specifically to employ the entropy-based approach to the three variable geometry constraint criteria (VG) established by Bergles [96]. 1.2.4.3 Mixed Approach Analysis It is important to highlight the importance and relevant applicability of each approach. On the one hand, the First Law analysis results in the non-dimensional ε-NTU relationship used in rating and sizing of HX’s [68]. On the other hand, the Second Law establishes the physical limitations and how the HX fits in the energy conservation scenario in a much bigger control volume including other relevant processes. A combination of both approaches is evidently beneficial by broadening perspectives from a decision-making viewpoint. The thermoeconomic analysis [103] attempts to tie everything together by evaluating the capital cost of energy degradation caused by the irreversibility from one or more HX’s (or components in general) within a system. One step before introducing the financial aspect of the overall design is determining the indexes that evaluate the HX bounded by the practical aspects (First Law and design constraints), and the possible liability and reliability of the HX in a system context and in a long term (Second Law). Bejan [107] first studied the relationship between the Number of Entropy Generation Units (Ns) and the Number of Transfer Units (NTU) for a balanced counter flow HX with no pressure drop. He encountered what was called the “entropy generation paradox” for the Ns went to zero for either NTU = 0 or ∞, but reached a maximum at an intermediate NTU. Shah and Skiepko [108] interpreted 18 such behavior as the irreversibility tend to zero whenever the heat transfer potential is zero; i.e. at NTU = 0 there is no heat flow, thus from the Second Law, Sgen has to be zero for it cannot be negative. When NTU  ∞ the hot and cold stream temperatures approach to the same value, thus nulling the heat transfer potential. Ogiso [109, 110] defined the dimensionless “entropy generation index”, and showed that the Bejan’s paradox can be eliminated [108] since the index is not defined at NTU = 0 or NTU  ∞. 1 genS SN NTU UA   (10) Shah and Skiepko [108] developed further analysis on different HX’s by evaluating the rate of change in irreversibilities with respect to temperature effectiveness (dS/dP1), NTU (dS/dNTU) and the rate of change at maximum entropy generation (dP1/dNTU and d²P1/dNTU²). They pointed out the importance of the identification of the maximum entropy generation point where temperature crossing may occur, thus supporting the need of combined First and Second Law analyses. Hermes [111] further developed this analysis by presenting an optimization methodology integrating the ε-NTU and the EGM methods for constant wall temperature HX’s. In his work, he formalized a straightforward equation relating NS and NTU, under pertinent assumptions for this particular case study, which allowed him to optimize a HX accounting for both First and Second Laws. 19 More recently, Gheorghian et al. [112] proposed the relative exergy destruction rate parameter, that was already somewhat already discussed by Shah [68, 108]. Nevertheless, they showed that such index behaves linearly with NS. 0 genT S Q   (11) The concept of “Entransy” [113] was first presented as a new physical quantity that, in analogy to electrical capacitor, is the thermal charge stored by a HX. The claim is that such quantity is fundamental for HX optimization as it better evaluates the potential of a HX to exchange heat. Analogous to exergy, the “entransy” can also be lost or dissipated. The minimization of the latter is said to be an efficient way of designing HX. Many authors, including Bejan [114], strongly oppose to this concept pointing out that it was made use of loose physical assumptions and mathematical tricks to define a physical quantity that is not dimensionally sound [114]. Additionally, the concept of “entransy dissipation minimization” does not bring anything new to the EGM already formulated decades ago. In fact, Guo and Xu [115] used the concept to optimize a shell-and-tube HX and concluded similar remarks as obtained by EGM method such as having larger HX. 1.2.5 Airside Heat Transfer and Friction Characterization in Crossflow The investigation of airflow over cylinders and tube bundles is not a recent problem and is, likely, one of the most common problem in thermal-fluid engineering due to their wide applicability, in particular to HX’s. From the general solutions of the external boundary layer problems [116, 117] the heat transfer and 20 friction are functions of the characteristic length, Reynolds number and Prandtl number (heat transfer only). Typically, they consist of a non-linear power function (equation 12), where the multiplier and exponents are a function of the geometry (design variables) and flow regimes (equation 12c, d, e). In many cases, it also pertinent to assume that the Prandtl number is constant.           Re ,Pr Re Pr (a) Re ,Pr Re (b) ,Re (c) ,Re (d) Re (e) m n Lc Lc m Lc Lc Lc Lc Lc Nu f C f f C C f x m f x n f           (12) For very specific/simple problems, or narrow design space ranges, the terms on equation 12c, and 12d can be approximated to constant values based on analytical solution or experimental data. For more complex problems, however, such terms become more complicated non-linear functions instead. For such situations analytical solutions are not a viable option, and solving this problem requires either a numerical simulation or actual testing. Many researchers have been putting huge efforts in developing such tools in form of correlations that can reasonably predict the airside thermal-hydraulic characteristics for a given set of design parameters and operating conditions. There is a high interest in the effort of developing these correlations in particular for conventional tube and fin HX’s using small diameters (<5.0mm), since there are no existing correlations for such range. The reason for the tube diameter being important is that for same Reynolds numbers, different tube sizes are subject to different velocities. Likewise, for same velocities, different tube diameters have 21 different Reynolds number and, therefore different flow regimes. Each tube diameter will result in a different j and f curves with respect to Reynolds number. In other words, the existing correlations were built for curves at flow regimes corresponding to the particular tube diameter ranges investigated, and cannot be extrapolated. In the following sub-sections, a literature survey on the most relevant correlations available in the literature for common fin and tube surfaces is presented. 1.2.5.1Finless Tube Heat Exchangers There are numerous studies on thermal-hydraulic performance of gas flow over tube banks. Grimison [118], then later Žukauskas [119] presented, perhaps, the most comprehensive experimental studies on the subject including the development of empirical correlations. Žukauskas [119] correlations are the most commonly used even nowadays. Starting in the late 1970’s numerical approaches became popular, especially as computational capabilities keep on continuously increasing. Launder and Massey [120] proposed a cost-effective computational method for laminar flow prediction over staggered tubes and compared against experimental data from Bergelin et al. [121]. Fujii et al. [122] focused on the in- line configuration for fixed number of tube rows and constant tube pitch ratios, varying only the Reynolds number. Hausen [123] presented modifications to Grimison correlations. You may find other correlations developed for shell-and- tube heat exchangers in Taborek et al. [124] and Gaddis & Gnielinski [125]. Wung and Chen [126, 127] presented a parametric analysis on Prandtl and Reynolds 22 numbers and correlated their numerical data into expressions. Their analysis however did not account for geometry variables. Dhaubhadel et al. [128] solved the same problem as Fujii et al. [122] but for staggered arrangement. Beale and Spalding [129] investigated unsteady flow on both in-line and staggered tube banks. Wilson and Bassiouny [130] studied single row and double row tube banks parameterizing tube pitches and its Reynolds number. They also compared their results with empirical data. Buyruk [131] made a similar study using fine grid resolutions. On an analytical approach Khan et al. [132] developed alternate equations for heat transfer and friction for both inline and staggered arrangements. Their equations are limited to tube pitch ratios ranging from 1.05 to 3. They found good agreement with Grimison [118] and Žukauskas [119] for a 16.4mm tube diameter. Table 3 presents more details on selected correlations. Table 3. Selected correlations for finless tube bundle. Author Arrangement Applicability range Equation format Grimison (1937) [118] Staggered / In- line 3 4 39.8 63.6 1.2 / 6.0 1.25 / 3.0 / 2 10 4 10 o l o t o D mm P D P D N N A Re            Re Pr Re m n Do f p Do Nu c f k      Žukauskas (1972) [119] Staggered / In- line 6 / 1.25 / 2.5 1.25 / 2.5 / 1.0 2 10 0.7 500 o l o t o D N A P D P D N N A Re Pr            0.25 0.36 , , Pr Re Pr Pr Re fm Do c f w p Do c Nu c f k z             Khan et al. (2006) [132] Staggered / In- line 3 5 / 1.05 / 3.0 1.05 / 3.0 / 10 10 o l o t o D N A P D P D N N A Re           0.212 0.285 0.55 / 1/2 1/3 , 0.053 0.091 1/2 1/3 ,1.09 / 0.25 Re Pr 0.61 Re Pr 1 2 l o l o P D l t in line Do c f o o l t staggered Do c fP D o o P P Nu e D D P P Nu e D D                                      23 1.2.5.2 Finned Tube Heat Exchangers Fins provide a substantial addition to the surface area on a tube bundle at large diameters, allowing reducing thermal resistance. Amongst fin types plain fins have much poorer performance compared to enhanced ones such as louver, slits and perforated. Plain fins are, however, less susceptible to material deposition from the airstream. Applications such as heat pumps in cold climates face an extra challenge of frosting in the outdoor unit, which ultimately compromises the overall system performance. For these systems, the commonly known high performance fins like slits and louvers are generally not suitable. Researchers have shown empirically that louver fins have a poorer performance compared to plain wavy and flat fins, respectively under frosting/defrosting operating modes [6, 30]. Plain flat fins have become quite uncommon but there are applications which they can be useful. There are few correlations in the literature that predict airside performance on those fins with relative large tube diameters. McQuiston (1978) [133] proposed the first correlations for this application that were later improved by Gray et al. [134], then Webb [135] and Kim et al. [136]. The most recent correlations for plate fin-and-tube heat exchangers include those from Wang et. al. (2000) [137]. The most relevant correlations for all fin types are summarized in Table 4. Table 4. Most relevant fin-and-tube airside correlations in the literature. 24 Author Fin type / Tube Arrangement Applicability range McQuiston (1978) [133] Flat / Staggered 9.675 16.13 ;25.4 50.8 25.4 50.8 ;4 14 0.15 0.25 ; / 1.0 4.0 / o l t t D mm P mm P mm FPI mm N N A u m s               Gray (1986) [134] Flat / Staggered 9.96 16.51 ;1.7 2.58 1.97 2.55;0.08 0.64 0.015 0.018;1 8 500 Re 24700 o l o t o s o t o D mm P D P D F D D N               Webb (1990) [135] Flat & Wavy Herringbone / Staggered 4 7.95 12.52 ;1.73 2.31 2.0 2.5;1.96 4.09 0.71 3.18 ;2.0 4.0 3 6;500 Re 2.47 10 c l c t c s d f l D mm P D P D F mm P mm X P N                  Kim et al. (1999) [136] Flat / Staggered 4 7.3 19.51 ;0.857 1.654 1.996 2.881;0.081 0.641 0.15 0.406 ;1 6 505 Re 2.47 10 o t l t o s o t D mm P P P D F D mm N                Wang et al. (2000) [137] Flat / Staggered 4 6.35 12.7 ;12.4 27.5 17.7 31.75 ;1.19 8.7 0.115 0.152 ;1 6 200 Re 2 10 o l t p f D mm P mm P mm F mm mm N                Kim et al. (1997) [138] Wavy Herringbone / In-line & Staggered 3 9.53 12.7 ;1.73 2.88 1.16 1.33;0.11 0.44 0.23 1.21;1.44 5.65 1 8;500 Re 9 10 o l o t l s o d s f d D mm P D P P F D P F X P N                  Wang et al. (1997) [139] Wavy Herringbone / In-line & Staggered 4 10.3 ;1.85 2.85 2.47 2.85;1.69 4.8 =1.5 ( ); =2.0 ( ) 0.25; 0.12 ( ) 0.2 ( );1 4 200 Re 10 c l c t c p d d f l f f D mm P D P D F mm P mm staggered P mm in line X P mm staggered mm in line N                   Wang et al. (1999) [140] Wavy Herringbone / Staggered 4 8.58 10.38 ;1.84 2.95 2.45 2.96;1.21 3.66 1.18 1.68 ; 0.25 0.115 0.12 ;1 6 200 Re 10 c l c t c p d f l f D mm P D P D F mm P mm X P mm N                  25 Author Fin type / Tube Arrangement Applicability range Wang et al. (2002) [141] Wavy Herringbone / Staggered 4 7.66 16.85 ;12.7 33 21.0 38.1;1.21 6.43 0.3 1.58 ; 0.25 0.11 0.25 ;1 6 300 Re 10 c l t p d f l f D mm P mm P F mm P mm X P mm N                  Wang et al. (1999) [142] Louver / Staggered 4 6.93 10.42 ;12.7 22 17.7 25.4 ;1.21 2.49 0.9 1.4 ;1.7 3.75 / ;1 6 100 Re 10 c l t p h p f D mm P mm P mm F mm L mm L mm N A N                  Wang et al. (1999) [143] Slit / Staggered 4 10.34 ; 22 25.4 ;1.22 2.48 11.0 ; 8.0 2.2 0.99 ; 0.12 ; 4 1 6;100 Re 10 c l t p lh ls w h f S D mm P mm P mm F mm S mm S mmS mm S mm mm N N                 Wang et al. (1998) [11] Louver & Wavy Herringbone / Staggered 4 8.54 ; 19.05 25.4 ;1.22 2.54 1 4;100 Re 10 c l t p D mm P mm P mm F mm N          1.2.6 Fabrication of Heat Exchangers with Complex Surfaces The urge for developing novel high-performing heat transfer surfaces has been well established and discussed in this chapter. Researchers have been creating innovative HX surface concepts aiming address the limitations the conventional heat transfer surfaces. Often, the challenge is the lack of manufacturing options to build these novel designs. In particular, metal heat exchangers have additional manufacturing constraints as opposed to other materials such as polymers. T’Joen et al. [144] published a review on the latest developments on Polymer heat exchangers. Due to their low conductivity, limited range of application temperature and low structural resistance, polymers are seldom the preferred material. However, plastics have 26 other advantages, but above all is the ease of manufacturing complex structures that researchers can leverage when investigating novel concepts. Chang and Van Der Geld [145] validated an air-to-water compact plate HX with rectangular channels using PolyVinyliDene-Fluoride (PVDF). Harris et al. [146] built and tested a radiator with sub-millimeter rectangular air and water channels. Their HX was fabricated in polymethylmethacrylate (PMMA) using the LIGA process [147] for two halves of the HX, then alignment and bonding. Cevallos et al. [148] built a webbed-tube HX inspired by the work of Abdelaziz et al. [72], where they used polytetrafluorethylene (PTFE) and injection molding. Recently, Felber et al. [149] used 3-D printing (additive manufacturing) technique to build a microchannel HX with cylindrical pin fins on the airside in staggered arrangement. Their HX was built in Acrylonitrile Butadiene Styrene (ABS). Additive manufacturing is likely the next generation of manufacturing technology since it eliminates most of the manufacturing constraints in current technologies. It will widen the design frontiers allowing the fabrication of countless innovative designs. Felber et al. [149] used this technology to build on plastic, Arie [150] designed a novel microchannel HX and built it on metal. Metal additive manufacturing is already available with some restrictions, but the possibilities are vast. As the HX design concepts evolves, it will potentially be undertaken by a pronounced paradigm shift. 1.2.7 Literature Gaps The previous sections in this dissertation covered the main background used in this work, and pointed out potential literature gaps which this research intends to 27 fill. There are three main gaps summarized in the following subsections that will be addressed in this thesis. 1.2.7.1High-Performance Compact Finless Heat Exchangers There is a gap in the literature with respect to comprehension of the underlying physics of small characteristic lengths on airside heat transfer, and how different scales affect the performance and the need for extended surfaces (fins). For this reason, the mainstream research heavily focuses on enhancing fins instead evaluating the potential improvement on primary surfaces. The literature shows a great deal of work on fins, some work on finless micro tubes, and other work on tube shapes. The last two have not been comprehensively studied together, and much of the work is limited to theoretical analysis only, and are not applied to a full-scale design of a HX. 1.2.7.2Multi-Scale and Shape Optimization Methodology HX optimization studies are commonly studied in literature. Most of them however, either focus on conventional HX’s using computationally affordable tools to evaluate performance, or investigate novel surfaces that require computationally expensive tools such as CFD and FEM. The latter however, is usually not applied to a HX context due to the increase in computational efforts that make it a waste of time. Abdelaziz et al. [72] presented a highly cost-effective multi-scale optimization that allows one to investigate and optimize novel HX concepts in a computationally affordable manner. The gap missing is the shape optimization which allows the optimizer to not only optimize the HX, but also find the best surface performance altogether. 28 1.2.7.3Airside Heat Transfer and Friction Correlations for Small Diameter Tubes In the literature review it was presented a survey on the most relevant correlations for airside on conventional tube-fin HX’s, and explained the need for computationally inexpensive tools. There are no explicit evidences that the available equations in the literature can predict the thermal-hydraulic performances for tube banks using small tube diameters (below 7.0mm). Currently, the only way to determine the thermal-hydraulic characteristics of fin-and-tube HX’s is by using small diameter tubes (either experimentally or numerically). Doing this requires computationally expensive tools. There is a demand for computationally inexpensive tools that can aid the design of new HX’s using small diameter tubes. 29 Chapter 2: Research Objectives 2.1 Summary This dissertation will approach the design of a new generation of HX’s with a set of objectives, reaching from fundamental analysis to tool development and finally, design, optimization & validation. 1- The first objective of this work is to discuss with, aid of numerical analyses, the fundamental aspects of airflow over primary (tubes) and secondary (fins) surfaces. Such analyses will serve to demonstrate how the reduction of characteristic length and optimizing shape impact finned and finless heat transfer surfaces and the trade-offs limiting each. 2- The second objective of this research entails developing a comprehensive Multi-Scale analysis with Topology and Shape Optimization Methodology applied to air-to-fluid HX’s design. The novel HX’s developed with this methodology are significantly superior in performance, size and material usage compared to current state-of- the art with minimal or no use of fins. Furthermore, these HX’s will provide additional material to support the first objective in the above paragraph, by proving that fins are unattractive or even necessary under certain scales. This methodology should serve as foundations for a HX design platform where one can leverage computational power to let the optimizer “create” and “invent” new HX’s with high design freedom. 30 3- The third, and last, objective, entails developing computationally inexpensive tools that can accurately predict CFD simulation responses for conventional tube and fin surfaces using small diameter tubes. One aspect of this objective is to fulfill the gap where there are no correlations available in the literature that can be used for small diameter tubes. Therefore, the contribution will be a computationally inexpensive set of tools that replace the need for CFD, which can potentially mean cost savings as well. Additionally, these tools are used to optimize equivalent finned and finless surfaces using different tube diameters. With this additional study will refer back to the first objective and narrow down the trade-offs and the advantages and limitations of finned and finless surfaces. 2.2 Dissertation Organization These objectives are developed and achieved across the next five Chapters in this dissertation. The dissertation organization workflow (Figure 4) summarizes the following Chapter general task list: Chapter 2:  Provide all the fundamental and technical background required in this dissertation. Chapter 3:  Present fundamental (first and second order) analyses on surface compactness and thermal-hydraulic performance when varying characteristics such as length and exploring alternate shapes. 31  Discuss the advantages and limitations of finned and finless surfaces.  Provide the solid foundations that justify the work of to the following chapters. Chapter 4:  Present a comprehensive HX design framework that includes design concept, airside modeling and simulation, design and optimization, verification and validation.  Propose a shape parameterization method to integrate the multi-scale analysis with topology and shape optimization methodology.  Leverage automated CFD simulations, approximation assisted optimization, and robust air-to-fluid HX simulation tool to explore novel concepts.  Present novel HX’s that outperform state-of-the art HX’s in more than 20% performance improvement, size reduction and material usage.  Design 1.0kW and 10kW air-to-water HX’s.  Explore alternate manufacturing technologies, such as metal additive manufacturing, to build proof-of-concept prototypes.  Present experimental validations for two distinct design concepts for the 1.0kW air-to-water design.  Present a road map containing all the novel HX’s and how they compare with current state-of-the-art, and discuss potential guidelines for the next generation of HX’s based upon lessons learned. 32  Design condensers and evaporators for a three ton air-conditioning system achieving 10%+ improvement in COP and 30%+ charge reduction. Chapter 5:  Present a comprehensive correlation development framework that leverages automated CFD simulations.  Present six novel correlations for finless and finned tubes, with different fin types, that addresses the use of small diameter tubes (<5.0mm).  Present preliminary experimental verification with available test data for one of the prototypes in Chapter 4. Chapter 6:  Present a surface optimization analysis with parameterization of key metrics that will allow an additional comprehensive analysis on finned and finless surfaces.  Demonstrate the robustness of these novel correlations. Chapter 7: Conclusions 33 Figure 4. Dissertation organization workflow. Chapter 1: Introduction • Motivation • Literature Review Chapter 3: Theoretical Background • Airside Modeling • Heat Exchanger Modeling • Numerical Optimization Chapter 4: First & Second Order Analyses • Surface Characteristic Lengths • Finned vs. Finless Designs • Alternate Shapes Chapter 5: Multi-Scale Analysis and Shape Optimization • Design Framework • Novel Heat Exchanger Concepts • Experimental Validations Chapter 6: CFD-Based Correlations • Novel Correlations for Diameters Below 5.0mm • Finless, Flat Fins and Wavy Fins Chapter 8: Conclusions • General Discussion • Summary of Contributions • Summary of Publications • Recommendations for Future Work Objective 1 Objective 3 Chapter 7: Surface Optimization Study • Finned vs. Finless • Correlations Robustness Objective 2 Start End Chapter 2: Research Objectives 34 Chapter 3: Theoretical Background 3.1 Airside Modeling The stream wise periodic flow numerical method introduced by Pantakar [75] is extensively used in Computational Fluid Dynamics (CFD) for heat exchanger problems. CFD is now a required tool in such applications, in spite the criticism regarding the numerical uncertainty associated with it. Shah [68] argued the uncertainties related to CFD simulations can be, in many cases, comparable to performance improvement obtained. For this reason, CFD uncertainty analysis and validations must be carried out. 3.1.1 CFD Modeling and Simulation The method proposed by Pantakar [75] aims reducing the computational cost by adequately reducing the computational domain without losing physical meaning. Typically, the end-effects can be neglected and the thermal-hydraulic characteristics of a surface can be determined by a segment of the HX where the lower, upper and longitudinal boundaries are assumed periodic or symmetric. In the literature the numerical analysis on finless surfaces commonly employ 2- dimensional computational domains [38, 41, 44, 66, 67], however, finned computational domains must be 3-D. 3.1.1.1CFD Physics and Settings When using CFD for heat transfer applications the three fundamental set of equations must be solved: momentum (Navier-Stokes) (equation 13), continuity (equation 14) and energy (equation 15). The assumptions used in this work include: 35 a) steady-state flow; b) non-existent energy and mass sources nor external forces; c) negligible gravitational effects; d) pressure work and kinetic energy are negligible. The physical model is then reduced to convection-diffusion problem with no external components. The resulting governing equations are described below.   0u  (13)     2u u P u      (14)   2 0pu c T k T    (15) There are three important aspects regarding this type of CFD simulation that are seldom discussed in detail including the near wall meshing, flow regime models and thermophysical properties. Both thermal diffusion and viscous resistance within the boundary layer are function of the temperature and velocity gradient at the surface (equations 16 and 17). One must consider a much finer mesh near the wall in order to better capture the boundary layer physics. Hilbert et al. [66] illustrated their computational domain with an unstructured pave mesh with uniform element size, however no refinement near the tube wall. In this work, we consider a two dimensional computational domain (Figure 5) with pave meshing scheme as well, however the near wall region mesh is a fine map scheme with growing layers at a ratio of at most 1.2.  x w w T h T T k y         (16) 36  2 2 1 1/ 2 1/ 2 w f M w u C u u r               (17) Figure 5. Typical CFD 2-D computational domain. For the two-dimensional computational domain, both triangle and quadrilateral mesh schemes were used depending upon the geometry. 37 Figure 6. Two-dimensional computational domain mesh schemes: a) triangle; b) quadrilateral. Hexahedron elements using Cooper scheme is the most efficient way of modeling 3-D computational domain. The periodicity requires mesh link between periodic boundaries and Cooper scheme becomes convenient since it uses a source face to project the mesh onto parallel faces. Figure 7. Three-dimensional computational domain. Flow regimes models are a very debatable issue. For instance both Hilbert et al. [66] and Ranut et al. [67] used laminar flow with the argument that the Reynolds number was low (~160). There are two considerations to their statement. One, they defined the Reynolds number based on the tube vertical spacing (which is fixed in their model), although the most adequate would be using the surface hydraulic diameter (equation 5), which for different shapes it can vary. Second, the 38 same Reynolds number for different surfaces can result in different flow regimes; i.e., eddies can be developed in the inevitable flow separation, generating wakes affecting the flow regime of subsequent tube banks, even if the first tube has a laminar flow. Although turbulence models are known to over predict heat transfer and friction for truly laminar flows, they can better solve a broader range of problems. This is preferable when one has to simulate a large number of samples using common CFD settings. There are many turbulence models available in commercial CFD packages. The two-equation k-ε realizable (RKE) [151] has proven to be a very robust model. The RKE ensures the solution obeys the non- negativity of turbulent normal stress [152], thus they are realistic (when converged) from the physical viewpoint. Additionally, the authors have observed a higher rate of convergence when using RKE for a large number of CFD simulations compared to other models, including laminar. The thermophysical properties also have an impact to the outcomes of the CFD simulations. In many heat transfer applications, the fluid flow is significantly subsonic (Ma<<0.3) which characterizes as incompressible flow. Many authors simplify the problem by using constant properties [66, 67]. The temperature, however, may have a significant impact particularly on density, conductivity and viscosity (Figure 8). There are consequences on both momentum and heat transfer. As the airstream gets warmer, the constant density assumption leads to under prediction of the accelerating airflow, the constant conductivity under predicts the thermal diffusion within the boundary layer and the constant viscosity over predicts the shear stress at the surface. Therefore, the ideal-gas model is reasonable for 39 density, whereas the other thermophysical properties can easily be estimated with polynomial curve fits as function of temperature (Figure 8). Figure 8. Dry air properties as function of temperature. Finally, the simulation convergence criteria are set to a maximum residual of 10-5 for momentum and continuity, 10-6 for energy and 10-3 (default) for turbulence. If the simulation does not meet the criteria, however it stabilizes into a solution, we assume that if the standard deviation of the last 100 iterations is less than 0.5% of the average of those same 100 iterations, then it is converged. 3.1.2 CFD Data Reduction This type of problem is convenient to define uniform wall temperature (Figure 5) allowing one to easily calculate the heat transfer coefficient from the UA-LMTD method (equation 18 and 19). It is also of interest, in particular when studying surface performance, to determine the non-dimensional heat transfer (Colburn j factor) as per equation 20.  p o i o o mlQ m c T T h A T      (18) 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 290 300 310 320 330 340 350 Temperature (K) @ P = 100kPa Cp (kJ/kg.K) ρ (kg/m³) 0.017 0.019 0.021 0.023 0.025 0.027 0.029 0.031 290 300 310 320 330 340 350 Temperature (K) @ P = 100kPa k (W/m.K) μ (mPa.s) 40               ln ln / p p po i w io i o o ml o o w ow i w o w i w o m c m c m cT T T TT T h A T A A T TT T T T T T T T                           (19) 2/3Pr c p h j u c     (20) For finless designs the fin effectiveness (ηo) is logically equal to unity, however when that is not the case, the fin efficiency / effectiveness and heat transfer coefficient are calculated using Schmidt [153] approach and iteratively using Newton-Raphson method [154].  1 1fro o A A     (21)  tanh 0.5 0.5 o o mD mD       (22) 0.5 2 f f h m k          (23)    1 1 0.35lneq eqR R      (24) 0.5 2 21 2 4 t L l P X P        (25) 0.5 2 1.27 0.3t Leq o t P X R D P        (26) The Newton-Raphson iteratively calculates the heat transfer coefficient for the following set of equations. 1 1 1 ( ) ( ) n n n n h h h h         (27) 41   0.5 1 1 1 0.5 1 2 tanh 0.5 ( ) 1 1 2 0.5 n o f f frn n a n o o f f h D kA h UA h A h D k                                              (28) For the pressure drop it is convenient to set the outlet boundary at uniform atmospheric pressure (0.0 gauge). Additionally, the dynamic pressure difference between inlet and outlet can be assumed insignificant compared to the static pressure difference. Lastly, the buoyance term is also negligible for gases, therefore the pressure drop is simply retrieved according to equation 29. Similarly, one can also obtain the non-dimensional pressure drop neglecting local effects (equation 30). 2 1 1 2 out in out in in in P P P u              (29) 2 2 hs c DP f u d    (30) 3.1.3 CFD Grid Uncertainty Analysis One standard approach to evaluating the CFD model uncertainty is the 5- step Grid Convergence Index (GCI) method [69, 70, 71]. Grid Convergence Index (GCI) [71] is a formal methodology, developed based on Richardson Extrapolation, to estimate the grid convergence error of a metric of interest (φ) [155]. Step 1: define the average element length of the grid (equation 31 and 32), determined as follows for two-dimensional and three-dimensional computational domains respectively. 42 1/2 2 i D A N          (31) 1/3 3 i D V N          (32) Step 2: select at least three grid resolutions (equation 33) where the element size ratio between subsequent grid resolutions is equal or greater than 1.3. The procedure is simplified when using constant refinement ratio (r) since it eliminates the iterative calculations [69]. 1( ) 1,i ( ) 1.3 i coarse i i fine r       (33) Figure 9. Sequentially increasing grid resolutions. Step 3: calculate the observed order of accuracy (p*) (equation 34). When the observed order of accuracy (p*) deviates in more than 10% from the formal (p) spatial discretization order of accuracy then the effective value (p**) (equation 37) must be bounded by a minimum of 0.5 and the formal value [156]. 32 21 21 21 32 1 * ln ln ln p p r s p r r s                  (34) 21 32 21 32 s      (35) 43 21 2 1    (36)   ** min max 0.5, , *p p p (37) Step 4: calculate the extrapolated values (equation 38) 21 21 1 2 21 1 p ext p r r       (38) Step 5: Calculate and report the estimated extrapolation error (equation 39) and the grid convergence index (GCI) (equation 40) 21 21 1 21 ext ext ext e      (39) 21 21 ** 21 1 s a fine p F e GCI r    (40) If p* deviates in more than 10% from p then the factor of safety (Fs) must be set to 3.0 [71], otherwise a value of 1.25 [71] is considered acceptable. In order to quantify the CFD uncertainty associated with an entire design space the premise that at the boundaries of the design space the uncertainties are fundamentally larger than for any other sample is assumed. The reason for that is that the combinations of lower and upper bounds yield the most skewed computational domains, thus having a higher potential for poorer mesh elements in terms of size and aspect ratios. For every surface investigated, the GCI method is employed for the 2n samples represented by all variable combinations of 0’s and 1’s for an n-dimension design space (e.g. n = 5, 25 = 32 samples). 44 3.1.4 Non-Uniform Rational B-Splines (NURBS) Non-Uniform Rational B-Splines (NURBS) [157] are very common in shape optimization problems [58, 59, 60, 66, 67]. Several algorithms are available, however the most efficient is perhaps the one developed by Piegl and Tiller [157]. NURBS can be applied to both curves and surfaces. A NURBS curve (equation 41) is usually presented in a vector format and is described by the rational piecewise base functions. The base functions are defined on u ∈ [0,1]. ,p , , ( ) ( ) ( ) , ( ) i i i p i i j p j N u w C u R u P P a u b N u w       (41) The Pi are the control points, wi is the weight vector and Ni are the p th-degree B-Spline base functions defined on the non-uniform knot vector (U). Figure 10. 3rd degree NURBS curve and base functions example from Piegl and Tiller [157]. Piegl and Tiller [157] define 14 properties of NURBS curves from which four are of most interest in this work.  Any NURBS curve have their first and last point coinciding with the first and last control point; i.e. C(0)=P0 and C(1)=Pn. 45  All derivatives of Ri,p(u) exist, i.e. C(u) is infinitely differentiable on the knot span and p-k differentiable at a knot of multiplicity k.  If the weight vector is unitary, the rational base functions are simply B- Spline base functions. If the B-Spline degree is equal to the number of control points minus one, then it is simply a Bezier curve, which has the base functions as the Bernstein polynomials. This property shows that NURBS contains both rational and non-rational B-Splines and Bezier curves, thus allowing one to describe almost any type of curve.  Local approximation: a change in a control point or a weight affects only portion of the curve. The method can essentially be applied to design any type of heat transfer surface; from tubes to fins. In a cross flow HX a tube shape can be described by compounding two or more curves, it can be symmetrical or asymmetrical and it can define a round shape or an airfoil shape. In this work, 4th and 5th order NURBS curves (equation 13) are considered where the coordinates of the control points are normalized between 0 and 1. The leading edge (le) and trailing edge (te) points are fixed to the (0,0) and (1,0), and the three mid-points are the shape design variables. The x-coordinate of the mid control points are bounded by equally spaced slices in order to avoid self- intersecting curves (Figure 11). 46 Figure 11. Tube shape parameterization. Refer to Appendix A for C# codes based on Piegl and Tiller [157] algorithms used in this work. 3.2 Heat Exchanger Modeling This section presents a brief overview on fluid-to-fluid HX in cross flow modeling. The two common, and equivalent, approaches are the ε-NTU and UA- ΔTml. Each method has its advantages and disadvantages; the first is well suited for sizing a HX for a determined capacity, however the effectiveness (ε) depends on knowing flow arrangement and passes configurations. If inlet and outlet conditions are known the second method is becoming simpler since the temperature difference can be easily calculated, otherwise additional information regarding the geometry must be known beforehand as well. The two models are detailed through the rest of this section. Figure 12. Air-to-fluid cross flow HX’s. 0.00 0.10 0.20 0.30 0.40 0.50 0.00 0.17 0.33 0.50 0.67 0.83 y n o rm (- ) xnorm (-)  ,le lex y  ,te tex y  0 0,x y  1 1,x y  2 2,x y 0 0 1 0 3 0 1 x y     1 1 1 2 3 3 0 1 x y     2 2 2 1 3 0 1 x y      C su Air Fluid 47 Figure 13. HX Temperature profile illustration. pQ mc T  (42) ml,max mlQ UA F T UA T     (43) Where the maximum temperature difference refers to counter flow HX configuration, and F is the correction factor applied to other flow configurations. On the other hand, if one knows all temperatures then the temperature difference can be readily calculated without needing to use the correction factor.         , , , , ,max , , , ,ln / h i c o CF h o CF c i ml h i c o CF h o CF c i T T T T T T T T T               (44)         , , , , , , , ,ln / h i c o h o c i ml h i c o h o c i T T T T T T T T T           (45) The overall HX thermal conductance (UA) is composed by the fluid thermal resistances, tube thermal resistance and other parasitic resistances such as contact and fouling. Essentially the fluid thermal resistances are significantly larger and, therefore, the parasitic resistances are assumed negligible. 48       1 1 1 2 lno o i oa rUA hA k D D hA       (46) Equivalently the metrics described previously can be found using the ε- NTU method.    max min max, ,minp h i c i Q Q Q Q C Tmc T T      (47) min UA NTU C  (48) The relations between effectiveness and NTU will depend on flow arrangement and the heat capacity ratio (Cmin/Cmax) as summarized by Incropera et al. [158]. In this work the airside performance will be evaluated using the UA-ΔTml from the CFD simulations, explained previously, whereas the overall HX model is evaluated using the segmented ε-NTU method from Jiang et al. [159]. In the HX model the momentum and energy equations are decoupled, i.e. the thermal and hydraulic characteristics are solved independently. 3.3 Numerical Optimization Abdelaziz et al. [72] introduced a very cost-effective multi-scale analysis and optimization method for novel air-to-refrigerant HX’s, which the framework (Figure 14) foundations are used in this work. Their method consisted of an approximation assisted optimization (AAO) using Parallel Parameterized CFD (PPCFD) [72], Kriging metamodeling [88], and Multi-Objective Genetic Algorithm (MOGA). The entire CFD modeling and simulation occur within 49 ANSYS® platform, where geometry and meshing are built in Gambit 2.4.6 and the simulations are performed in Fluent 14.5. All other input/output and processed data occur within an external C# code tailored for the specific problem. Figure 14. Numerical optimization framework. Figure 15. Parallel Parameterized CFD (PPCFD) framework. Define Design Space Start Airside h, ΔP Perform CFD Uncertainty Analysis Acceptable? Refine mesh, revise CFD settings Run PPCFD Airside h, ΔP Create metamodel Run metamodel Design of Experiments Random samples Run PPCFD Evaluate metamodel Acceptable? Create New HX Design Evaluate HX in CoilDesigner® Finish? Optimum HX’s Airside h, ΔP Run PPCFD Evaluate metamodel Acceptable? End Approximation Assisted Optimization yes yes yes yes no no no no Run MOGA Metamodel Metamodel / Correlation Development CFD Model Verification Concept Surface Journal and executable files CFD Simulations ANSYS Platform Geometry and Meshing Parameterized Designs Post Processed Data 0.01 0.1 1 10 10 100 1000 10000 Re (-) j f External C# Code 50 3.3.1 Design of Experiments The Design of Experiments consists of a systematic approach for appropriately sampling the design space in order to retrieve the highest quality of information that will truly portray the impact each design variable has over the simulations responses. Such step is crucial to develop a good metamodel without biasing. There are different methods for space sampling, from which in this work both the Maximum Entropy Sampling (MES) [160] and Latin Hypercube Sampling LHS) [161] are used. Figure 16. Space sampling example: a) biased; b) unbiased (LHS). 3.3.2 Kriging Metamodeling Kriging is a metamodeling technique that predicts the response of an unknown design based on its linear distance from known designs and their response values through a stochastic process (i.e. random distributions) [88]. According to Wang and Shan [89] stochastic metamodels have superior performance over their counterpart deterministic methods, especially for non-linear problems. Kriging is recommended when the design space has 50 or less variables making it suitable for the application in this work. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 2 x1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x 2 x1 a) b) 51 Metamodeling is a simplified version of an actual physical model, such as CFD, with reasonable prediction accuracy. The last is measured by the metamodel’s ability to predict ( ˆ iy ) the simulation responses ( iy ) from random samples within a preset threshold deviation (eth) (usually 5% to 10%). The metamodel is considered accurate (Maximum Acceptance Score) if the percentage of the random predicted responses within eth is higher than the remainder of 1 - eth (equation 49). 1 ˆ1, if 100 ; ; ; 1 0, if th N i i th i ii i i e th i th i j e e y y MAS j e MAS e e eN y            (49) 3.3.3 Multi-Objective Optimization Multi-Objective optimization problem (equation 50) typically consists of 2 or more objective functions, subject to a set of equality and inequality constrains, and the design space boundaries. min ( ) 1,... . . ( ) 1,... ( ) 1,... m j i lower upper f x m M s t g x j J h x i I x x x      (50) The problem above represented can be suitably solved using Multi- Objective Genetic Algorithms (MOGA) [83]. 52 Chapter 4: First & Second Order Analyses 4.1 First Order Analysis As previously stated, for conventional tube sizes, fins are an undesired necessity for it provides sufficient surface area to attend the thermal performance required. However, first and second order analyses can readily show the benefits of moving towards smaller diameters. The following analyses are undertaken assuming, for all surfaces: same refrigerant side cross section area, same tube pitch ratios, same number of tube banks, constant airflow rate and velocities. Additionally, all results are based on numerical simulations using the modeling approach described in this section. Figure 17 shows the compactness (surface-to-volume ratio), material utilization (surface to material volume ratio) and internal volume as a function of diameter for finless finned (plain fins) tubes. The reduction of internal volume translates into less refrigerant charge which will consequently reduce the weight and potential environmental concerns depending on the on the working fluid used. Moreover, the fin-to-tube surface ratio is linearly proportional to the diameter, thus the contribution to the total surface area from fins is significantly reduced for smaller diameters (Figure 18). 53 Figure 17. First order analyses I: compactness, material utilization and internal volume. Figure 18. First order analyses II: fin-to-tube surface ratio. 4.2 Second Order Analysis The reduction of the tube size has, most importantly, a significant impact on heat transfer coefficient. The relation between Nusselt and Reynolds numbers shows that as the characteristic length is reduced the heat transfer coefficient is increased [38] (equation 51). Additionally, the rate at which the heat transfer coefficient increases with respect to pumping power is much higher as the tube diameter is reduced for finless tubes compared to finned tubes. For larger tube 0 10 20 30 40 50 60 70 80 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 A ir si d e S u rf ac e D en si ty ( cm ²/ cm ³) Tube Diameter (mm) Finless Round Tubes Finned Round Tubes (20 FPI) Material Utilization (cm²/cm³) 100 100010 Internal Volume (cm³) 80 8008 / 2tP / 2lP lP D tN x y z   2 1 2 2 2 4 2 1 2 2 / 4 t fin t l f t t fin Pt Pl t t t P D A N P N A D l N A FPI r r N D A N                 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 F in -t o -T u b e S u rf ac e R at io ( m ²/ m ²) Tube Diameter (mm) FPI=10 FPI=20 FPI=30 FPI=40 54 diameters the finned surface is preferred as for the same heat transfer coefficient the pumping power cost is lower; however, as the diameter decreases the thermal- hydraulic ratio is favorable to finless surfaces (Figure 20). 1Re ;0 1m mc L c h L Nu h L m k       (51) 4.2.1 Surface Level Analysis Typically, we understand that the relationship between Reynolds number and the heat transfer and friction characteristics as fixed for the same type of geometry, i.e. the scale has no impact since Reynolds is a dimensionless number. Under same Reynolds numbers the flow over different diameters have different velocities; i.e. a higher velocity over smaller tubes will have a direct effect on the developing boundary layer over the tube surface, thus yielding different heat transfer and hydraulic characteristics (Figure 20 and Figure 20). Figure 19. Second order analysis I: thermal-hydraulic characteristics. 0 50 100 150 200 250 300 0 0.5 1 1.5 2 2.5 h ( W /m ². K ) Ẇ" (W/m²) Finless Tubes Finned Tubes (20 FPI) 0.5oD mm 0.6oD mm 1.0oD mm 2.0oD mm 10.0oD mm 0.5oD mm 0.6oD mm oD 2.0oD mm " o P V W A    oD 60 1.7d oS D 1.0 /oou m s 55 Figure 20. Thermal characteristics for same Reynolds and different diameters. Figure 21. Hydraulic characteristics for same Reynolds and different diameters Under same velocities the flow over different diameters are in different regimes, or, at least, different regions of the same regime which will result in higher heat transfer and friction for smaller tubes (Figure 22 and Figure 23). Figure 22. Thermal characteristics for same velocities and different diameters. 0 5 10 15 20 25 100 1000 u o o (m /s ) ReDo (-) Do=0.5mm Do=1mm Do=5mm Do=8mm Do=10mm 0.0 200.0 400.0 600.0 800.0 1,000.0 150 250 350 450 h ( W /m ². K ) ReDo (-) Do=10mm Do=8mm Do=5mm Do=1mm Do=0.5mm 0.020 0.022 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 150 250 350 450 j (- ) ReDo (-) 0.0 200.0 400.0 600.0 800.0 150 250 350 450 Δ P ( P a) ReDo (-) Do=10mm Do=8mm Do=5mm Do=1mm Do=0.5mm 0.205 0.210 0.215 0.220 0.225 0.230 150 250 350 450 f (- ) ReDo (-) 0 5 10 15 20 25 100 1000 u o o (m /s ) ReDo (-) Do=0.5mm Do=1mm Do=5mm Do=8mm Do=10mm 0.0 200.0 400.0 600.0 800.0 1,000.0 150 250 350 450 h ( W /m ². K ) ReDo (-) Do=10mm Do=8mm Do=5mm Do=1mm Do=0.5mm 0.020 0.022 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 150 250 350 450 j (- ) ReDo (-) 10 100 1000 10000 100000 0 1 2 3 4 5 6 7 8 9 R e D o (- ) uoo (m/s) Do=0.5mm Do=1mm Do=5mm Do=8mm Do=10mm 56 Figure 23. Hydraulic characteristics for same velocities and different diameters. This section intends to provide a detailed perspective at the surface level using numerical simulations according to the procedures described in the previous section (3.1). The following study comprises of a parametric analysis on a single cylinder with air in cross flow while varying the diameter and cross-section shapes. The numerical and visualization results shall provide good insights on the underlying physics behind it and help understand Figure 20, Figure 20, Figure 22 and Figure 23. 4.2.1.1Round Tube with Parameterized Diameter The first parametric analysis consists of varying the tube diameter and evaluating the performance characteristics for three different velocities. The normalized momentum boundary layer (Figure 24) is much thinner for smaller tubes which will result in higher velocity gradient, in particular for lower velocities. Likewise, the temperature gradient is much higher (Figure 25) since air has Prandtl number of ~0.7, therefore its development grows at similar rate. The local heat transfer and friction characteristics are show in Figure 26and Figure 27, respectively. 0.0 200.0 400.0 600.0 800.0 150 250 350 450 Δ P ( P a) ReDo (-) Do=10mm Do=8mm Do=5mm Do=1mm Do=0.5mm 0.205 0.210 0.215 0.220 0.225 0.230 150 250 350 450 f (- ) ReDo (-) 10 100 1000 10000 100000 0 1 2 3 4 5 6 7 8 9 R e D o (- ) uoo (m/s) Do=0.5mm Do=1mm Do=5mm Do=8mm Do=10mm 57 At higher velocities the flow regime on larger tube diameters change to fully turbulent, which result in a higher enhancing effect on smaller tubes. At 1.0m/s the 0.63mm diameter tube has Reynolds of ~40, while the 10mm diameter has ~634 and the average velocity and temperature gradients have a factor of ~4 between the two. For 15m/s, on the other hand, the respective Reynolds numbers raise to ~600 and 9500 and the enhancing factor increases to ~5-6. Figure 24. Momentum boundary layer over different tube diameters and air velocities. Figure 25. Normalized temperature and velocity profiles within the boundary layer at 25% of the tube surface for same velocity. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h (- ) x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Separation 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h (- ) x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Separation 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h (- ) x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Separation 1.0 /u m s  5.0 /u m s  15.0 /u m s  0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h (- ) x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.02 0.04 0.06 0.08 0.1 0.12 0.0 0.3 0.5 0.8 1.0 1.3 1.5 N o rm al iz ed w al l d is ta n c e (- ) u/uoo (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.05 0.1 0.15 0.2 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed w al l d is ta n c e (- ) θ(r)/θmax(-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 5.0 /u m s  max ( ) w oo w T y T T T       58 Figure 26. Surface temperature gradient over different tube diameters and air velocities. Figure 27. Surface velocity gradient over different tube diameters and air velocities. The second parametric analysis consists of varying the tube diameter and evaluating the performance characteristics for three different Reynolds numbers (Figure 28). Even for the same Reynolds number, both the temperature and velocity profiles (Figure 29) change at much higher rate for the smaller diameters. Figure 28. Momentum boundary layer over different tube diameters and Reynolds. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d T /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 1.0 /u m s  Separation 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d T /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 5.0 /u m s  Separation 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d T /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 15.0 /u m s  Separation 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d u /d r) s (- ) Normalized xs (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.02 0 0.5 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d u /d r) s (- ) Normalized xs (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d u /d r) s (- ) Normalized xs (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 1.0 /u m s  Separation 5.0 /u m s  Separation 15.0 /u m s  Separation 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h (- ) x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Separation Re 50Dh  0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h (- ) x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Re 500Dh  Separation 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Re 2000Dh  Separation 59 Figure 29. Normalized temperature and velocity profiles within the boundary layer at 25% of the tube surface for same Reynolds number. The purpose is to demonstrate how the thermal-hydraulic characteristics change as function of the diameters (Figure 30 and Figure 31). Figure 30. Surface temperature gradient over different tube diameters and Reynolds. Figure 31. Surface velocity gradient over different tube diameters and Reynolds. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.3 0.5 0.8 1.0 1.3 1.5 N o rm al iz ed w al l d is ta n c e (- ) u/uoo (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed w al l d is ta n c e (- ) θ(r)/θmax(-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /D h (- ) x/Dh (-) Tube Wall Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Re 50Dh  0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d T /d r) w (- ) x/Dh(-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d T /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d T /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Re 50Dh  Re 500Dh  Re 2000Dh  Separation Separation Separation 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d u /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.003 0.006 0 0.5 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d u /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 N o rm al iz ed d u /d r) w (- ) x/Dh (-) Dh=10 mm Dh=5 mm Dh=2 mm Dh=1 mm Dh=0.63 mm Re 50Dh  Re 500Dh  Re 2000Dh  Separation Separation Separation 60 4.2.1.2Alternate Shapes The impact of the tube shape on the performance can be significant, as demonstrated in the literature. In this section we present a brief analysis for the tube shapes on Figure 32 on how they perform, for the same hydraulic diameter (1.0mm), in a wide range of air velocities. The purpose is to evaluate whether different shapes will indeed impact positively on the thermal-hydraulic performance. Figure 32. Tube shapes: a) Round; b) Ellipse; c) Eye; d) Airfoil leading edge; e) Airfoil trailing edge. The top two plots in Figure 33 clearly indicate that ROU shape yields both the highest heat transfer and hydraulic resistance. The ratio of j over f, however, indicates a better balance for the ALE, ATE and EYE shapes. The non-symmetric shapes with respect to the longitudinal axis to the flow, have a clear advantage over the other shapes. The j/f curves and the dimensioned heat transfer and friction power per unit area suggest a great overall performance improvement. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.2 0.3 0.8 1.3 1.8 2.3 2.8 3.3 3.8 Round (ROU) Ellipse (ELL) Eye (EYE) Airfoil Leading Edge (ALE) Airfoil Trailing Edge (ATE) a) b) c) d) e) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.2 0.3 0.8 1.3 1.8 2.3 2.8 3.3 3.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.20.30.81.31.82.32.83.33.8 61 Figure 33. Thermal-hydraulic characteristics of airflow over different shapes. 0.000 0.020 0.040 0.060 0.080 0.100 10 100 1000 10000 j (- ) ReDh (-) ROU ELL EYE ALE ATE 0.000 0.005 0.010 0.015 0.020 0.025 0.030 10 100 1000 10000 f (- ) ReDh (-) ROU ELL EYE ALE ATE 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 10 100 1000 10000 j/ f (- ) ReDh (-) ROU ELL EYE ALE ATE 0 100 200 300 400 500 600 700 500 5000 50000 h ( W /m ². K ) Ẇ" (W/m²) ROU ELL EYE ALE ATE 62 Chapter 5: Multi-Scale Analysis and Shape Optimization 5.1 Design Framework The HX design framework (Figure 34) employed in this work consists of six main sub-groups. The first - airside characterization - includes the 3 first sub- steps from the numerical optimization (Figure 14) (surface concept, CFD model and metamodeling). The second entails defining the problem, i.e. flow arrangements and operating conditions. The third step is the actual design and optimization using the approximation assisted optimization (AAO) methodology. The following step consists in the evaluation of the optimum designs with respect to manufacturability and potentially including multi-physics analysis such as mechanical stress evaluation, noise and vibration etc. The fifth step is conditional as to whether the HX was designed for a system level application, where the system performance is evaluated. The last step is the prototyping and experimental validation. On Appendix B stress analysis for one of the key HX’s from this analysis is presented. The detailed dimensions and performance characteristics for every HX investigated in this work is disclosed in Appendix C. All details with respect to experimental facility, procedures, uncertainties and data are presented in Appendix D. 5.2 Concept Surfaces Four types of design variables are defined in this work with which represent all investigated surfaces, however not all concepts will make use of the four types. 63 The first type, named “Scaling Variables”, which contain all variables that have absolute dimensions range pre-established. The second type, “Topology Variables”, quantify relative dimensions that are function of the “Scaling Variables”. The third type, “Operating Variables”, i.e. any quantity related to the flow operating conditions or physical state of the fluid. Lastly, the “Shape Variables”, which define the surface shape independent from the other variable types. Table 5. Design variable types. Type Characteristic Examples Scaling Quantifiable Diameter, height, length, width, rows of tubes, fin density, fin thickness Topology Non-Dimensional Longitudinal / transverse pitch ratios, wall thickness ratio, corrugation angle Operating Fluid related Velocity, temperature, pressure Shape Non-Dimensional Spline control points, polynomial coefficients / order 5.2.1 Round Tube Heat Exchangers (RTHX & FTHX) The simplest HX surface is the round tube bundle. From the first and second order analyses in Chapter 3 we observed great potential for such HX’s when using very small diameters. In this research, investigate finless round tube bundle in both staggered and in-line arrangement (Figure 35) using diameters ranging from 0.5mm up to 2.0mm are investigated. In addition to the finless version, tube bundle in staggered arrangement with low fin densities is also studied. 64 Figure 34. Heat exchanger design framework. Define Design Problem Define flow arrangement, passes Define Operating Conditions Evaluate Options Evaluate system performance Selected design Process specifications Numerical Design & Optimization Reality check System analysis Validation Feasible? No Yes No Yes Start End No Yes Experimental validation Standalone? Yes No Define Design Space Airside h, ΔP Perform CFD Uncertainty Analysis Acceptable? Refine mesh, revise CFD settings Run PPCFD Airside h, ΔP Create metamodel Run metamodel Design of Experiments Random samples Run PPCFD Evaluate metamodel Acceptable? yes yes no no Metamodel Metamodel CFD Model Concept Surface Create New HX Design Evaluate HX in CoilDesigner® Finish? Optimum HX’s Airside h, ΔP Run PPCFD Evaluate metamodel Acceptable? Approximation Assisted Optimization yes yes no no Run MOGA Verification Airside Characterization Manufacturing constraints Multi-physics analysis Acceptable? Acceptable? 65 Figure 35. Round finless tubes (RTHX): a) In-line; b) Staggered. Figure 36. Flat fin and tube HX (FTHX) Table 6. RTHX and FTHX Design space. Variable Type Design Variable Unit RTHX FTHX Scaling Do mm 0.5 – 2.0 0.5 – 2.0 FPI in-1 N/A 5 – 10 Fin Thickness mm N/A 0.115 Nr - 2 – 20 2 – 10 Topology Pt ratio (Do) - 1.2 – 4.0 1.5 – 3.0 Pl ratio (Do) - 1.2 – 4.0 1.5 – 3.0 Operating u m/s 0.5-3.0 0.5-3.0 d l d lTube Banks (Nr) Tube Banks (Nr) Tube Rows (Nt) Tube Banks (Nr) Tube Banks (Nr) Tube Rows (Nt) a) b) 2Pl oD tP lP pF f 66 5.2.1.1 CFD Model The CFD model for BTHX consists a 2-D computational domain (Figure 37) with symmetric boundaries on top and bottom. The GCI analysis (Figure 38) used constant refinement ratio of 1.3 and a factor of safety of 3.0 for all samples. Unlike the BTHX model, the FTHX model requires a 3-D computational domain (Figure 39) with symmetric boundaries on top and bottom, and periodic boundaries on the sides. The GCI settings are the same as for the BTHX models. Figure 37. RTHX computational domain and mesh: a) staggered; b) in-line. Figure 38. CFD GCI Analysis for BTHX in staggered and in-line arrangements. ,u T  Symmetry a) b) 0% 18% 35% 53% 70% 0% 18% 35% 53% 70% G C IΔ P GCIh Median 0% 5% 10% 15% 20% 25% 30% 0% 10% 20% 30% G C I Δ P GCIh Median 67 Figure 39. FTHX Computational domain and mesh. Figure 40. CFD GCI Analysis for FTHX. Figure 41. Example of contour plots on different grid resolutions for the FTHX. 5.2.1.2Metamodel Verification The following plots (Figure 42 and Figure 43) show the metamodel verifications. Symmetry Periodic ,u T  0% 15% 30% 45% 60% 75% 90% 0% 15% 30% 45% 60% 75% 90% G C I Δ P GCIh Median 68 Figure 42. Heat transfer coefficient metamodel verification for RTHX in staggered and in-line arrangements for 50 random samples. Figure 43. Pressure drop metamodel verification for RTHX in staggered and in-line arrangements for 50 random samples. 45 95 145 195 245 295 345 45 95 145 195 245 295 345 h M et am o d el (W /m ². K ) hCFD (W/m².K) 95 145 195 245 295 345 395 445 495 95 195 295 395 495 h M et am o d el (W /m ². K ) hCFD (W/m².K) 10% 10% 10% 96MAS  10% 10% 10% 94MAS  0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Δ P M et am o d el (P a) ΔPCFD (Pa) 0 50 100 150 200 250 0 50 100 150 200 250 Δ P M et am o d el (P a) ΔPCFD (Pa) 10% 10% 10% 100MAS  10% 10% 10% 94MAS  69 Figure 44. Metamodel verification for FTHX for 50 random samples. 5.2.1.3 RTHX Preliminary Analysis In this section is presented a brief analysis comparing staggered and inline arrangements with a discussion of the benefits from each. The common sense always points to staggered arrangement as the best option for having higher heat transfer coefficient. On the other hand, it is also expected a higher hydraulic resistance. Zukauskas [119] had pointed out that there are certain configurations and operating conditions where the in-line may outperform the staggered version. The analysis here presented is for an arbitrary design where both in-line and staggered arrangement have equivalent geometries; i.e. same hydraulic diameter, same surface area and so forth. Figure 45. Equivalent round tube arrangements. 50 75 100 125 150 175 200 225 250 275 50 75 100 125 150 175 200 225 250 275 h M et am o d el (W /m ². K ) hCFD (W/m².K) 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 Δ P M et am o d el (P a) ΔPCFD (Pa) 10% 10% 10% 100MAS  10% 10% 10% 100MAS  70 The designs above are evaluated under same velocity spectrum. The thermal hydraulic performance of each design, with respect to velocity is shown in Figure 46. Figure 46. In-line vs. Staggered. Figure 46 clearly shows how the staggered arrangement has both higher heat transfer coefficient and hydraulic resistance. The thermal-hydraulic performance of the in-line arrangement is less sensitive as velocity increases; the ratio between in-line over staggered decreases from 0.6-0.7 to 0.4-0.5 on both h and ΔP. The underlying physics behind was discussed in section 4.3. The staggered arrangement has an abrupt flow impingement in every tube; furthermore, aside from the first tube bank, all other banks have an accelerated flow impinging on them due to the tube arrangement. The main differences between the two arrangements can be observed in Figure 47 and Figure 48 showing detailed results for one frontal velocity. 0 5 10 15 20 25 0 25 50 75 100 h /Δ P ( W /m ². K .P a) Re (-) In-line Staggered 2.5 3 3.5 4 4.5 5 60 70 80 90 100 h /Δ P ( W /m ². K .P a) Re (-) Break Even 71 Figure 47. Contours of velocity angle. Figure 48. Local heat transfer coefficient and skin friction coefficient at the tube wall. 5.2.2 NURBS Tube Heat Exchangers (NTHX) The NURBS Tube Heat Exchanger (NTHX) concept (Figure 49) is essentially equivalent to the round finless tube bundle in staggered arrangement, with the addition of the shape variables that describe the cross section profile of the tube. The design space consists of 12 design variables (Table 7) from which 6 are the x and y normalized coordinates of the control points used to describe the NURBS curve. With two fixed control points demarking the width of the tube over the centerline and the three variable points a 4th order NURBS curve (Figure 50). The waterside tube shape is a function of the constant wall thickness. Preliminary structural analysis showed that a wall thickness equivalent to 20% (NTHX-001 is 72 30%) of the tube height (Figure 50) is a safe assumption to ensure no deformation nor mechanical collapse for an internal pressure at most of 6.0MPa. Figure 49. NTHX surface concept. Table 7. NTHX Design space. Variable Type Design Variable Unit Range Scaling ht mm 0.5 - 3.0 wt/ ht - 1.0 - 3.0 Nr - 2 – 20 Topology Pt/ ht - 2.0 - 3.0 Pl/ wt - 0.75 – 3.0 Shape xi - 0.0 – 1.0 yi - 0.0 – 1.0 Fluid u m/s 0.5 - 5.0 Figure 50. NTHX Profile parameterization. Uniform Air Flow l Pt Pl wt ht -1 -0.5 0 0.5 1 1.5 2 2.5 3 -1 0 1 2 3 4 5 6 7 tw th lP 2 tP  ,le lex y  ,te tex y  0 0,x y  1 1,x y  2 2,x y 0.2t th   tN rN u T 73 5.2.2.1 CFD Model The CFD model for NTHX consists a 2-D computational domain (Figure 51) with symmetric boundaries on top and bottom. The GCI analysis (Figure 52) used constant refinement ratio of 1.3 and a factor of safety of 3.0 for all samples. Figure 51. NTHX Computational domain. Figure 52. NTHX GCI Analysis. 5.2.2.2Metamodel Verification A Design of Experiments (DoE) containing 7096 samples generated using Latin Hypercube Sampling (LHS) was simulated using PPCFD. Due to geometry/mesh fails or simulation divergence an effective 3286 samples could be used to create the metamodels. These metamodels were tested against 961 random designs as shown in Figure 53. 0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 0.0% 20.0% 40.0% 60.0% G C I Δ P GCIh 0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% G C I Δ P GCIh Average Median 74 Figure 53. NTHX Metamodel verification against 961 random samples. 5.2.3 Webbed-NURBS Tube Heat Exchangers (WTHX) Abdelaziz et al. [76] and Cevallos et al. [148] have studied the webbed- round tube surface concept, showing great potential for performance improvement. This work combines the same concept with the NURBS shape parameterization (Figure 54). In this case four variable control points are used as opposed to three, thus resulting in a 5th order NURBS curve (Figure 55). Figure 54. WTHX Surface concept. 0 300 600 900 1200 1500 0 300 600 900 1200 1500 Δ P m et am o d el (P a) ΔPCFD (Pa) 0 130 260 390 520 650 0 130 260 390 520 650 h m et am o d el (W /m ². K ) hCFD (W/m².K) 10% 10% 10% 20% 95.4 99.5 MAS MAS   10% 20% 53.1 83.1 MAS MAS   10% 10% Uniform Air Flow Uniform Water Flow Uniform Water Flow Uniform Air Flow 75 Figure 55. WTHX Profile parameterization. 5.2.3.1 CFD Model The computational domain (Figure 56) includes one tube only, with periodic boundaries. The mean GCI for heat transfer and pressure drop are 0.7% and 1.8%, respectively. The WTHX design space (Table 8) covers the same type of design variables as the NTHX concept. Figure 56. WTHX Computational domain. Table 8. WTHX Design space. Variable Type Design Variable Unit Range Scaling ht mm 0.5 - 3.0 wt/ ht - 1.0 - 3.0 Nr - 2 – 20 Topology Pt/ ht - 2.0 - 3.0 Pl/ wt - 0.75 – 3.0 Shape xi - 0.0 – 1.0 yi - 0.0 – 1.0 Fluid u m/s 0.5 - 5.0 δt (xtoi,ytoi) (xtii,ytii) γi δa ≥ δt δb ≥ δt (x2,y2) (x1,y1) (xle,yle) (x3,y3) (x4,y4) (xte,yte) wt = xte - xle wt / 4 wt / 4 wt / 4 wt / 4 ht x y δt/2 Pl/2 wt Pl / 2 Pt -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Periodic Boundaries ,u T  P wT T Coupled 76 5.2.3.2 Metamodel verification Figure 57. WTHX Metamodel verification. 5.2.4 Airfoil-Shaped Tube Heat Exchangers (AFHX) The Airfoil-Shaped tube HX (AFHX) is a concept inspired by the rotating air cooler [162]. The latter has the blades arranged as such the air flow passage gap is constant, thus avoiding boundary layer separation. While such characteristic is desirable for lowering pressure drop, the fully developed flow result in lower heat transfer coefficient. The AFHX concept (Figure 58) has two banks where the second is rotated 180° from the first and shifted half the gap. The tube shape, gap passage and leading/trailing edges are all ellipses or part of ellipses, where the radii and coefficients can be the shape design variables. The design space is shown in Table 9. 0 50 100 150 200 250 0 50 100 150 200 250 h M et am o d el (W /m ². K ) hCFD (W/m².K) 0 200 400 600 800 1000 1200 1400 0 500 1000 1500 Δ P M et am o d el (P a) ΔPCFD (Pa) +10% -10% 10% 20% 89 95 MAS MAS   +10% -10% 10% 20% 90 99 MAS MAS   77 Figure 58. AFHX Concept. Table 9. AFHX Design space. Variable Type Design Variable Unit Range Scaling r1 mm 0.5 - 3.0 δ1 - 1.0 - 3.0 Topology δ2/ δ1 - 2 – 20 Shape a - 2.0 - 3.0 Fluid u m/s 0.5 - 5.0 5.2.4.1 CFD Model The computational domain (Figure 58) is trimmed according to the ellipses at the centerline of the air passage and tubes. The mean GCI for heat transfer and pressure drop are 0.2% and 0.5%, respectively. Figure 59. AFHX Computational domain. l Uniform Air Flow Uniform Water Flow Periodic Boundaries ,u T  P wT T 78 5.2.4.2 Metamodel Verification Figure 60. AFHX Metamodel verification. 5.3 Design Problems (DP) 5.3.1 DP I: 1.0kW Single-Phase Heat Exchangers The first application of the methodology is a 1.0kW air-to-water HX. A MCHX [163] radiator was used as baseline for comparison. This HX is a non- conventional MCHX that was designed to deliver a higher performance than the current state-of-the art MCHX technologies for such application. The HX MCHX is a one slab of 14 tubes with 22 ports each (Dh = 0.75mm), vertically spaced by 4mm; and 18 louvered fins per inch fill the tube spacing. The core volume is 230cm³ with 0.0102m² of face area; the airside hydraulic diameter is 1.64mm. Table 10. 1.0kW Baseline MCHX. Metric Unit Value Air flow rate m³/s 0.03 Air inlet temperature K 300 Water flow rate g/s 25 Water inlet temperature K 347.5 Heat load W 1053 Pumping power W 2.35 Air pressure drop Pa 78 Air heat transfer coefficient W/m².K 144 Airside thermal resistance K/W 0.022 0 10 20 30 40 50 0 10 20 30 40 50 Δ P M et am o d el (P a ) ΔPCFD (Pa) 50 75 100 125 150 50 75 100 125 150 h M et am o d el (W /m ². K ) hCFD (W/m².K) +10% -10% 10% 100MAS  +10% -10% 10% 100MAS  79 5.3.1.1Proof-of-Concept NTHX-001 The proof-of-concept NTHX-001 was designed to deliver similar capacity as the baseline MCHX while reducing 20% the envelope volume and approximately 20% reduction in airside pressure drop while maintaining the same approach temperature (50K). Additionally, we established the air frontal velocity should be at most 3.0m/s which corresponds to 2% reduction in face area compared to the MCHX. For simplicity, we determined the face area should have aspect ratio equal to 1.0. The tube shape is similar to the surface ALE from the previous section with minor adjustments to the control point coordinates. Additionally, the available manufacturing option imposed a minimum wall thickness of 0.3mm, tube height of 1.0mm and tube width of 3.0mm. The airside thermal conductance of the baseline MCHX is approximately 45W/K, therefore a similar value was obtained by the NTHX-001 surface. Several CFD simulations (Figure 61) were carried out in order to find a potential candidate. A final surface with 7 tube banks, 1.1mm tube height, 3.0mm tube width, 2.2mm vertical spacing and 2.4 mm horizontal spacing was found to be a viable candidate (Figure 62). The GCI for this CFD model is 0.1% for heat transfer and 0.397% for pressure drop. The resulting HX then has 315 tubes (7x45) with an airside thermal conductance of 42.2W/K and pressure drop of 64 Pa. 80 Figure 61. CFD Results for the NTHX-001: a) velocity; b) pressure; c) temperature. Figure 62. Proof-of-concept NTHX-001 dimensions. Following the CFD analysis, comes the HX simulation, which occurs within the CoilDesigner® [159] environment. This platform can handle any type of crossflow air-to-fluid HX with either headers or complex tube circuitry. The airside is an external input from CFD, whereas the refrigerant side is handled with existing correlations available in the literature using the equivalent inner hydraulic diameter for round channels. The last is reasonable since these correlations work well for single-phase laminar flows [164, 165]. To account for differences in area and perimeter of the inner the pressure drop on the waterside needs correction (ζ) according to equations (52) and (53). The HX analysis and comparison results against the MCHX are shown in Table 11. Magnitude Velocity (m/s) 0.0 9.0 Static Pressure (Pa) -20.0 69.0 Temperature (K) 308 338 a) b) c) Air Flow Water Inlet Water Outlet Air Flow Direction100l mm 100h mm 17.4d mm / 2 1.1tP mm 1.1th mm 3.0tw mm 2.4lP mm 0.3t mm  81 _ _ 2 2 2 _ 1 ; 2 h in h in D w h in D actual Al m P f D A A                (52) 1 0 _ 2 1 0 ( ) ( ) 4 4 ( ) 1 ( ) u x y actual u h in u y u x dC u dC uA D P dC u du dC u                 (53) Table 11. NTHX-001 Numerical results compared to the baseline MCHX. Metric Unit MCHX NTHX- 001 Relative Diff. Face Area (Af) m² 0.0102 0.0100 -2.00% Water Cross Section Area (Acs) mm² 173 186 7.40% Airside Heat Transfer Area (Ao) m² 0.312 0.211 -32.3% Envelope Volume (VHX) cm³ 230 174 -24.3% Internal Volume (waterside) cm³ 32.9 18.6 -43.5% Material Volume (tube + fins) cm³ 77.0 46.8 -39.2% Compactness (Ao/VHX) cm²/cm³ 44.3 57.5 29.8% Air Frontal Velocity (u) m/s 2.94 3.00 2.00% Airside Heat Transfer Coefficient (hair) W/m².K 144 200 38.9% Airside Pressure Drop (ΔPair) Pa 78 64 -17.9% Airside Conductance (UAair) W/K 44.9 42.2 -5.90% Heat Load (Q) W 1109 1072 -3.30% 5.3.1.2 Design and Optimization – RTHX Two optimization problems (equation 54) were investigated, where the second comprised of fixed diameter tubes due to the availability of tubes to build a prototype. The final results are displayed in Figure 63. The proof-of-concept RTHX-001 was verified against CFD (Figure 41) to evaluate the metamodel prediction, which exhibited 0.6% deviation in heat transfer coefficient, and 3.88% in pressure drop. The uncertainty analysis resulted in GCI of 1.64% for heat transfer 82 coefficient and 2.21% for pressure drop, for the group of the finest meshes from 5 grid resolutions. Optimization I: Optimization II: : min min min min . . air air HX HX P P V V s t   _ _ _ . . 1.0 1.1 1.0 1.1 0.8 0.8 1.0 1.0 0.8 air air baseline air air baseline water water HX HX baseline s t Q kW Q kW P P P P P kPa P kPa V V                 _ 0.8 0.8 HX HX baseline o V V D mm    (54) Figure 63. DP I: RTHX & FTHX Optimization results. MCHX RTHX-0.8mm (In-line) RTHX-0.5mm RTHX-0.8 mm FTHX-0.5mm Proof-of-Concept RTHX-001 0.8oD mm 1.24tP mm 1.19lP mm 0.6oD mm 4.37d mm 152l mm 121tN  Face Area (m²) 0.0102 0.04 Material Volume (cm³) 11.4 77 83 Figure 64. RTHX-001 CFD verification contour plots: a) velocity; b) pressure; c) temperature. The numerical results compared against the baseline are displayed in Table 12. Table 12. RTHX-001 Numerical results compared to the baseline MCHX. Metric Unit MCHX RTHX-001 Relative Difference Face Area (Af) m² 0.0102 0.0228 123.53% Water Cross Section Area (Acs) mm² 173 137 -20.90% Airside Heat Transfer Area (Ao) m² 0.312 0.185 -40.74% Envelope Volume (VHX) cm³ 230 109 -52.61% Internal Volume (waterside) cm³ 77 16.2 -78.99% Material Volume (tube + fins) cm³ 32.9 20.8 -36.78% Compactness (Ao/VHX) cm²/cm³ 13.57 16.96 25.05% Air Frontal Velocity (u) m/s 2.94 1.32 -55.25% Airside Heat Transfer Coefficient (hair) W/m².K 144 308 113.89% Airside Pressure Drop (ΔPair) Pa 78 27 -65.38% Airside Conductance (UAair) W/K 44.9 56.9 26.83% Heat Load (Q) W 1109 1200 8.21% 5.3.1.3 Design and Optimization – NTHX Three optimization problems (equation 55) are investigated each including additional constraints in a stepwise manner, bridging the gap between theoretical and real (i.e. NTHX-001). The last optimization problem entails finding optimum 84 designs with similar manufacturing constraints imposed to the NTHX-001, with a thinner wall thickness. Optimization I: Optimization II: Optimization III: min min min min air air air HX P P P V    min min . . . . . . 1.0 1.1 HX HXV V s t s t s t Q kW  _ _ _ 1.0 1.1 1.0 1.1 0.8 0.8 0.8 1.0 1.0 air air baseline air air baseline air air baseline water water Q kW Q kW P P P P P P P kPa P k                  _ _ _ _ 1.0 0.8 0.8 0.8 water HX HX baseline HX HX baseline HX HX baseline f f baseline Pa P kPa V V V V V V A A          _ 1.0 f f baseline t A A h mm   / 3.0t tw h  (55) Figure 65. DP I: NTHX Optimization results I. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Face Area (m²) 0.009 0.017 Material Volume (cm³) 11.4 77 NTHX-001 NTHX-051 NTHX-002 NTHX-030 NTHX-019 NTHX-029 NTHX-045 MCHX 2.0mm Optimization III Optimization II O p ti m iz a ti o n I airu 85 Figure 66. DP I: NTHX Optimization results II. Figure 67. DP I: NTHX Metamodel verification for the optimum designs. 5.3.1.4Design and Optimization – WTHX & AFHX For the AFHX and WTHX surfaces only one optimization problem was investigated (equation 56). The results are shown in Figure 68. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 NTHX-001 NTHX-051 NTHX-002 NTHX-030 NTHX-019 NTHX-029 NTHX-045 MCHX Optimization III Optimization II O p ti m iz a ti o n I airu h (W/m².K) 144 300 175 225 275 325 375 175 225 275 325 375 h M et am o d el (W /m ². K ) hCFD (W/m².K) 0 15 30 45 60 0 15 30 45 60 Δ P M et am o d el (P a) ΔPCFD (Pa) +10% -10% 10% 20% 48.8 80.2 MAS MAS   +20% -20% 10% 20% 88.3 98.8 MAS MAS   +10% -10% +20% -20% 86 _ _ _ Optimization I: min min . . 1.0 1.1 0.8 1.0 0.8 air HX air air baseline water HX HX baseline f f baseline P V s t Q kW P P P kPa V V A A            (56) Figure 68. DP I: WTHX & AFHX Optimization results. 5.3.1.5 Heat Exchanger Optimization Map In this section, the most relevant optimum designs are combined in single optimization maps (Figure 69 and Figure 70) showing different metrics and how they compare overall. The following CFD results (Figure 71 and Figure 72) show contour plots for selected designs at their operating design point. MCHX NGHX13 (Abdelaziz et al., 2010) AFHX WTHX Face Area (m²) 0.01 0.03 87 Figure 69. DP I HX Optimization map I. Face Area (cm²) 90 400 Material Volume (cm³) 8.7 77 MCHXNTHX-001 RTHX-0.8mm (In-line) NTHX-OPT03 NGHX13 (Abdelaziz et al., 2010) NTHX-OPT01 NTHX-OPT02 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 RTHX-0.5mm RTHX-0.8 mm FTHX-0.5mm 88 Figure 70. DP I Optimization map II. h (W/m².K) 70 400 MCHXNTHX-001 RTHX-0.8mm (In-line) NTHX-OPT03 NGHX13 (Abdelaziz et al., 2010) NTHX-OPT01 NTHX-OPT02 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 -1 0 1 2 3 4 5 6 7 8 9 -1 4 9 14 19 RTHX-0.5mm RTHX-0.8 mm FTHX-0.5mm 89 Figure 71. Velocity magnitude and angle contour plots for selected designs for DP I: a) RTHX-001; b) NTHX-001; c) NTHX-030; d) WTHX-011; e) AFHX-001. Velocity Magnitude (m/s) 0.0 10.0 a) b) c) d) e) Velocity Angle ( ) -180.0 180.0 5.0mm 90 Figure 72. Static pressure and temperature contour plots for selected designs for DP I: a) RTHX-001; b) NTHX-001; c) NTHX-030; d) WTHX- 011; e) AFHX-001. Static Pressure (Pa) -25 70.0 a) b) c) d) e) Temperature (K) 300 340 5.0mm 91 From Figure 71 on the left hand side plot, one can observe a much more streamlined flow over the alternate shape designs compared to the round tube. The right hand side plot in the same figure illustrates the intensity of the stagnation point and flow separation. The latter is much less intense with the optimum shapes which, in combination to the bundle effect, reduce the vortex shed region, thus reducing the flow resistance per unit depth (Figure 72). On the other hand, the high circulation regions for round tubes promotes higher mixing, therefore enhancing the heat transfer. The round tube design has much lower frontal velocity and much shorter flow passage, allowing an overall low pressure drop. The shape optimization allows more flexibility to the thermal-hydraulic compromise compared to the round shape tubes. 5.3.1.6 Discussion The optimization map in Figure 70 show the heat transfer coefficients of each design. The most important message from this map is to show that most of the concepts developed in this work resulted in an actual heat transfer enhancement, i.e. higher heat transfer coefficients. In a HX scale, having high heat transfer coefficients mean needing less surface area. The concept proposed by Abdelaziz et al. [76] has similar or lower heat transfer coefficient than the baseline, in other words it requires similar or more surface area. The only way to achieve the desired capacity in a small envelope is by greatly reducing tube diameter in order to attain enough compactness as illustrated in Figure 17. 92 5.3.1.7 Parametric Analysis In this section includes a parametric analysis (Figure 73) over a wide range of Reynolds number comparing the airside performance between the baseline MCHX, RTHX-001 and NTHX-001/2/30 designs. Figure 73. DP I: Airside performance parametric analysis. Although there are many ways to evaluate a heat transfer surface performance as discussed in chapter 2, the particular analysis above brings some useful insights. First, the curve for the RTHX-001 is evidently higher in the y-axis compared to the others, however significantly shifted to the right. This is the characteristic of surfaces with high heat transfer performance with high friction costs, such as round tubes. To the other end, there is the MCHX which is the lowest curve, but the closest to the y-axis. This is the characteristic of lower friction cost surfaces, which can be partially attributed to the flat shape nature of the MCHX tube. In between, there are the three NTHX surfaces showing the balancing between heat transfer performance and friction cost. The optimized NTHX surfaces resulted in higher and leaning to the left curves, i.e. overall improvement. 0 200 400 600 800 1000 0.1 1 10 100 1000 10000 h ( W /m ². K ) Ẇ" (W/m²) MCHX NTHX-001 NTHX-002 NTHX-030 RTHX-001 93 5.3.1.8 Prototypes and Experimental Validations The proof-of-concepts RTHX-001 and NTHX-001 were prototyped and tested in the wind tunnel facility built in the University lab. The details on the facility, data acquisition uncertainty analysis and details on the test matrices are presented in the Appendix D at the end of this manuscript. Two versions of the RTHX-001 concept (Figure 74 and Figure 75) were fabricated; one using stainless steel tubes brazed to a stainless steel header while the second using copper tubes and headers. The first was successfully tested and validated. The NTHX-001 prototype (Figure 76 and Figure 77) was fabricated using metal additive manufacturing technique. The prototype is a single piece component printed in Titanium grade 5. 94 Figure 74. RTHX-001 Prototype drawing. Figure 75. Stainless steel RTHX-001 sample images. RTHX-001 Water Inlet Water Outlet Air Flow 100mm 95 Figure 76. NTHX-001 Prototype drawing. Figure 77. NTHX-001 sample images. 100mm 96 Both prototypes were tested for 15 operating conditions consisting of 5 air flow rates and 3 water flow rates. The inlet approach temperature was kept at 25K which corresponds to 50% of the design approach temperature, thus resulting in lower capacities (<1.0kW). The average experimental capacities were compared to the HX simulation in CoilDesigner® [159], agreeing in less than 5% (Figure 78). The experimental data was reduced using Wilson plot method and the heat transfer coefficients obtained matched within 10%, while the pressure drop matched within 20% (Figure 79 and Figure 80). The latter was particularly off for the RTHX-001 surface, likely due to the turbulence model that over predicted the friction resistance. For the NTHX-001, the good agreement to the pressure drop may have been a combination of factors; the CFD models could have over predicted the pressure drop. An inherited aspect from the printing process is higher roughness, which could have balanced out the numerical prediction. Nevertheless, the results are very encouraging and satisfactory from a validation viewpoint. Figure 78. Experimental validation: energy balance and overall capacity. -20% -15% -10% -5% 0% 5% 10% 15% 20% 0 2 4 6 8 10 12 14 16 E n er g y B al an ce E rr o r (% ) Test Point RTHX-001 NTHX-001 +5% -5% 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 H ea t L o ad - S im u la ti o n ( k W ) Heat Load - Experimental (kW) RTHX-001 NTHX-001 97 Figure 79. Experimental validation: airside heat transfer coefficient and pressure drop. Figure 80. NTHX-001 CFD Validation: contour plots. 180 230 280 330 380 430 480 180 230 280 330 380 430 480 h ai r - C F D ( W /m ². K ) hair - Experimental (W/m².K) RTHX-001 NTHX-001 +10% -10% 25 75 125 175 225 25 75 125 175 225 Δ P ai r - C F D ( P a ) ΔPair - Experimental (Pa) RTHX-001 NTHX-001 +10% -10% +20% -20% Static Pressure (Pa) -130 25070 100 175 Velocity Magnitude (m/s) 0.0 21 3.0 /m s 4.0 /m s 5.0 /m s 6.0 /m s 7.0 /m s 98 5.3.2 DPII: 10.0kW Single-Phase Heat Exchangers The second design problem (DP II) is a scaled version of the DP I for a 10.0kW application. The general optimization formulation and operating conditions are scaled based on the 1.0kW baseline. The main difference between this application and the previous is the water side pressure drop, which naturally will increase since longer tubes will be required. A maximum of 5kPa was established as a reasonable constraint as opposed to the 1.0kPa from the previous problem. For this application only the RTHX surface was studied with the purpose of prototyping. Since the tubes for the RTHX-001 were available, a similar optimization problem (equation 57) from DP I was performed for DP II applied to the RTHX for fixed tube diameter. The optimization results (Figure 81) are presented as such the geometrical aspects are per unit capacity so that the different scales can be put side by side. The design RTHX-468 indicated in the optimization plot (Figure 81) was selected for prototyping. 3 min min . . 62 5.0 1800 10 11 0.8 air HX air water HX o P V s t P Pa P kPa V cm Q kW D mm          (57) 99 Figure 81. DP II: Optimization results. 5.3.2.1 Prototype RTHX-468 A prototype of the design RTHX-468 (Figure 82) was fabricated using copper tubes brazed to the copper headers. This prototype was tested and resulted in a consistent 50% over prediction compared to experimental data (Figure 83). Thermal imaging tests (Figure 84) revealed that a good portion of the tubes were blocked, thus compromising the overall performance. The details on experimental data are included in Appendix D. Figure 82. RTHX-468 Prototype. MCHX RTHX-0.8mm (In-line) RTHX-0.5mm RTHX-0.8 mm RTHX-0.8mm / 10kWProof-of-Concept RTHX-468 0.8oD mm 1.39tP mm 1.19lP mm 0.6oD mm 6.75d mm 444l mm380tN  Face Area (m²/kW) 0.0102 0.04 Material Volume (cm³/kW) 11.4 77 100 Figure 83. RTHX-468 Experimental capacity results. Figure 84. Thermal imaging on RTHX-468 prototype. Although the results did not match at the 45° line (Figure 83), they line up quite well over the 50% line, which suggests a strong correlation between simulation and the real system. The blockage results suggest that the deviations were likely due to the faulty HX instead of potentially poor numerical prediction. 2 3 4 5 6 7 8 2 3 4 5 6 7 8 Q si m u la ti o n (k W ) Qexperimental (kW) 50% 50% Blocked tubes 101 5.3.3 DP III: Two-Phase Heat Exchangers This study comprised of optimizing HX’s to deliver a 3.0Ton (~10kW) capacity in a Heat Pump / Air-Conditioning Unit. The baseline system is a rated SEER (Seasonal Energy Efficiency Ratio) 16, using R410A as working fluid. For this study the cooling operating mode was considered. The cycle was modeled and verified (Table 13) against the rated performance using VapCyc® [166]. The HX’s were modeled in CoilDesigner® [159] according to the manufacturer specifications. The compressor was modeled using the manufacturer 10-coefficient model for mass flow rate and power predictions. Table 13. Baseline cycle verification. Cycle COP* COP Q Sub- cooling Super heating Ref. ṁ Evap. AFR Cond. AFR - - kW K K kg/s m³/s m³/s Baseline (rated) 4.507 3.900 10.029 5.447 3.890 0.06224 0.505 1.84 Baseline (simulated) 4.506 3.858 10.025 5.445 3.901 0.06040 0.505 1.84 * w/o fan power Using Engineering Equation Solver (EES®) the potential of reducing the pressure lift was investigated, while maintaining the sub cooling, superheating, air flow rates and assuming constant isentropic efficiency for the compressor. The approach temperatures were monitored to avoid potential Second Law violations. The new HX specifications were retrieved from the EES model according to a theoretical COP (Coefficient of Performance) improvement of 15% and outlet approach temperatures near 1.0°C (Figure 85). 102 Figure 85. System level study for COP improvement. 5.3.3.1 HX Design and Optimization The baseline HX’s have conventional tube and fins with tube diameters of 7.0mm and 9.5mm in the outdoor and indoor units, respectively. The fins are enhanced with louvers and slits. The HX operating conditions for both the baseline cycle and the expected improved cycle are presented in Table 14. Table 14. Two-Phase HX’s operating conditions. HX Evaporator Condenser Metric Psat xin Vair Tair,in ΔPair Psat Tin Vair Tair,in ΔPair kPa - m³/s K Pa kPa K m³/s K Pa Baseline 1159 0.22 0.505 299.8 57.2* 2675 345.1 1.84 308.2 4.0** Improved 1179 0.19 0.505 299.8 --- 2488 339.7 1.84 308.2 --- * Rated value ** Estimated using Wang et al. correlation [167] The fan power is estimated based on the total power to move air through both HX’s. For design and optimization purposes the baseline condenser pressure drop of 4.0Pa is highly restrictive, thus the optimizer was allowed to go up to 10Pa. The evaporator pressure drop, however, was constrained as such the total fan power is no higher than the baseline. The optimization problem (equation 58) applied to each HX has the air pressure drop and volume as objective functions, while Baseline Improved Cycle Refrigerant Air Condenser Evaporator Baseline Improved 4.619 1.2 baseline improved T C T C       1.36 0.96 baseline improved T C T C       Baseline Improved 4.69 5.65( 1.15 ) baseline improved baseline COP COP COP     3.9subT C  5.4shT C  10baseline improvedQ Q kW  103 constraining capacity, refrigerant pressure drop and the rebalanced air pressure drops. min min min min . . . . air air HX HX Evaporator Condenser P P V V s t s t   , , 10.0 11.8 35 10 air air ref ref baseline ref ref baseline Q kW Q kW P Pa P Pa P P P P             (58) In addition to the design variables used in the DP I and II the pass configuration (Figure 86) was introduced. For the evaporator two passes are considered as such the design variable indicates the fraction of the tubes as inlet whilst the remainder being the outlet. The condenser has three passes where two design variables define the fraction of the inlet tubes and the mid-section tubes respectively. Figure 86. HX Pass configurations. Airflow 10 0.9x  2 10 0.9(1 )x x   1 21 x x  10 0.9x  11 x CondenserEvaporator 104 This study considered only the RTHX concept both in in-line and staggered arrangements. In addition to the optimum designs and the baseline HX’s, as reference, the optimization performed for a 3Ton SEER 13 unit [168] with HX’s using tube diameters of 3, 4 and 5mm was included. Optimization results are shown in Figure 87. Figure 87. DP III: Optimization results. 5.3.3.2 System Level Analysis The designs RTHX-528, 574, 607 and 619 indicated in Figure 87 were selected for the system level analysis. Two novel cycles were simulated in Face Area (m²) 1.39 3.09 Tube Diameter (mm) 0.5 7.0 Refrigerant ΔP (kPa) 3.7 40 Material Volume (cm³) 1550 8390 Baseline RTHX-Staggered RTHX-In-line Beshr et al. (2016) Baseline RTHX-Staggered RTHX-In-line Beshr et al. (2016) RTHX-528 RTHX-574 RTHX-528 RTHX-574 Face Area (m²) 0.26 0.55 Tube Diameter (mm) 0.5 9.5 Baseline RTHX-Staggered RTHX-In-line Beshr et al. (2016) Baseline RTHX-Staggered RTHX-In-line Beshr et al. (2016) Refrigerant ΔP (kPa) 0.9 17 Material (cm³) 330 6900 RTHX-607 RTHX-619 RTHX-607 RTHX-619 a) b) 105 VapCyc® [166]; Cycle I with the RTHX-528 and RTHX-607 designs and Cycle II with RTHX-574 and RTHX-619 designs. Both cycles resulted in significant reduction of refrigerant charge; approximately 50% reduction in the condenser, and up to 90% in the evaporator. The overall charge reduction in the system reached approximately 30%-40% reduction. From a performance perspective the COP was improved in up to 14% with these new HX’s. Additionally, these charge reductions in the HX’s result in the pipes accumulating a more relative amount of charge. The system results are summarized in Figure 88. Figure 88. DP III: System level analysis. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Baseline Cycle I Cycle II C h ar g e/ C h ar g e b as el in e (- ) Evaporator Condenser Tubes 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Baseline Cycle I Cycle II C O P /C O P ra te d (- ) w/o fan power w/ fan power 12-14%↑ 11-13%↑ 106 Chapter 6: CFD-Based Correlation Development The procedure to develop the CFD-based correlations follows the similar framework (Figure 89) to develop the metamodels used in the AAO, following three main parts. The first consists of defining the design space within which the correlation will be valid for; next, the CFD uncertainty analysis following the GCI procedure explained in the Chapter 2; last, with the aid of PPCFD a large DoE is simulated and the post-processed data is further used in the correlation development. Additional random samples are simulated and used for final verification. Figure 89. CFD-Based correlation development. Define Design Space Start Airside h, ΔP Perform CFD Uncertainty Analysis Acceptable? Refine mesh, revise CFD settings Run PPCFD Airside h, ΔP Create correlation Run correlation Design of Experiments Random samples Run PPCFD Evaluate correlation Acceptable? End yes yes no no Correlation CFD Model Concept Surface Correlation development 107 Two correlation approaches are investigated in this work. One (equations 59 to 62), where a non-linear equation form is defined as a function of the geometry and operating conditions, and use an optimization algorithm to find the coefficients of the present equation that result in the minimum square error compared to the CFD source data. Alternatively, (equation 63) the correlation can be found using a stepwise linear regression algorithm which is very robust, although it results in a very large expression. The matrix M contains the power value of each parameter (columns of M) for each of the regression term (rows of M), and the array c contains the coefficients of each term. Both approaches are employed within the Matlab® environment using its built-in optimization and regression engines.   2 , , 0 ( ) ( ) n corr i CFD i i f x x     (59) Where, , , , , ....h j Nu P f   (60) [ , , , , , , ,Re....]o l t p f rx D P P F N  (61) min ( ) . . lb ub f x s t x x x  (62) , 1 1 ( ) ColumnsRows i j nn M corr i j i j x c x            (63) 6.1 Round Finless Tubes The previous Chapters in this dissertation discussed and demonstrated the benefits of using small finless diameter tubes. Among current available tools only 108 CFD can actually be used to predict the thermal-hydraulic performance of such surfaces. This gap is fulfilled by providing computationally affordable correlations that accurately predict the CFD response. In this section three sets for correlations are presented, including diameters from 0.5mm to 2.0mm for both staggered and in-line arrangements and the staggered arrangement for tube diameters ranging from 2.0mm to 5.0mm. 6.1.1 Data Reduction Since the CFD models serve to determine the airside thermal and hydraulic resistances, there is no need to account for additional thermal resistances. Thus with constant wall temperature, the capacitance ratio yields Cmin / Cmax = 0, then the heat transfer coefficient can be easily calculated through ε-Ntu method as per equations (64 to 67). The pressure drop is determined as the difference between inlet and outlet static pressures, assuming that local losses are negligible.      ln 1 ln 1tu out in wall inN T T T T          (64) min/ /o tu oh UA A N C A   (65)  2/3Pr c pj h u c (66)    22 2 1 1c m in in o in outm c A P f A u                    (67) 6.1.2 Correlations The CFD models and grid uncertainty analysis were carried out in Chapter 4, thus will not be presented in this section again. The design space investigated is presented in Table 15. 109 Table 15. Finless tubes correlations design space. Variable Type Design Variable Unit Correlations I Correlation II Correlation III Scaling Do mm 0.5 – 2.0 0.5 – 2.0 2.0 – 5.0 Nr - 2 – 40 2 – 40 2 - 20 Topology Pt ratio (Do) - 1.2 – 4.0 1.2 – 4.0 1.5 – 3.0 Pl ratio (Do) - 1.2 – 4.0 1.2 – 4.0 1.5 – 3.0 Operating u m/s 0.5 - 7.0 0.5 - 7.0 0.5 – 7.0 Arrangement - - Staggered In-line Staggered The correlations developed for the finless tubes are based on the non-linear equation approach. For correlations I and II there are four sets of equations for each correlation: 2 to 9 banks, 10 to 24 banks, 25 to 34 banks and 35 to 40 banks. The source data for each fin type consisted of a Design of Experiments with 750 samples sampled using Latin Hypercube Sampling method. The correlation III used 500 samples also generated with Latin Hypercube Sampling. Equations 68 to 74 present the correlations I and II. The coefficients are presented in Table 16 and Table 17. 3 4 2 1 2 1 ,Re o p p c p p l t l D c t o o t P P P j c N D D P                    (68) 2 3 4 1 2 1 ,Re o p p p p cl l t D c t o o P P P f c N P D D                    (69) ,Re o c o D c u D   (70) 6 4 1 3 5 , ln ln(Re ) o c t D c o Pc N p c c N D              (71) 9 8 2 7 ,ln(Re )o c l D c o c P p c D         (72) 110 113 10 ,ln(Re )oD c c N p c  (73) , 4 12 13 Re ln o c D p c c N   (74) Table 16. Correlations I coefficients. j f N 2-9 10-24 25-34 35-40 2-9 10-24 25-34 35-40 c1 6.5374 6.5490 6.5405 6.5070 1.4559 6.3104 0.0007 0.2559 c2 0.1193 0.0918 0.0998 0.3534 -0.5227 -0.4716 -0.7261 0.5290 c3 -0.7805 -0.7731 -0.7672 -1.1185 -0.3987 -0.6044 4.7749 -0.5908 c4 0.0369 0.0038 0.0033 0.0158 0.0284 -0.0167 0.4822 -0.0553 c5 0.1202 0.1164 0.1326 0.3026 0.0707 0.0964 -1.7070 0.1430 c6 1.9813 1.9942 1.9788 1.9948 0.5907 4.2753 0.1779 -0.0107 c7 -1.2644 -1.0895 -1.2085 -1.7800 -0.4592 0.7463 0.4904 -0.4653 c8 1.2039 1.2676 1.2227 0.7869 -2.2383 0.5998 -6.9567 3.4932 c9 0.3549 0.3341 0.3670 0.1953 -1.4243 1.1010 -0.0456 0.3160 c10 -0.3391 -0.3283 -0.3143 0.1690 0.2957 -1.1875 1.8617 -0.0951 c11 -0.0313 -0.0522 -0.0483 -0.1202 0.1688 -0.0203 -0.3269 -0.0532 c12 -0.8338 -0.7955 -0.7895 -0.5598 -0.2976 0.2579 -0.4149 1.6296 c13 -0.1545 -0.1754 -0.2351 -0.9993 0.0571 -0.2939 0.8621 -0.1635 Table 17. Correlations II coefficients. j f N 2-9 10-24 25-34 35-40 2-9 10-24 25-34 35-40 c1 6.808 1.079 4.072 0.059 4.357983 0.834137 3.626557 1.905177 c2 -0.019 0.283 0.819 0.732 -1.50004 0.159886 -1.2549 -3.4275 c3 -0.865 -0.694 -1.668 0.300 -0.59284 -0.61397 -0.94665 1.840706 c4 -0.072 0.018 -0.151 0.025 -0.05845 -0.04546 0.148834 0.308742 c5 0.215 0.091 0.476 -0.099 0.209748 0.068112 0.080344 -0.61705 c6 -0.557 -0.671 -0.831 -0.012 -1.5117 2.004688 -4.95244 0.395123 c7 -1.390 -0.925 -0.362 -0.514 -1.09594 -0.71962 4.49158 0.313471 c8 2.861 2.297 1.130 0.665 4.546346 0.138192 10 10 c9 -3.997 0.439 -0.234 1.116 -0.23323 2.779024 -2.03421 -2.73658 c10 -0.114 0.359 -0.584 -0.081 -0.64347 0.733198 8.397073 5.097817 c11 0.696 -0.056 0.446 0.003 0.94127 0.147212 -0.59114 -0.64904 c12 -1.072 -1.739 -0.315 -0.806 0.144438 -1.68447 -3.11616 1.813604 c13 0.285 0.393 0.541 -0.043 0.556941 0.278091 0.321952 -0.22785 Equations 75 to 80 present the correlations III. The coefficients are presented in Table 18. 111 3 4 2 1 2 1 Re o P P c P P l t l D t o o t P P P j c N D D P                    (75) 3 4 2 1 2 1 Re o P P c P P l t l D t o o t P P P f c N D D P                    (76) 6 4 1 3 5 ln ln(Re ) o c t l t D o c N P P c c N D              (77) 9 8 2 7 ln(Re ) o c t D o c P P c D         (78) 113 10 ln(Re ) o t D c N P c  (79) 4 12 13 Re ln o D t P c c N   (80) Table 18. Correlations III coefficients. j f c1 0.4220555168 0.9981645207 c2 -0.1327145700 0.8632429086 c3 -0.4550155190 -0.3179116696 c4 -0.0090645460 -0.0006687375 c5 -0.0096188420 0.0005922714 c6 2.4745395710 -9.9249274428 c7 0.2262063170 0.2550841764 c8 -0.2659972990 -4.3313552005 c9 0.5645583060 -2.5323165527 c10 0.2455957950 -1.0237980350 c11 0.0232402000 0.0203235731 c12 0.0021002020 0.5366315096 c13 -0.0163369050 0.1651970285 The correlations verification is respectively shown in Figure 90and Table 19 against source data and Figure 91 against random data. 112 Figure 90. Correlations I, II and III verification against source data. Table 19. Round finless tubes correlations fitness. Heat Exchanger Correlation I Correlation II Correlation III Air side performance metrics j f j f j f Predicted data (e=10.0%) 86.9% 79.2% 59.0% 45.7% 91.6% 83.1% Predicted data (e=15.0%) 92.9% 88.8% 75.2% 62.7% 97.7% 91.3% Predicted data (e=20.0%) 95.1% 92.9% 83.7% 74.9% 99.1% 95.2% Predicted data (e=30.0%) 96.9% 96.7% 91.7% 85.7% 99.6% 98.4% R² 98.4% 95.8% 95.6% 97.9% 97.6% 97.3% Mean Absolute Relative Error 6.07% 8.39% 12.41% 17.52% 4.48% 5.55% Median Absolute Relative Error 2.90% 4.64% 8.15% 10.96% 2.50% 3.39% Figure 91. Correlations I and III verification against random samples. 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 j C o rr el at io n (- ) jCFD (-) Correlation I Correlation II Correlation III +15% -15% +15% -15% 0 0.3 0.6 0.9 1.2 1.5 0 0.3 0.6 0.9 1.2 1.5 f C o rr el at io n (- ) fCFD (-) Correlation I Correlation II Correlation III 0 0.03 0.06 0.09 0.12 0.15 0 0.03 0.06 0.09 0.12 0.15 j C o rr el at io n (- ) jCFD (-) Correlation I Correlation III 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 f C o rr el at io n fCFD (-) Correlation I Correlation III +15% -15% +15% -15% 113 6.1.3 Verification The proof-of-concept RTHX-001 falls in the correlations I application range. Using the same experimental data for the CFD validations, it was verified that the correlations agree in 10% for the heat transfer coefficient, however they consistently over predict the pressure drop by a factor of 1.64. One reason is the fact that the CFD simulations in this work have consistently over predicted pressure drop, potentially due to the turbulence model used. On the other hand, this consistency suggests that with additional experimental data only small adjustments to the proposed equations might be required. Furthermore, the experimental verification shows that the proposed equations have significantly better prediction capability when compared to existing correlations in the literature. Figure 92. Correlations I verification against experimental data. 200 300 400 500 600 700 200 300 400 500 600 700 h P re d ic ti o n ( W /m ². K ) hExperimental (W/m².K) Žukauskas Wung & Chen Khan et al. New equations +10% -10% 24 48 72 96 120 144 168 24 48 72 96 120 144 168 Δ P P re d ic ti o n (P a) ΔPExperimental (Pa) Žukauskas Corrected +5% -5% 114 6.2 Plain Fin-and-Tubes The second order analyses in Chapter 3 suggested that for tubes larger than 2.0mm diameter, having fins is performance wise more attractive than finless tubes. In this section correlations for flat fin (Figure 93 and Figure 94) and tubes, with diameters between 2.0mm and 5.0mm are presented. Figure 93. Flat fin. Figure 94. Flat fin and tube contour plots: a) velocity; b) temperature; c) pressure. Magnitude Velocity (m/s) 0.0 2.7 a) b) c) Temperature (K) 300 330 Static Pressure (Pa) -1.8 4.0 115 The CFD models and grid uncertainty analysis were carried out in Chapter 4, thus will not be presented in this section again. The design space investigated is presented in Table 20. Table 20. Flat fin and tube correlations design space. Design Variable unit Range Do mm 2.0 - 5.0 Pt ratio (Do) - 1.5 - 3.0 Pl ratio (Do) - 1.5 - 3.0 Nr - 2 - 10 FPI in-1 8 - 24 Air face velocity m/s 0.5 - 7.0 Fin thickness mm 0.115 (fixed) 6.2.1 Data Reduction The heat transfer coefficient can be retrieved using the Schmidt method [153] described in the theoretical background chapter, whilst the friction factor can be calculated the same way for the finless tubes (equation XX). 6.2.2 Correlation The correlations developed for the finless tubes are based on the non-linear equation approach. The source data for each fin type consisted of a Design of Experiments with 500 samples sampled using Latin Hypercube Sampling method. Equations 81 to 82 present the correlations I and II. The coefficients are presented in Table 21. 3 4 2 1 2 1 Re 2o P P c pP P t l D t o f o o F P P j c N D D D                    (81) 3 4 2 1 2 1 Re 2o P P c p p pP P D t o f o t F F F f c N D D P                    (82) 116 6 4 1 3 5 ln ln(Re ) 2 o c pt t D o f Fc N P c c N D               (83) 9 8 2 7 ln(Re ) o c t D o c P P c D         (84) 113 10 ln(Re ) o t D c N P c  (85) 2 4 12 13 Re ln o t D t P c c N    (86) Table 21. Fin-and-tube correlations coefficients. j f c1 0.14766977237669 1.71188871245298 c2 -0.28005133537990 0.92946487673730 c3 -0.38888826762694 -0.22854500443404 c4 -0.04370010021825 0.04029790563157 c5 0.28331914903762 -0.00430627203978 c6 0.44735912969069 -4.91278551282918 c7 -2.52843968547746 -0.62616159134051 c8 5.29660856066235 1.31700831350020 c9 -0.22444322963679 0.27195519072632 c10 -1.00067471783319 -2.42919816587607 c11 0.30250006880624 0.06332710290257 c12 2.08539578403170 0.97021840449916 c13 -0.27444087385649 0.10375729681002 Figure 95. Flat fin correlations verification against source data. 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 j C o rr el at io n (- ) jCFD (-) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 f C o rr el at io n (- ) fCFD (-) +15% -15% +15% -15% 117 Table 22. Flat fin-and-tube correlations fitness. Air side performance metrics j f Predicted data (e=10.0%) 64.8% 78.9% Predicted data (e=15.0%) 82.1% 91.8% Predicted data (e=20.0%) 91.5% 96.4% Predicted data (e=30.0%) 96.8% 98.8% R² 97.8% 98.0% Mean Absolute Relative Error 9.51% 6.59% Median Absolute Relative Error 7.29% 5.07% 6.3 Wavy Fin-and-Tubes As discussed in the literature review, wavy fins are suitable for applications such as heat pumps in cold climates due to its higher resiliency to performance degradation. Additionally, reducing tube diameters improve performance and for diameters above 2.0mm fins are desirable. This section presents a correlation development for both Herringbone and smooth-wavy fins (Figure 96) using tube diameters from 2.0 to 5.0mm. Figure 96. Wavy fin-and-tube surface: a) Herringbone; b) Smooth (Sinusoidal). oD lP 2tP pF 2 2f lX P dP f oD lP 2tP pF 2 2f lX P dP f )a )b Uniform airflow Uniform airflow 118 Table 23. Wavy fin-and-tube correlation design space. Variable Unit Range Do mm 2.0 - 5.0 Pl/Do - 1.25 – 4.0 Pt/Do - 1.25 – 4.0 Fp mm 0.5 – 2.5 Pd/Xf - 0.088 – 0.84 δt mm 0.05 – 0.1 Nr - 2-20 u m/s 0.5 – 7.0 6.3.1 CFD model The CFD computational domain (Figure 97) is a three dimensional cross section segment of the HX, assuming any end effects to be negligible. The inlet boundary has uniform velocity and uniform temperature (300K), whereas the outlet boundary is at constant atmospheric pressure. The upper and lower boundaries are symmetric, while the lateral boundaries are periodic, and the tube walls are at constant temperature of 340K, whilst the fin walls are coupled to the tubes. The faces parallel to the fins on the sides are periodic. The fluid properties use ideal gas model, and the turbulence is evaluated using the k-ε realizable model. The convergence criteria used is 10-5. The near wall region mesh is a fine map scheme with growing layers at a ratio of 1.2 (Figure 97). The core of the computational domain is a pave mesh scheme with an average element size equal to the last row of the boundary layer mesh. 119 Figure 97. Wavy fin computational domain and mesh. The following sample CFD results (Figure 98, Figure 99, Figure 100 & Figure 101) show a comparison for an equivalent design using Herringbone and smooth fins. Figure 98. Equivalent wavy fins: a) Herringbone; b) Smooth. Fin wall (Coupled) Periodic Fine mesh ,u T  P Symmetry Tube wall (constant T) a) b) 120 Figure 99. Sample velocity contour plots: a) Herringbone and b) smooth wavy fins. Figure 100. Sample temperature contour plots: a) Herringbone and b) smooth wavy fins. Figure 101. Sample pressure contour plots: a) Herringbone and b) smooth wavy fins. Magnitude Velocity (m/s) 0.0 2.7 a) b) Temperature (K) 300 330 a) b) Static Pressure (Pa) -1.8 4.0 a) b) 121 Figure 102. Grid resolution uncertainty for wavy fins: a) fine; b) base; c) coarse meshes. 6.3.2 Correlation The correlations developed for the wavy fins are based on the multiple regression approach (equation 63). The coefficients and power matrices for the correlations developed are presented in Appendix E. There are two sets of equations for each correlation: one for 2 to 10 tube banks and one for 11 to 20 tube banks. The source data for each fin type consisted of a Design of Experiments with 1300 designs sampled using Latin Hypercube Sampling method.    ln , lnh Dh P fNu C   (87)              ,ln ,ln ,ln ,ln ,ln ,ln ,ln Re o cp o l o t o d f f p D ux F D P D P D P X F N    (88) Dh hNu hD k (89)    20.5 4f c hC P u D d   (90) 4h c oD A d A (91) ,Re o cD u c ou D  (92) 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 0.02 0.03 0.04 0.05 0.06 0.07 Average Element Size (mm) Nu Cf Avg. element size: 0.025mm Avg. element size: 0.031mm Avg. element size: 0.039mm a) b) c) 21 0.69% fineGCI  21 4.3% fineGCI   21 32 21 21 , 1 3.0 1.3 sfine p e e s F e GCI r F r       a) b) c) a) b) c) 122 The non-dimensional heat transfer and pressure drop are calculated for dry air properties at 300K and 1atm. The property values used are presented in Table 24. Table 24. Air thermophysical properties for wavy fin correlations. T (K) P (kPa) ρ (kg/m³) μ (Pa.s) k (W/m.K) cp (J/kg.K) 300 101.325 1.177 1.86E-05 2.57E-02 1005 The correlations verification is respectively shown in Figure 103 and Table 25 against source data and Figure 104 against random data. Figure 103. Wavy fin correlations verification against source data. Table 25. Wavy fins correlations fitness. Fin Type Herringbone Smooth Metric NuDh Cf NuDh Cf Predicted data (e=10.0%) 84.73% 83.92% 80.84% 81.88% Predicted data (e=12.5%) 92.63% 91.22% 88.95% 89.43% Predicted data (e=15.0%) 96.17% 94.54% 94.28% 93.48% Predicted data (e=20.0%) 99.04% 98.08% 98.97% 97.62% Predicted data (e=25.0%) 99.56% 99.04% 99.60% 98.97% R² 0.9937 0.9881 0.9927 0.9889 Mean Absolute Relative Error 5.344% 5.665% 5.747% 6.038% Median Absolute Relative Error 3.940% 4.288% 4.253% 4.750% 0 0.3 0.6 0.9 1.2 1.5 0 0.3 0.6 0.9 1.2 1.5 C f- C o rr el at io n (- ) Cf - CFD (-) Herringbone Smooth 0 3 6 9 12 15 18 21 24 27 0 3 6 9 12 15 18 21 24 27 N u D h - C o rr el at io n ( -) NuDh - CFD (-) Herringbone Smooth +10% -10% +10% -10% 123 Figure 104. Herringbone correlations verification against 120 random samples. This section presents a comparison between the proposed correlations with existing ones for the design space investigated (Figure 105). The existing correlations not only largely deviate from the CFD simulations but they are also not consistent, suggesting they cannot and should not be extrapolated. Figure 105. Herringbone correlation comparison. 0 3 6 9 12 15 18 0 3 6 9 12 15 18 N u D h ,c o rr el at io n (- ) NuDh,CFD (-) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.1 0.2 0.3 0.4 0.5 C f, c o rr e la ti o n (- ) Cf,CFD (-) +15% -15% +15% -15% 0.02 0.08 0.14 0.2 0.02 0.08 0.14 0.2 C f, co rr el at io n (- ) Cf,CFD (-) Wang et al. (1997) Wang et al. (2002) This work 0 2 4 6 8 10 12 14 16 18 20 0 5 10 15 20 N u co rr el at io n (- ) NuCFD (-) Wang et al. (1997) Wang et al. (2002) This work 124 Chapter 7: Surface Optimization Study This Chapter is dedicated to surface optimization using the correlations developed in the previous Chapter. The goal is to verify whether optimizing finless and finned surfaces have an actual impact regarding the trade-off shown in Figure 19 from Chapter 3. The study consists of a comprehensive parametric optimization analysis, where the tube diameter, the surface hydraulic diameter and the air frontal velocity are the parametric variables (Table 26), while the other design variables are optimized with respect to heat transfer coefficient and friction power per unit area (equation 93). * * * * * * max min " . . ; ; 0.99 4 1.01 o o o c h h h o h W s t D D D parameterized u u u parameterized A D D d D A        (93) By parameterizing the tube and hydraulic diameters, the evaluation of the characteristic length impact over performance becomes more comprehensive. Additionally, the surface hydraulic diameter is the indication of the surface dimension, thus allowing a fair comparison using dimensioned thermal-hydraulic performance as discussed in the literature review. The detailed dimensions and performance of the investigated surfaces, as well as comparison plots for each combination of parametric variables are presented in Appendix F, whilst the general results are presented in the following sub-section. 125 Table 26. Parametric Variables. Do Dh u mm mm m/s 0.5,1, 1.5, 2, 3, 4, 5 0.5, 1.0, 1.5, 2.5, 3.0 1.0, 2.0, 3.0, 5.0 On conventional tube and fin HX’s the tubes are typically arranged on an equilateral configuration (square for in-line and triangle for staggered) so the same U-bends can be applied everywhere. In these analyses, the surfaces were optimized with unconstrained tube pitches and constraining them as such the transverse pitch is a function of the longitudinal pitch ensuring the equilateral configuration. Only staggered arrangement is investigated for both finless and wavy Herringbone surfaces. Another important aspect of this study is to demonstrate the robustness and computational affordability of these correlations. On Table 27 one can see that given the parametric variables the number of parameter combinations total in 300 optimization runs. Typically, for MOGA using 500 iterations and a population of 150 with 10% replacement, the optimizer investigates approximately 5000 designs. Therefore, this study, has investigated approximately 1.5 million designs at a cost of less than 3min per optimization. Table 27. Surface Optimization Study Computational Cost. Finless Finned Total No. of parametric combinations 140 160 300 No. of correlations (sets) used 2 1 3 No. of correlation calls per optimization (approx..) 5,000 5,000 10,000 Total No. of correlation calls (approx..) 700,000 800,000 1,500,000 Machine time (s) 28,800 24,000 52,800 Time per optimization (s) 205.7 150.0 176.0 126 7.1 Optimization Results The following plots include all Pareto sets, i.e. all optimization results from each parametric study are combined in a single plot. For detailed results regarding each optimization study refer to Appendix F. Figure 106. Finless tubes surface optimization results I: tube diameter. Figure 107. Finless tubes surface optimization results II: tube diameter. 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 3.0oD mm 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 60 127 Figure 108. Finless tubes surface optimization results I: hydraulic diameter. Figure 109. Finless tubes surface optimization results II: hydraulic diameter. 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 1.5hD mm 2.5hD mm 3.0hD mm 1.0hD mm 0.5hD mm 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 1.5hD mm 2.5hD mm 3.0hD mm 1.0hD mm 0.5hD mm 60 128 Figure 110. Finless tubes surface optimization results I & II: pitch ratio. Figure 111. Wavy fin surface optimization results I: tube diameter. 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s Pt / Pl (-) 0.3 2.6 0.5oD mm 3.0oD mm 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s Pt / Pl (-) 0.3 2.6 0.5oD mm 3.0oD mm 60 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 129 Figure 112. Wavy fin surface optimization results II: tube diameter. Figure 113. Wavy fin surface optimization results I: hydraulic diameter. 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 60 1.5hD mm 2.5hD mm 3.0hD mm 1.0hD mm 0.5hD mm 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 130 Figure 114. Wavy fin surface optimization results II: hydraulic diameter. Figure 115. Wavy fin surface optimization results I and II: pitch ratio. 7.1.1 Discussion The plots shown in Figure 106 to Figure 115 contain a lot of valuable information regarding surface size and surface type. First, again it has been demonstrated that the tube diameter has a clear correlation with heat transfer coefficient, regardless whether the surface is finned or finless; the plots are very stratified, although there is some overlapping, in particular for the finned surface. 1.5hD mm 2.5hD mm 3.0hD mm 1.0hD mm 0.5hD mm 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 60 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 0.5oD mm 3.0oD mm 60 Pt / Pl (-) 0.4 3.2 1.0 /u m s 2.0 /u m s 3.0 /u m s 5.0 /u m s 0.5oD mm 3.0oD mm Pt / Pl (-) 0.4 3.2 131 Second, the finless surfaces consistently achieve higher heat transfer coefficients than their finned counterparts, for all surface sizes (hydraulic diameters), Additionally, the general trend for finless surfaces show a steeper slope between h and Ẇ”, which has been suggested in the second order analysis presented in Figure 19 from Chapter 3. Therefore, supporting the fact that such trends are an intrinsic characteristic of the surfaces and not to a particular pairwise comparison; the finned surfaces have very small increments in heat transfer coefficient as the diameter is reduced, while the finless tubes benefit greatly from it. Third, Figure 106 and Figure 107 have an important message regarding the compactness of finless tubes. Although the optimization considered all diameters from 0.5mm to 5.0mm, only 3.0mm or less were found to be feasible. The reason is depicted in Figure 17 from Chapter 3, where the compactness falls abruptly for diameters larger than 2.0mm, in particular for finless tubes; the optimization imposed specific constraints to the hydraulic diameter, which is an indirect way of measuring the compactness. Furthermore, for equilateral tube arrangement (Figure 107) the largest diameter obtained from the optimization was 2.0mm. The main reason for this, however, was not the arrangement itself, but the fact that the correlations for finless tubes ranging from 2.0mm to 5.0mm are limited to pitch ratios down to 1.5, whereas the correlations for smaller tubes are valid for pitch ratios as low as 1.2. Nevertheless, this characteristic only supports the fact that for finless designs the tubes have to be very small, while finned designs don’t have the same limitation. 132 Finally, a few optimization problems (Figure 116) were selected for one velocity and one hydraulic diameter in order to discuss the impact of tube diameter and surface type under a fair comparison. The first thing that is clear is that the surface types are clustered in very distinct regions of the plot (Figure 116). There is a clear trade-off where for larger diameters the preference is for finned surfaces and the small diameters lean towards finless tubes. Near the 2.0mm is where the plots seem to have similar slopes and are almost continuing, which may also suggest where the breakeven occurs. Not surprisingly this was observed in both Figure 17 and Figure 19 from Chapter 3, where the compactness rapidly increases below 1.0mm to 2.0mm, so does the heat transfer coefficient, since both are inversely proportional to the tube diameter. The non-dominated sorting illustrates very well this trade-off, but also shows that the finless tubes are more sensitive to the heat transfer coefficient, remaining only the 0.5mm diameter designs. Figure 116. Selected surface optimization case. A few surfaces form Figure 116 were selected for a further investigation for varying velocity (Figure 117). Since all have same hydraulic diameter varying the velocity results in same Reynolds to all surfaces at same velocities. The curves in Figure 117 show an almost linear increase of the heat transfer coefficient with the 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm All non-dominated designs 3.0 /u m s 4 1.5ch o A D d mm A   133 log of friction power for the finned surfaces, while the finless show a much faster, non-linear, grow relating the same variables. Additionally, for both surface types, the smaller the tube the higher the rate of heat transfer coefficient. Furthermore, the finless curves show no trade-off with respect to diameter, the smallest diameter always performs better. The finned surfaces, on the other hand, show potential trade-offs of varying diameter. The latter observations were already shown in Figure 116. Lastly, again the 2.0mm diameter seem to be a turning point for either surface types. For the finned surface the 2.0mm curve suggest that at low Reynolds number it actually performs worse than the 3.0mm. Figure 117. Equivalent surfaces (same Dh) under wide range of Reynolds numbers. 0 100 200 300 400 500 600 700 0.01 0.1 1 10 100 1000 h ( W /m ². K ) Ẇ" (W/m²) RFTS-0.5mm RFTS-1.0mm RFTS-1.5mm RFTS-2.0mm WFTS-2.0mm WFTS-3.0mm WFTS-4.0mm WFTS-5.0mm Re 47.5Dh  Re 665Dh  0.5 7.0 /u m s  4 1.5ch o A D d mm A   " o P V W A    134 Chapter 8: Conclusions 8.1 Summary of Contributions The main contributions of this Ph.D. are to shed light on the next generation of heat exchangers, with focus on air-to-fluid applications. The following summary lists the most important aspects of each chapter. 1- Fundamental aspects of air-to-fluid heat exchangers  Reduction of tube diameter o In Chapter 3 it was clearly demonstrated in the first order analysis that regardless the surface type, and that the compactness, material utilization and internal volume are inversely proportional to the tube diameter. o Thermal performance is also enhanced when reducing the diameter, as first suggested on Chapter 3, then verified multiple times along the dissertation (Chapters 4 and 6). The surface level analysis showed how the temperature gradient within the boundary layer significantly increases when reducing the tube size. Moreover, the characteristic length has a stronger influence than the flow regime. With either same frontal velocity, or same Reynolds number, the heat transfer coefficient is always higher in smaller tubes. o In Chapter 4 it was demonstrated with actual HX applications, the benefits of reducing the tube diameter with novel 135 HX concepts that outperform current state-of-the art HX’s greatly in size, material and performance. o The reduction of tube size also has an inverse proportionality to the friction resistance, which was highlighted in the second order analysis. It was also highlighted it in the boundary layer analysis, where the velocity gradient grows much faster on smaller tubes. Such characteristic had an impact on the RTHX designs investigated in Chapter 4. All round tube designs with small diameter ended up having larger face area in order to reduce the frontal velocity and satisfy the pressure drop.  Finned vs. Finless Surfaces o The first and second order analyses in Chapter 3 suggested that the contribution from conventional fins are not always beneficial. The fin-to-tube surface ratio is directly proportional to the tube diameter, thus for smaller tubes, the ratio can decrease one or two orders of magnitude. o Additionally, the finned surfaces consistently have lower heat transfer coefficients than finless surfaces. Thus at very small diameters fins not only are much less helpful in reducing the thermal resistance, but will still offer additional friction resistance. This was explained in Chapter 4 when the FTHX, with similar tube diameters than the RTHX, resulted in designs with higher pressure drop for the 136 same volume. Moreover, the heat transfer coefficients were much lower, thus requiring even more tubes than the RTHX o Chapter 6 also served as an additional comparison, where it was extensively verified the trade-off proposed in Chapter 3 with the second order analysis when comparing optimized finless and finned surfaces.  Tube shapes o The nature of the flow over conventional round shape results in a large wake region due to the flow separation. The latter has a mixing effect which benefits heat transfer, however it naturally increases hydraulic resistance. Alternate shapes such as oval and flat tubes led to reduced flow resistance. o In Chapter 3 it was demonstrated with a comprehensive study on various alternate shapes that when the shape has an aspect ratio (i.e. tube height per tube width) less than unity the hydraulic resistance is significantly less. Instead, the round tube has consistently the highest heat transfer coefficient. Shapes with non- symmetric leading and trailing edges (i.e. airfoils) provide much better thermal-hydraulic ratio, despite the lower heat transfer coefficient compared to round tubes. o When using airfoil shaped tubes in a scaled HX, the aerodynamics allow the air velocity to increase with less pressure loss penalty, but it also allows packing additional tube banks, which 137 can provide additional surface area to compensate for the reduction in heat transfer coefficient. The resulting HXs have significantly smaller face areas; the NTHX-001 concept, from Chapter 4, has more than 50% smaller face area than the RTHX-001, while delivering the 1.0kW 2- Multi-Scale analysis with Topology and Shape Optimization Framework  In Chapter 4 it was presented a comprehensive HX design framework that includes design concept, airside modeling and simulation, design and optimization, verification and validation. The modeling tools leveraged the automated CFD simulations and approximation assisted optimization techniques.  It was developed a shape parameterization method that was incorporated to the multi-scale analysis and topology design and optimization methodology, which the foundations were first introduced by Abdelaziz et al. [72].  The methodology was used to optimize air-to-water HX’s which are 20% to 80% smaller, with at least 20% better performance and have more than 50% reduction in material compared to a state-of-the-art MCHX.  Advanced manufacturing techniques were leveraged, such as metal additive manufacturing, to build a prototype of the proof-of-concept NTHX-001 138  Two prototypes were tested, RTHX-001 and NTHX-001, and validated it in less than 5% in capacity, 10% in air heat transfer coefficient, and 20% in airside pressure drop.  This methodology should serve as foundations for a HX design platform where one can leverage computational power to let the optimizer “create” and “invent” new HX’s with high design freedom.  Finally, it was demonstrated the potential of using small finless tubes in three-ton heat exchangers using R410A as refrigerant. The resulting HX’s can be more than 50% smaller with more than 50% reduction in charge and improving COP in 10-15% of a SEER 16 baseline unit. Furthermore, the reduction in refrigerant charge within the HX’s allows the new system to have more charge in the pipes. 3- CFD-Based correlations for small diameter tubes  Six novel sets of correlations were developed for airside characterization for finless, flat fin and tube and wavy fin (smooth and Herringbone) and tube surfaces with diameters smaller than 5.0mm, fulfilling the literature gap  These correlations are a computationally inexpensive set of tools that, at a small accuracy cost, replace the need for CFD or other numerical methods, which can potentially mean cost savings in the event of not having this type of software available. In Chapter 6 it was presented a study with 280 optimization runs using these correlations from which the software made an estimated 1.5 million correlation calls, and the overall time needed 139 was just 14.7 hours. During the course of this doctorate the amount of CFD simulations performed was two orders of magnitude smaller than the number of correlation calls. In other words, the study in Chapter 6 could have never been made without these correlations.  All correlations are currently available in the latest version of CoilDesigner® [159] and is ready to be used to evaluate coils with small diameter tubes. 8.2 List of Publications The following peer-reviewed journal papers were published or submitted as outcomes of this research. 1- Huang, L. Bacellar, D., Aute, V., Radermacher, R., Variable geometry microchannel heat exchanger modeling under dry, wet, and partially wet surface conditions accounting for tube-to-tube heat conduction, Science and Technology for the Built Environment (2015) 21, 703–717 2- Bacellar, D., Aute, V., Huang, Z. Radermacher, R, Airside friction and heat transfer characteristics for staggered tube bundle in crossflow configuration with diameters from 0.5 mm to 2.0 mm, International Journal of Heat and Mass Transfer, 98, p. 448-454 3- Bacellar, D., Aute, V., Huang, Z., Radermacher, R, High Performance Compact Air-to-Fluid Heat Exchangers Using Multi-Scale Analysis and Shape Optimization with Experimental Validation of a 3-D Printed Prototype (Journal: Science and Technology for the Built Environment) 140 4- Huang, Z., Bacellar, D., Aute, V., Radermacher, R, Air side performance of a novel air-to-refrigerant heat exchanger, (Journal: Experimental Thermal and Fluid Sciences) 5- Bacellar, D., Aute, V., Radermacher, R, Thermal-hydraulic optimum topology configurations for fin and tube heat exchangers with diameters below 5.0mm, (Journal: International Journal of Refrigeration) 6- Li, Zhenning, Bacellar, D., Aute, V., Radermacher, R, Review on Correlations for Small Diameter Tube Heat Exchangers, (Journal: International Journal of Refrigeration) The following peer-reviewed conference papers were published or accepted and resulted from this research. 1- Bacellar, D., Aute, V., Huang, Z. Radermacher, R., Novel Airside Heat Transfer Surface Designs Using an Integrated Multi-Scale Analysis with Topology and Shape Optimization, 16th International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016 2- Bacellar, D., Aute, V., Huang, Z. Radermacher, R, Airside Performance Correlations and Optimal Heat Pump Heat Exchanger Designs Based on 0.5mm-2mm Finless Round Tube Bundles, 16th International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016 3- Bacellar, D., Aute, V., Radermacher, R., Performance Evaluation Criteria Analysis of Compact Air-to-Refrigerant Heat Exchangers and Selection Utility Function for Single Phase Applications, 16th 141 International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016. 4- Bacellar, D., Aute, V., Radermacher, R., Wavy Fin Profile Optimization Using NURBS for Air-To-Refrigerant Tube-Fin Heat Exchangers with Small Diameter Tubes, 16th International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016 5- Bacellar, D., Aute, V., Radermacher, R., CFD-Based Correlation Development for Air Side Performance of Wavy Fin Tube Heat Exchangers using Small Diameter Tubes, 16th International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016 6- Bacellar, D., Aute, V., Huang, Z. Radermacher, R., High Performance Gas-to-Fluid Crossflow Heat Exchangers using Micro Tubes with Round and Novel Shapes, Thermal Fluids Analysis Workshop (TFAWS16) at NASA-Ames Research Center, August 01-04, 2016 7- Bacellar, D., Aute, V., Radermacher, R., Verification & Validation of CFD Models Used in Automated Simulations Applied to Novel Air Heat Transfer Surfaces Optimization, ASME V&V Symposium, 2016, Las Vegas, NV. 8- Bacellar, D., Ling, J., Abdelaziz, O., Aute, V., Radermacher, R., Design of Novel Air-to-Refrigerant Heat Exchangers Using Approximation Assisted Optimization, ASME 2014 Verification & Validation Symposium, May 7-9, 2014 – Las Vegas, Nevada. 142 9- Bacellar, D., Aute, V., Radermacher, R., CFD-Based Correlation Development for Air Side Performance of Finned and Finless Tube Heat Exchangers with Small Diameter Tubes, 15th International Refrigeration and Air Conditioning Conference at Purdue, July 14-17, 2014. 10- Bacellar, D., Ling, J., Abdelaziz, O., Aute, V., Radermacher, R., Multi- scale modeling and approximation assisted optimization of bare tube heat exchangers, Proceedings of the 15th International Heat Transfer Conference, IHTC-15, August 10-15, 2014, Kyoto, Japan. 11- Bacellar, D., Abdelaziz, O., Aute, V., Radermacher, R., Novel Heat Exchanger Design using Computational Fluid Dynamics and Approximation Assisted Optimization, ASHRAE 2015, Winter Conference, January 24-28, 2015 - Chicago, IL. 12- Bacellar, D., Aute, V., Radermacher, R., A Method for Air-To- Refrigerant Heat Exchanger Multi-Scale Analysis and Optimization with Tube Shape Parameterization, 24th IIR International Congress of Refrigeration, August 16 – 22, 2015 – Yokohama, Japan. 13- Bacellar, D., Aute, V., Radermacher, R., CFD-Based Correlation Development for Air Side Performance on Finned Tube Heat Exchangers with Wavy Fins and Small Tube Diameters, 24th IIR International Congress of Refrigeration, August 16 – 22, 2015 – Yokohama, Japan. 14- Huang, L. Bacellar, D., Aute, V., Radermacher, R., Fin Performance Analysis for Microchannel Heat Exchangers Under Dry, Wet and 143 Partial Wet Conditions, 15th International Refrigeration and Air Conditioning Conference at Purdue, July 14-17, 2014. 15- Bhanot, V., Bacellar, D., Ling, J., Alabdulkarem, A., Aute, V., Radermacher, R., Steady State and Transient Validation of Heat Pumps Using Alternative Lower-GWP Refrigerants, 15th International Refrigeration and Air Conditioning Conference at Purdue, July 14-17, 2014 16- Saleh, K., Bacellar, D., Aute, V., Radermacher, R., An Adaptive Multiscale Approximation Assisted Multiobjective Optimization Applied to Compact Heat Exchangers, 4th International Conference of Engineering Optimization, EngOpt 2014, September 8-11, Lisbon, Portugal. The following invention disclosures/provisional patents have been developed as a result of the work presented in this dissertation. 1- Air-to-Refrigerant Heat Exchangers with Parameterized Tube Shapes, Invention Disclosure No. PS-2015-112, September/2015 2- High-Performance Air-to-Refrigerant Heat Exchangers Using Small Round Tubes, Invention Disclosure No. PS-2015-130, October/2015 3- Integrated Air-to-Refrigerant Heat Exchanger and Impeller, Invention Disclosure No. PS-2014-181, Provisional Patent No. 62/264692, December/2015 8.3 Recommendations for Future Work This work has opened new frontiers to the next generation of heat This work has opened new frontiers to the next generation of heat exchangers and created 144 opportunities to great advances in the art. Future researches can benefit greatly from the fundamentals and technical contributions of this work by addressing the following:  Although it was demonstrated that conventional fin concepts can become detrimental at a certain scale, the conclusions do not imply that other methods of surface enhancement should not be investigated. My suggestion is to focus on the primary heat transfer surfaces and, in addition to the shape optimization and size reduction, by investigate adding other potential enhancement mechanisms, including, but not limited to: o Surface coating/treatment o Winglets/vortex generators (Figure 118); such mechanisms, in combination with novel shapes, may contribute to reduce flow separation even more and induce turbulence within the boundary layer to enhance heat transfer o Extended surfaces with same shape as the tubes in order to achieve comparable performance and add surface area (Figure 119) Figure 118. Winglets on high-performance tube shape. Winglets/vortex generators 145 Figure 119. High-performance tube and extended surface shapes.  Leverage the flexibility and powerful capabilities of the multi-scale analysis and shape optimization methodology o Optimization of tube path shape and even tube arrangement shape (Figure 120) o Design of coil and fan as single unit, i.e. make the tubes as the fan blades (Figure 121) Figure 120. Extension of the multi-scale analysis and shape optimization methodology. High performance tubes High performance extended surfaces Hollow Tube Cross Section Scaling and Parameterization y x lP Ports (Np) tP z x Tube Flow Path Scaling and Parameterization L x y z Tube Arrangement Scaling and Parameterization 2D Single Tube 3D Single Tube 3D Heat Exchanger 146 Figure 121. Fan-coil single unit concept [169].  Address other physics that may have other unforeseen impacts, including: degradation due to fouling/frosting, vibration and noise, static and dynamic stress analysis, and corrosion  Investigate the physics of in-tube fluid when exploring alternate shapes to ensure the correlations are applicable, in particular to two-phase flows  Include manufacturing constraints to the optimization problem, but keeping up to date to the new advances and opportunities. Investigate solutions to larger scale HX’s that may pose additional challenges when using small tubes including: tube length / bending; tube blockage, tube brazing and others 1. Fixed header cap 2. Rotating sealing 3. Upper rotating header 4. Rotating coil 5. Lower rotating header 6. Sealed internal tube Air Flow In Air Flow Out Refrigerant Flow In Refrigerant Flow Out Air Flow In Air Flow Out Refrigerant Flow In Refrigerant Flow Out Free flow Blocked flow 147  Develop a high level platform with a comprehensive User Interface, allowing any user to perform the entire design framework based on their needs  Investigate the possibility of optimizing an entire HVAC system addressing some of the issues found in this work including: charge migration to pipes, high airside pressure drop in the condenser and manufacturing challenges  Investigate the possibility of 3D printing the entire HVAC unit (HX’s and pipes), including fan blades, and leaving space for fan motor, compressor and valves As the industry matures small diameter tube HX’s may become available for testing which will be a great opportunity to test and improve the CFD- based correlations developed in this work. 148 Appendices Appendix A – Non-Uniform Rational B-Spline C# code Sample Call Function: public void GetNURBS(double[] xControlPolygon, double[] yControlPolygon, int p, double[] w, double[] xNURBS, double[] yNURBS) // xControlPolygon & yControlPolygon - the coordinates of all control points (any number); xControlPolygon.Length = yControlPolygon.Length // p – interpolation order < xControlPolygon.Length // w – weight vector; w.Length = xControlPolygon.Length // xNURBS & yNURBS - output { int Nv = 201; //Subject to change double t = 0.0; double dt = 1.0 / (Nv - 1); int nCP = xControlPolygon.Length - 1; double[] U = getKnotVector(nCP, p); if(w.Length != xControlPolygon.Length) { w = new double[nCP]; for (int i = 0; i <= nCP; i++) w[i] = 1.0; } xNURBS = new double[Nv]; yNURBS = new double[Nv]; for (int i = 0; i < xNURBS.Length; i++) { xNURBS[i] = ratBSpline(t, p, U, w, xControlPolygon); yNURBS[i] = ratBSpline(t, p, U, w, yControlPolygon); t += dt; } } Support Functions based on Tiller and Piegl algorithms [157]: Basis Function public double[] basisFun(int i, double u, int p, double[] U) { double[] N = new double[p + 1]; double[] l = new double[p + 1]; double[] r = new double[p + 1]; double saved = 0.0; double temp; N[0] = 1.0; for (int j = 1; j <= p; j++) { l[j] = u - U[i + 1 - j]; 149 r[j] = U[i + j] - u; saved = 0.0; for (int k = 0; k < j; k++) { temp = N[k] / (r[k + 1] + l[k + 1]); N[k] = saved + r[k + 1] * temp; saved = l[j - k] * temp; } N[j] = saved; } return N; } Find Span (interval) Function public int findSpan(int p, double u, double[] U) { int span = 0; int count = 0; int n = U.Length - p - 1; if (Math.Abs(u - U[n + 1]) < 0.0000001) return n - 1; double lo = p; double hi = n + 1; int mid = (int)Math.Floor((0.5 * (lo + hi))); do { if (u < U[mid]) hi = mid; else lo = mid; mid = (int)Math.Floor((0.5 * (lo + hi))); count++; } while (u < U[mid] || u >= U[mid + 1]); span = mid; return span; } Rational B-Spline Function public double ratBSpline(double u, int p, double[] U, double[] w, double[] x) { double xCurve = 0.0; int n = p + 1; int s = findSpan(p, u, U); double[] N; N = basisFun(s, u, p, U); int m = x.Length; double[] Nn = new double[m]; double b = 0.0; for (int i = 0; i < n; i++) Nn[s - p + i] = N[i]; for (int i = 0; i < m; i++) b += Nn[i] * w[i]; for (int i = 0; i < m; i++) xCurve += Nn[i] * w[i] / b * x[i]; 150 return xCurve; } Get Uniform/Non-Uniform Knot Vector Function public double[] getKnotVector(int n, int p) { double[] U = new double[2 * (p + 1) + n - p]; for (int i = U.Length - p - 1; i < U.Length; i++) U[i] = 1.0; int midKnots = n - p; if (p < n) for (int i = 0; i < midKnots; i++) U[p + 1 + i] = ((double)(i + 1) / ((double)n + 1.0 - (double)p)); return U; } Appendix B – NTHX-001 Stress Analysis The stress analysis carried entailed evaluating the stress and elastic deformation when submitted to a static uniform internal pressure (6.0MPa) with fixed end supports and no additional loads (Figure 122). The main assumption is isotropic behavior, i.e. the properties are independent to stress direction. The objective is to evaluate whether the maximum VonMises (equation 94) stress falls within the elastic region, and if so, how far is it from achieving the yield stress. The factor of safety (equation 95) is then defined as the ratio between yield stress and maximum VonMises stress. The present analysis is performed in ANSYS Mechanic®. Figure 122. Stress analysis problem setup. internalP 151        2 2 2 2 2 211 22 22 33 33 11 12 23 31 1 6 2 VonMises                    (94) Figure 123. Isotropic stress components and stress-strain engineering curve. , Yield VonMises Max FOS    (95) The analysis described above was performed for the NTHX-001 (Figure 124) header and tube separately. For the latter two alternate inner shapes were studied; the first was a simple ellipse with a minimum distance from the outer shape of 0.3mm. The second was a B-Spline ensuring constant thickness of 0.3mm. Figure 124. NTHX-001 Cut views. Elastic / Plastic yield VonMises ( )Stress MPa (%)Strain  ( )E Young Modulus      1111 22 22 33 33 12 23 31 32 23 21 x z y 152 Figure 125. NTHX-001 Header and tubes cross sections. Figure 126. NTHX-001 Header and tube meshes. Figure 127. VonMises stress contour plots for the NTHX-001 tube. 153 Figure 128. Deformation contour plots for the NTHX-001 tube. Table 28. Material yield strength (SolidWorks® database). Yield Strength MPa Stainless Steel (304) 207 Copper (99.9%) 70 Aluminum (1060) 27 Titanium (Grade 2) 78 Titanium (Grade 5) 206 Table 29. NTHX-001 Stress analysis results. Unit Header Tube (Ellipse) Tube (B-Spline) Simulation Results Max. deformation μm 2.63 0.22 0.53 Max. Strain % 0.07 0.04 0.08 Max. VonMises MPa 125.7 76.4 150.4 FOS (-) Stainless Steel (304) - 1.65 2.71 1.38 Copper (99.9%) - 0.56 0.92 0.47 Aluminum (1060) - 0.21 0.35 0.18 Titanium (Grade 2) - 0.62 1.02 0.52 Titanium (Grade 5) - 1.64 2.69 1.37 154 Appendix C – Optimum HX Designs RTHX Figure 129. Round finless tubes (BTHX): a) in-line; b) staggered. Table 30. Optimum RTHX dimensions. Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-001 Staggered 1 0.7920 0.5940 1.1903 1.2379 4 121 100 0.1524 0.1486 0.0048 0.0226 107.81 15.77 RTHX-002 Staggered 1 0.7919 0.5939 1.1901 1.1983 4 101 100 0.1777 0.1198 0.0048 0.0213 101.36 15.31 d l d lTube Banks (Nr) Tube Banks (Nr) Tube Rows (Nt) Tube Banks (Nr) Tube Banks (Nr) Tube Rows (Nt) a) b) 2Pl 155 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-003 Staggered 1 0.7928 0.5946 1.1916 1.1997 4 101 100 0.1777 0.1200 0.0048 0.0213 101.60 15.35 RTHX-004 Staggered 1 0.7936 0.5952 1.1927 1.2008 4 101 100 0.1777 0.1201 0.0048 0.0213 101.79 15.38 RTHX-005 Staggered 1 0.7928 0.5946 1.1916 1.2020 4 101 100 0.1777 0.1202 0.0048 0.0214 101.80 15.35 RTHX-006 Staggered 1 0.7928 0.5946 1.1916 1.2044 4 101 100 0.1777 0.1204 0.0048 0.0214 102.00 15.35 RTHX-007 Staggered 1 0.7916 0.5937 1.1944 1.2049 4 101 100 0.1777 0.1205 0.0048 0.0214 102.28 15.30 RTHX-008 Staggered 1 0.7916 0.5937 1.2037 1.2049 4 101 100 0.1777 0.1205 0.0048 0.0214 103.08 15.30 RTHX-009 Staggered 1 0.7928 0.5946 1.1916 1.2020 4 101 100 0.1803 0.1202 0.0048 0.0217 103.32 15.58 RTHX-010 Staggered 1 0.7922 0.5941 1.1906 1.2243 4 186 100 0.0959 0.2265 0.0048 0.0217 103.47 15.31 RTHX-011 Staggered 1 0.7922 0.5942 1.1907 1.2244 4 186 100 0.0959 0.2265 0.0048 0.0217 103.48 15.31 RTHX-012 Staggered 1 0.7916 0.5937 1.1920 1.2396 4 196 100 0.0919 0.2417 0.0048 0.0222 105.97 15.44 RTHX-013 Staggered 1 0.7916 0.5937 1.1944 1.2396 4 196 100 0.0919 0.2417 0.0048 0.0222 106.17 15.44 RTHX-014 Staggered 1 0.7916 0.5937 1.1943 1.2396 4 196 100 0.0933 0.2417 0.0048 0.0225 107.70 15.66 RTHX-015 Staggered 1 0.7916 0.5937 1.1944 1.2396 4 196 100 0.0933 0.2417 0.0048 0.0225 107.71 15.66 RTHX-016 Staggered 1 0.7919 0.5939 1.1902 1.2378 4 121 100 0.1524 0.1485 0.0048 0.0226 107.79 15.77 RTHX-017 Staggered 1 0.7916 0.5937 1.1943 1.2419 4 196 100 0.0933 0.2422 0.0048 0.0226 107.90 15.66 RTHX-018 Staggered 1 0.7916 0.5937 1.1874 1.2501 4 191 100 0.0959 0.2375 0.0047 0.0228 108.21 15.70 RTHX-019 Staggered 1 0.7916 0.5937 1.1874 1.2501 4 196 100 0.0946 0.2438 0.0047 0.0231 109.52 15.89 RTHX-020 Staggered 1 0.7916 0.5937 1.1874 1.2512 4 196 100 0.0946 0.2440 0.0047 0.0231 109.62 15.89 RTHX-021 Staggered 1 0.7916 0.5937 1.1874 1.2513 4 196 100 0.0946 0.2440 0.0047 0.0231 109.63 15.89 RTHX-022 Staggered 1 0.7922 0.5942 1.1906 1.2522 4 196 100 0.0946 0.2442 0.0048 0.0231 110.01 15.91 RTHX-023 Staggered 1 0.7922 0.5942 1.1907 1.2523 4 196 100 0.0946 0.2442 0.0048 0.0231 110.02 15.91 RTHX-024 Staggered 1 0.7922 0.5942 1.1883 1.2522 4 181 100 0.1032 0.2254 0.0048 0.0233 110.61 16.03 RTHX-025 Staggered 1 0.7908 0.5931 1.1896 1.2534 4 181 100 0.1032 0.2256 0.0048 0.0233 110.83 15.97 RTHX-026 Staggered 1 0.7916 0.5937 1.1897 1.2570 4 181 100 0.1032 0.2263 0.0048 0.0234 111.15 16.00 RTHX-027 Staggered 1 0.7916 0.5937 1.1897 1.2570 4 181 100 0.1032 0.2263 0.0048 0.0234 111.16 16.00 RTHX-028 Staggered 1 0.7917 0.5938 1.1898 1.2572 4 181 100 0.1032 0.2263 0.0048 0.0234 111.19 16.01 RTHX-029 Staggered 1 0.7917 0.5938 1.1899 1.2572 4 181 100 0.1032 0.2263 0.0048 0.0234 111.19 16.01 RTHX-030 Staggered 1 0.7922 0.5942 1.1907 1.2580 4 181 100 0.1032 0.2264 0.0048 0.0234 111.34 16.03 RTHX-031 Staggered 1 0.7923 0.5943 1.1908 1.2582 4 181 100 0.1032 0.2265 0.0048 0.0234 111.37 16.03 RTHX-032 Staggered 1 0.7910 0.5932 1.1888 1.2572 4 106 100 0.1777 0.1320 0.0048 0.0235 111.53 16.04 RTHX-033 Staggered 1 0.7910 0.5932 1.1888 1.2572 4 106 100 0.1777 0.1320 0.0048 0.0235 111.54 16.04 RTHX-034 Staggered 1 0.7916 0.5937 1.1897 1.2593 4 181 100 0.1039 0.2267 0.0048 0.0236 112.07 16.11 RTHX-035 Staggered 1 0.7967 0.5975 1.1974 1.2675 4 181 100 0.1032 0.2281 0.0048 0.0236 112.80 16.21 RTHX-036 Staggered 1 0.7973 0.5979 1.1994 1.2684 4 181 100 0.1032 0.2283 0.0048 0.0236 113.07 16.23 RTHX-037 Staggered 1 0.7922 0.5942 1.1907 1.2743 4 181 100 0.1039 0.2294 0.0048 0.0238 113.50 16.13 RTHX-038 Staggered 1 0.7923 0.5942 1.1908 1.2745 4 181 100 0.1039 0.2294 0.0048 0.0238 113.53 16.14 RTHX-039 Staggered 1 0.7924 0.5943 1.1910 1.2746 4 181 100 0.1039 0.2294 0.0048 0.0238 113.56 16.14 RTHX-040 Staggered 1 0.7924 0.5943 1.2003 1.2746 4 181 100 0.1039 0.2294 0.0048 0.0238 114.45 16.14 RTHX-041 Staggered 1 0.7925 0.5944 1.2003 1.2747 4 181 100 0.1039 0.2294 0.0048 0.0238 114.46 16.14 RTHX-042 Staggered 1 0.7925 0.5943 1.2015 1.2747 4 181 100 0.1039 0.2294 0.0048 0.0238 114.57 16.14 RTHX-043 Staggered 1 0.7958 0.5968 1.2042 1.2800 4 196 100 0.0959 0.2496 0.0048 0.0239 115.33 16.28 RTHX-044 Staggered 1 0.7958 0.5969 1.2065 1.2801 4 196 100 0.0959 0.2496 0.0048 0.0239 115.56 16.28 RTHX-045 Staggered 1 0.7925 0.5943 1.1910 1.2735 4 181 100 0.1059 0.2292 0.0048 0.0243 115.65 16.45 RTHX-046 Staggered 1 0.7913 0.5934 1.1892 1.2785 4 181 100 0.1059 0.2301 0.0048 0.0244 115.92 16.40 156 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-047 Staggered 1 0.7916 0.5937 1.1897 1.2791 4 181 100 0.1059 0.2302 0.0048 0.0244 116.03 16.42 RTHX-048 Staggered 1 0.7919 0.5939 1.1902 1.2796 4 181 100 0.1059 0.2303 0.0048 0.0244 116.12 16.43 RTHX-049 Staggered 1 0.7925 0.5943 1.1910 1.2805 4 181 100 0.1059 0.2305 0.0048 0.0244 116.28 16.45 RTHX-050 Staggered 1 0.7925 0.5944 1.1910 1.2794 4 186 100 0.1039 0.2367 0.0048 0.0246 117.16 16.59 RTHX-051 Staggered 1 0.7950 0.5962 1.1948 1.2846 4 186 100 0.1032 0.2376 0.0048 0.0245 117.25 16.59 RTHX-052 Staggered 1 0.7950 0.5962 1.1948 1.2834 4 186 100 0.1039 0.2374 0.0048 0.0247 117.89 16.70 RTHX-053 Staggered 1 0.7950 0.5962 1.1948 1.2834 4 186 100 0.1039 0.2374 0.0048 0.0247 117.90 16.70 RTHX-054 Staggered 1 0.7922 0.5941 1.1906 1.2731 4 191 100 0.1032 0.2419 0.0048 0.0250 118.92 16.92 RTHX-055 Staggered 1 0.7922 0.5941 1.1906 1.2754 4 191 100 0.1032 0.2423 0.0048 0.0250 119.14 16.92 RTHX-056 Staggered 1 0.7925 0.5944 1.1922 1.2759 4 191 100 0.1032 0.2424 0.0048 0.0250 119.34 16.93 RTHX-057 Staggered 1 0.7922 0.5942 1.1907 1.2790 4 191 100 0.1032 0.2430 0.0048 0.0251 119.48 16.92 RTHX-058 Staggered 1 0.7925 0.5944 1.1922 1.2794 4 191 100 0.1032 0.2431 0.0048 0.0251 119.67 16.93 RTHX-059 Staggered 1 0.7922 0.5942 1.1907 1.2790 4 186 100 0.1066 0.2366 0.0048 0.0252 120.08 17.01 RTHX-060 Staggered 1 0.7924 0.5943 1.1909 1.2792 4 186 100 0.1066 0.2367 0.0048 0.0252 120.13 17.01 RTHX-061 Staggered 1 0.7924 0.5943 1.1909 1.2792 4 186 100 0.1066 0.2367 0.0048 0.0252 120.13 17.01 RTHX-062 Staggered 1 0.7916 0.5937 1.1897 1.2790 4 191 100 0.1039 0.2430 0.0048 0.0252 120.15 17.00 RTHX-063 Staggered 1 0.7917 0.5938 1.1898 1.2792 4 191 100 0.1039 0.2431 0.0048 0.0253 120.19 17.01 RTHX-064 Staggered 1 0.7972 0.5979 1.1982 1.2882 4 191 100 0.1032 0.2448 0.0048 0.0253 121.10 17.13 RTHX-065 Staggered 1 0.7973 0.5979 1.1982 1.2882 4 191 100 0.1032 0.2448 0.0048 0.0253 121.11 17.14 RTHX-066 Staggered 1 0.7974 0.5981 1.1985 1.2885 4 191 100 0.1032 0.2448 0.0048 0.0253 121.16 17.14 RTHX-067 Staggered 1 0.7910 0.5932 1.1888 1.3001 4 191 100 0.1032 0.2470 0.0048 0.0255 121.26 16.87 RTHX-068 Staggered 1 0.7920 0.5940 1.1903 1.3018 4 191 100 0.1032 0.2473 0.0048 0.0255 121.57 16.91 RTHX-069 Staggered 1 0.7922 0.5941 1.1906 1.3021 4 191 100 0.1032 0.2474 0.0048 0.0255 121.64 16.92 RTHX-070 Staggered 1 0.7917 0.5938 1.1898 1.3048 4 191 100 0.1032 0.2479 0.0048 0.0256 121.81 16.90 RTHX-071 Staggered 1 0.7916 0.5937 1.1909 1.3047 4 191 100 0.1032 0.2479 0.0048 0.0256 121.91 16.89 RTHX-072 Staggered 1 0.7922 0.5941 1.1906 1.3056 4 191 100 0.1032 0.2481 0.0048 0.0256 121.96 16.92 RTHX-073 Staggered 1 0.7919 0.5939 1.1914 1.3052 4 191 100 0.1032 0.2480 0.0048 0.0256 122.00 16.91 RTHX-074 Staggered 1 0.7916 0.5937 1.1909 1.3046 4 186 100 0.1066 0.2414 0.0048 0.0257 122.51 16.98 RTHX-075 Staggered 1 0.7917 0.5938 1.1898 1.3048 4 191 100 0.1039 0.2479 0.0048 0.0258 122.59 17.01 RTHX-076 Staggered 1 0.7922 0.5941 1.1906 1.3056 4 191 100 0.1039 0.2481 0.0048 0.0258 122.75 17.03 RTHX-077 Staggered 1 0.7922 0.5942 1.1906 1.3056 4 191 100 0.1039 0.2481 0.0048 0.0258 122.75 17.03 RTHX-078 Staggered 1 0.7973 0.5979 1.1982 1.3139 4 191 100 0.1032 0.2497 0.0048 0.0258 123.53 17.14 RTHX-079 Staggered 1 0.7973 0.5979 1.1994 1.3139 4 191 100 0.1032 0.2497 0.0048 0.0258 123.65 17.14 RTHX-080 Staggered 1 0.7965 0.5973 1.1970 1.3115 4 191 100 0.1039 0.2492 0.0048 0.0259 123.96 17.21 RTHX-081 Staggered 1 0.7972 0.5979 1.1993 1.3139 4 191 100 0.1039 0.2496 0.0048 0.0259 124.43 17.24 RTHX-082 Staggered 1 0.7902 0.5926 1.1876 1.3012 4 196 100 0.1032 0.2537 0.0048 0.0262 124.43 17.28 RTHX-083 Staggered 1 0.7916 0.5937 1.1897 1.3034 4 196 100 0.1032 0.2542 0.0048 0.0262 124.87 17.34 RTHX-084 Staggered 1 0.7918 0.5938 1.1900 1.3038 4 196 100 0.1032 0.2542 0.0048 0.0262 124.94 17.35 RTHX-085 Staggered 1 0.7917 0.5938 1.1898 1.3048 4 191 100 0.1059 0.2479 0.0048 0.0263 124.94 17.33 RTHX-086 Staggered 1 0.7922 0.5942 1.1918 1.3057 4 196 100 0.1032 0.2546 0.0048 0.0263 125.31 17.37 RTHX-087 Staggered 1 0.7922 0.5942 1.1919 1.3150 4 196 100 0.1032 0.2564 0.0048 0.0265 126.20 17.37 RTHX-088 Staggered 1 0.7916 0.5937 1.1909 1.3290 4 196 100 0.1032 0.2592 0.0048 0.0268 127.45 17.34 RTHX-089 Staggered 1 0.7917 0.5937 1.2003 1.3291 4 196 100 0.1032 0.2592 0.0048 0.0268 128.46 17.34 RTHX-090 Staggered 1 0.7958 0.5969 1.1972 1.3361 4 196 100 0.1032 0.2605 0.0048 0.0269 128.80 17.52 157 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-091 Staggered 1 0.7971 0.5979 1.1992 1.3383 4 196 100 0.1032 0.2610 0.0048 0.0269 129.23 17.58 RTHX-092 Staggered 1 0.7964 0.5973 1.2074 1.3370 4 196 100 0.1032 0.2607 0.0048 0.0269 129.99 17.55 RTHX-093 Staggered 1 0.7971 0.5979 1.2086 1.3383 4 196 100 0.1032 0.2610 0.0048 0.0269 130.24 17.58 RTHX-094 Staggered 1 0.7922 0.5942 1.1907 1.3417 4 196 100 0.1052 0.2616 0.0048 0.0275 131.12 17.70 RTHX-095 Staggered 1 0.7922 0.5942 1.1907 1.3428 4 196 100 0.1059 0.2619 0.0048 0.0277 132.06 17.81 RTHX-096 Staggered 1 0.7920 0.5940 1.1950 1.3425 4 196 100 0.1059 0.2618 0.0048 0.0277 132.51 17.80 RTHX-097 Staggered 1 0.7920 0.5940 1.1996 1.3424 4 196 100 0.1059 0.2618 0.0048 0.0277 133.02 17.80 RTHX-098 Staggered 1 0.7923 0.5942 1.2094 1.3430 4 196 100 0.1059 0.2619 0.0048 0.0277 134.16 17.82 RTHX-099 Staggered 1 0.7920 0.5940 1.2136 1.3425 4 196 100 0.1059 0.2618 0.0049 0.0277 134.57 17.80 RTHX-100 Staggered 1 0.7922 0.5941 1.1906 1.3428 4 206 100 0.1032 0.2753 0.0048 0.0284 135.34 18.25 RTHX-101 Staggered 1 0.7923 0.5942 1.1908 1.3418 4 201 100 0.1066 0.2684 0.0048 0.0286 136.22 18.39 RTHX-102 Staggered 1 0.7950 0.5962 1.1948 1.3475 4 206 100 0.1032 0.2762 0.0048 0.0285 136.29 18.38 RTHX-103 Staggered 1 0.7923 0.5942 1.1908 1.3430 4 201 100 0.1066 0.2686 0.0048 0.0286 136.33 18.39 RTHX-104 Staggered 1 0.7938 0.5953 1.1930 1.3501 4 206 100 0.1039 0.2768 0.0048 0.0288 137.23 18.45 RTHX-105 Staggered 1 0.7916 0.5937 1.1909 1.3615 4 206 100 0.1032 0.2791 0.0048 0.0288 137.26 18.23 RTHX-106 Staggered 1 0.7922 0.5941 1.1906 1.3637 4 206 100 0.1032 0.2796 0.0048 0.0289 137.44 18.25 RTHX-107 Staggered 1 0.7922 0.5942 1.1907 1.3637 4 206 100 0.1032 0.2796 0.0048 0.0289 137.46 18.26 RTHX-108 Staggered 1 0.7910 0.5932 1.1888 1.3709 4 206 100 0.1032 0.2810 0.0048 0.0290 137.96 18.20 RTHX-109 Staggered 1 0.7911 0.5934 1.1890 1.3711 4 206 100 0.1032 0.2811 0.0048 0.0290 138.01 18.21 RTHX-110 Staggered 1 0.7916 0.5937 1.1909 1.3720 4 206 100 0.1032 0.2813 0.0048 0.0290 138.32 18.23 RTHX-111 Staggered 1 0.7922 0.5942 1.1907 1.3730 4 206 100 0.1032 0.2815 0.0048 0.0291 138.39 18.26 RTHX-112 Staggered 1 0.7922 0.5941 1.1953 1.3730 4 206 100 0.1032 0.2815 0.0048 0.0291 138.92 18.25 RTHX-113 Staggered 1 0.7924 0.5943 1.1909 1.3733 4 116 100 0.1890 0.1579 0.0048 0.0298 142.18 18.76 RTHX-114 Staggered 1 0.7919 0.5939 1.1901 1.3840 4 116 100 0.1890 0.1592 0.0048 0.0301 143.20 18.73 RTHX-115 Staggered 1 0.7920 0.5940 1.1904 1.3843 4 116 100 0.1890 0.1592 0.0048 0.0301 143.25 18.74 RTHX-116 Staggered 1 0.7922 0.5942 1.1906 1.3846 4 116 100 0.1890 0.1592 0.0048 0.0301 143.32 18.75 RTHX-117 Staggered 1 0.7930 0.5948 1.1919 1.3861 4 116 100 0.1890 0.1594 0.0048 0.0301 143.61 18.79 RTHX-118 Staggered 1 0.7922 0.5941 1.1906 1.3846 4 116 100 0.1916 0.1592 0.0048 0.0305 145.32 19.01 RTHX-119 Staggered 1 0.7922 0.5942 1.1906 1.3846 4 116 100 0.1916 0.1592 0.0048 0.0305 145.33 19.01 RTHX-120 Staggered 1 0.7922 0.5942 1.1907 1.3847 4 116 100 0.1916 0.1592 0.0048 0.0305 145.35 19.01 RTHX-121 Staggered 1 0.7922 0.5942 1.1918 1.3846 4 116 100 0.1916 0.1592 0.0048 0.0305 145.47 19.01 RTHX-122 Staggered 1 0.7916 0.5937 1.1898 1.3882 4 116 100 0.1930 0.1596 0.0048 0.0308 146.61 19.11 RTHX-123 Staggered 1 0.7925 0.5943 1.1910 1.3897 4 116 100 0.1930 0.1598 0.0048 0.0308 146.93 19.15 RTHX-124 Staggered 1 0.7922 0.5941 1.1906 1.4020 4 116 100 0.1916 0.1612 0.0048 0.0309 147.15 19.01 RTHX-125 Staggered 1 0.7919 0.5939 1.1901 1.4073 4 116 100 0.1916 0.1618 0.0048 0.0310 147.65 18.99 RTHX-126 Staggered 1 0.7913 0.5935 1.1893 1.4063 4 216 100 0.1059 0.3023 0.0048 0.0320 152.31 19.59 RTHX-127 Staggered 1 0.7916 0.5937 1.1898 1.4068 4 216 100 0.1059 0.3025 0.0048 0.0320 152.43 19.61 RTHX-128 Staggered 1 0.7913 0.5935 1.1892 1.4108 4 216 100 0.1059 0.3033 0.0048 0.0321 152.80 19.59 RTHX-129 Staggered 1 0.7916 0.5937 1.1897 1.4114 4 216 100 0.1059 0.3034 0.0048 0.0321 152.92 19.61 RTHX-130 Staggered 1 0.7916 0.5937 1.1897 1.4160 4 216 100 0.1059 0.3044 0.0048 0.0322 153.42 19.61 RTHX-131 Staggered 1 0.7916 0.5937 1.1897 1.4218 4 216 100 0.1059 0.3057 0.0048 0.0324 154.05 19.61 RTHX-132 Staggered 1 0.7916 0.5937 1.1898 1.4219 4 216 100 0.1059 0.3057 0.0048 0.0324 154.06 19.61 RTHX-133 Staggered 1 0.7916 0.5937 1.1898 1.4231 4 216 100 0.1059 0.3060 0.0048 0.0324 154.19 19.61 RTHX-134 Staggered 1 0.7916 0.5937 1.1898 1.4277 4 216 100 0.1059 0.3070 0.0048 0.0325 154.69 19.61 158 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-135 Staggered 1 0.7923 0.5943 1.1908 1.4290 4 216 100 0.1059 0.3072 0.0048 0.0325 154.97 19.65 RTHX-136 Staggered 1 0.7913 0.5934 1.1938 1.4270 4 216 100 0.1059 0.3068 0.0048 0.0325 155.15 19.59 RTHX-137 Staggered 1 0.7916 0.5937 1.1909 1.4253 4 111 100 0.2083 0.1568 0.0048 0.0327 155.54 19.73 RTHX-138 Staggered 1 0.7940 0.5955 1.1933 1.4319 4 216 100 0.1059 0.3079 0.0048 0.0326 155.61 19.73 RTHX-139 Staggered 1 0.7938 0.5953 1.1976 1.4316 4 216 100 0.1059 0.3078 0.0048 0.0326 156.14 19.72 RTHX-140 Staggered 1 0.7939 0.5955 1.1944 1.4296 4 111 100 0.2083 0.1573 0.0048 0.0327 156.47 19.85 RTHX-141 Staggered 1 0.7966 0.5975 1.1973 1.4367 4 216 100 0.1059 0.3089 0.0048 0.0327 156.65 19.86 RTHX-142 Staggered 1 0.7910 0.5932 1.1888 1.4265 4 221 100 0.1059 0.3138 0.0048 0.0332 158.03 20.03 RTHX-143 Staggered 1 0.7915 0.5936 1.1895 1.4274 4 221 100 0.1059 0.3140 0.0048 0.0333 158.23 20.06 RTHX-144 Staggered 1 0.7916 0.5937 1.1909 1.4253 4 111 100 0.2136 0.1568 0.0048 0.0335 159.51 20.23 RTHX-145 Staggered 1 0.7920 0.5940 1.1903 1.4261 4 111 100 0.2136 0.1569 0.0048 0.0335 159.52 20.25 RTHX-146 Staggered 1 0.7920 0.5940 1.1915 1.4261 4 111 100 0.2136 0.1569 0.0048 0.0335 159.67 20.25 RTHX-147 Staggered 1 0.7920 0.5940 1.1915 1.4261 4 111 100 0.2136 0.1569 0.0048 0.0335 159.68 20.26 RTHX-148 Staggered 1 0.7923 0.5943 1.1920 1.4267 4 111 100 0.2136 0.1569 0.0048 0.0335 159.81 20.27 RTHX-149 Staggered 1 0.7928 0.5946 1.1927 1.4276 4 111 100 0.2136 0.1570 0.0048 0.0335 160.01 20.30 RTHX-150 Staggered 1 0.7916 0.5937 1.1897 1.4532 4 221 100 0.1059 0.3197 0.0048 0.0339 161.10 20.06 RTHX-151 Staggered 1 0.7948 0.5961 1.1946 1.4592 4 221 100 0.1059 0.3210 0.0048 0.0340 162.44 20.23 RTHX-152 Staggered 1 0.7916 0.5937 1.1897 1.4566 4 221 100 0.1066 0.3205 0.0048 0.0341 162.50 20.19 RTHX-153 Staggered 1 0.7916 0.5937 1.1897 1.4717 4 221 100 0.1059 0.3238 0.0048 0.0343 163.16 20.06 RTHX-154 Staggered 1 0.7916 0.5937 1.1897 1.4717 4 221 100 0.1059 0.3238 0.0048 0.0343 163.16 20.06 RTHX-155 Staggered 1 0.7916 0.5937 1.1898 1.4753 4 221 100 0.1059 0.3246 0.0048 0.0344 163.57 20.07 RTHX-156 Staggered 1 0.7922 0.5941 1.1906 1.4764 4 221 100 0.1059 0.3248 0.0048 0.0344 163.80 20.09 RTHX-157 Staggered 1 0.7916 0.5937 1.1897 1.4752 4 221 100 0.1066 0.3245 0.0048 0.0346 164.57 20.19 RTHX-158 Staggered 1 0.7924 0.5943 1.1886 1.4814 4 221 100 0.1066 0.3259 0.0048 0.0347 165.12 20.23 RTHX-159 Staggered 1 0.7920 0.5940 1.1891 1.4794 4 176 100 0.1358 0.2589 0.0048 0.0352 167.24 20.49 RTHX-160 Staggered 1 0.7904 0.5928 1.1948 1.4810 4 226 100 0.1059 0.3332 0.0048 0.0353 168.65 20.46 RTHX-161 Staggered 1 0.7913 0.5934 1.1892 1.4804 4 116 100 0.2089 0.1702 0.0048 0.0356 169.19 20.67 RTHX-162 Staggered 1 0.7909 0.5932 1.1887 1.4798 4 116 100 0.2103 0.1702 0.0048 0.0358 170.13 20.79 RTHX-163 Staggered 1 0.7913 0.5934 1.1892 1.4804 4 116 100 0.2103 0.1702 0.0048 0.0358 170.27 20.81 RTHX-164 Staggered 1 0.7934 0.5951 1.1925 1.4845 4 116 100 0.2103 0.1707 0.0048 0.0359 171.21 20.92 RTHX-165 Staggered 1 0.7934 0.5951 1.1925 1.4857 4 116 100 0.2103 0.1709 0.0048 0.0359 171.35 20.92 RTHX-166 Staggered 1 0.7958 0.5968 1.1960 1.4889 4 116 100 0.2103 0.1712 0.0048 0.0360 172.23 21.05 RTHX-167 Staggered 1 0.7918 0.5939 1.1878 1.4815 4 116 100 0.2129 0.1704 0.0048 0.0363 172.34 21.10 RTHX-168 Staggered 1 0.7918 0.5939 1.1901 1.4815 4 116 100 0.2129 0.1704 0.0048 0.0363 172.68 21.10 RTHX-169 Staggered 1 0.7928 0.5946 1.1915 1.4833 4 116 100 0.2129 0.1706 0.0048 0.0363 173.11 21.15 RTHX-170 Staggered 1 0.7928 0.5946 1.1916 1.4834 4 116 100 0.2129 0.1706 0.0048 0.0363 173.11 21.15 RTHX-171 Staggered 1 0.7909 0.5932 1.1887 1.4798 4 116 100 0.2142 0.1702 0.0048 0.0365 173.36 21.18 RTHX-172 Staggered 1 0.7916 0.5937 1.1898 1.4811 4 116 100 0.2142 0.1703 0.0048 0.0365 173.66 21.22 RTHX-173 Staggered 1 0.7924 0.5943 1.1910 1.4826 4 116 100 0.2142 0.1705 0.0048 0.0365 174.01 21.26 RTHX-174 Staggered 1 0.7940 0.5955 1.1933 1.4855 4 116 100 0.2142 0.1708 0.0048 0.0366 174.69 21.35 RTHX-175 Staggered 1 0.7946 0.5959 1.1942 1.4867 4 116 100 0.2142 0.1710 0.0048 0.0366 174.97 21.38 RTHX-176 Staggered 1 0.7948 0.5961 1.1946 1.4871 4 116 100 0.2142 0.1710 0.0048 0.0366 175.08 21.39 RTHX-177 Staggered 1 0.7939 0.5955 1.2026 1.4855 4 116 100 0.2142 0.1708 0.0048 0.0366 176.05 21.35 RTHX-178 Staggered 1 0.7940 0.5955 1.2026 1.4855 4 116 100 0.2142 0.1708 0.0048 0.0366 176.06 21.35 159 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-179 Staggered 1 0.7940 0.5955 1.2026 1.4867 4 116 100 0.2142 0.1710 0.0048 0.0366 176.19 21.35 RTHX-180 Staggered 1 0.7946 0.5959 1.2035 1.4878 4 116 100 0.2142 0.1711 0.0048 0.0367 176.47 21.38 RTHX-181 Staggered 1 0.7904 0.5928 1.1960 1.4764 4 186 100 0.1358 0.2731 0.0048 0.0371 177.45 21.57 RTHX-182 Staggered 1 0.7928 0.5946 1.1916 1.4834 4 186 100 0.1358 0.2744 0.0048 0.0373 177.63 21.71 RTHX-183 Staggered 1 0.7930 0.5947 1.1918 1.4836 4 186 100 0.1358 0.2745 0.0048 0.0373 177.69 21.71 RTHX-184 Staggered 1 0.7931 0.5948 1.1920 1.4839 4 186 100 0.1358 0.2745 0.0048 0.0373 177.76 21.72 RTHX-185 Staggered 1 0.7908 0.5931 1.1886 1.4796 4 116 100 0.2209 0.1702 0.0048 0.0376 178.69 21.84 RTHX-186 Staggered 1 0.7911 0.5934 1.1890 1.4802 4 116 100 0.2209 0.1702 0.0048 0.0376 178.83 21.85 RTHX-187 Staggered 1 0.7928 0.5946 1.1915 1.4833 4 116 100 0.2209 0.1706 0.0048 0.0377 179.59 21.95 RTHX-188 Staggered 1 0.7900 0.5925 1.1943 1.4781 4 186 100 0.1385 0.2734 0.0048 0.0379 180.87 21.97 RTHX-189 Staggered 1 0.7903 0.5927 1.1948 1.4787 4 186 100 0.1385 0.2736 0.0048 0.0379 181.02 21.99 RTHX-190 Staggered 1 0.7904 0.5928 1.1948 1.4787 4 186 100 0.1385 0.2736 0.0048 0.0379 181.03 21.99 RTHX-191 Staggered 1 0.7916 0.5937 1.1897 1.4810 4 121 100 0.2142 0.1777 0.0048 0.0381 181.19 22.14 RTHX-192 Staggered 1 0.7923 0.5943 1.1908 1.4825 4 116 100 0.2235 0.1705 0.0048 0.0381 181.54 22.18 RTHX-193 Staggered 1 0.7925 0.5943 1.1922 1.4827 4 121 100 0.2142 0.1779 0.0048 0.0381 181.78 22.19 RTHX-194 Staggered 1 0.7938 0.5954 1.1930 1.4852 4 121 100 0.2142 0.1782 0.0048 0.0382 182.22 22.27 RTHX-195 Staggered 1 0.7924 0.5943 1.1909 1.4825 4 191 100 0.1365 0.2817 0.0048 0.0384 183.12 22.38 RTHX-196 Staggered 1 0.8021 0.6016 1.2055 1.5007 4 121 100 0.2136 0.1801 0.0048 0.0385 185.46 22.66 RTHX-197 Staggered 1 0.8024 0.6018 1.2059 1.5012 4 121 100 0.2136 0.1801 0.0048 0.0385 185.58 22.68 RTHX-198 Staggered 1 0.8024 0.6018 1.2060 1.5013 4 121 100 0.2136 0.1802 0.0048 0.0385 185.62 22.68 RTHX-199 Staggered 1 0.8021 0.6016 1.2126 1.5007 4 121 100 0.2136 0.1801 0.0049 0.0385 186.55 22.66 RTHX-200 Staggered 1 0.7911 0.5934 1.1890 1.4802 4 121 100 0.2209 0.1776 0.0048 0.0392 186.60 22.80 RTHX-201 Staggered 1 0.7928 0.5946 1.1916 1.4834 4 196 100 0.1358 0.2893 0.0048 0.0393 187.23 22.88 RTHX-202 Staggered 1 0.7922 0.5941 1.1906 1.4798 4 116 100 0.2315 0.1702 0.0048 0.0394 187.65 22.97 RTHX-203 Staggered 1 0.7922 0.5941 1.1906 1.4810 4 116 100 0.2315 0.1703 0.0048 0.0394 187.79 22.97 RTHX-204 Staggered 1 0.7922 0.5942 1.1907 1.4822 4 196 100 0.1365 0.2890 0.0048 0.0394 187.86 22.96 RTHX-205 Staggered 1 0.7922 0.5941 1.1906 1.4822 4 116 100 0.2315 0.1704 0.0048 0.0395 187.94 22.97 RTHX-206 Staggered 1 0.7938 0.5953 1.1930 1.4851 4 196 100 0.1365 0.2896 0.0048 0.0395 188.60 23.05 RTHX-207 Staggered 1 0.7938 0.5953 1.1930 1.4839 4 196 100 0.1371 0.2894 0.0048 0.0397 189.36 23.16 RTHX-208 Staggered 1 0.7916 0.5937 1.1967 1.4810 4 196 100 0.1371 0.2888 0.0048 0.0396 189.57 23.03 RTHX-209 Staggered 1 0.7916 0.5937 1.1967 1.4811 4 196 100 0.1371 0.2888 0.0048 0.0396 189.58 23.03 RTHX-210 Staggered 1 0.7909 0.5932 1.1980 1.4798 4 126 100 0.2142 0.1850 0.0048 0.0396 189.91 23.03 RTHX-211 Staggered 1 0.7916 0.5937 1.1990 1.4811 4 126 100 0.2142 0.1851 0.0048 0.0397 190.24 23.07 RTHX-212 Staggered 1 0.7904 0.5928 1.1948 1.4787 4 196 100 0.1385 0.2884 0.0048 0.0399 190.82 23.18 RTHX-213 Staggered 1 0.7922 0.5942 1.1906 1.4822 4 186 100 0.1464 0.2742 0.0048 0.0402 191.24 23.37 RTHX-214 Staggered 1 0.6217 0.4663 0.9380 1.2616 4 246 100 0.1105 0.3091 0.0038 0.0342 128.21 14.39 RTHX-215 Staggered 1 0.6173 0.4630 0.9296 1.2265 4 251 100 0.1119 0.3066 0.0037 0.0343 127.55 14.65 RTHX-216 Staggered 1 0.6217 0.4663 0.9326 1.1732 4 241 100 0.1099 0.2816 0.0037 0.0309 115.41 14.01 RTHX-217 Staggered 1 0.6672 0.5004 1.0066 1.3754 4 246 100 0.1105 0.3370 0.0040 0.0373 149.99 16.57 RTHX-218 Staggered 1 0.6217 0.4663 0.9362 1.1450 4 236 100 0.1046 0.2691 0.0037 0.0281 105.36 13.05 RTHX-219 Staggered 1 0.6188 0.4641 0.9309 1.0579 4 246 100 0.0893 0.2592 0.0037 0.0231 86.16 11.51 RTHX-220 Staggered 1 0.6188 0.4641 0.9381 1.1532 4 251 100 0.0992 0.2883 0.0038 0.0286 107.37 13.06 RTHX-221 Staggered 1 0.6217 0.4663 0.9362 1.2671 4 246 100 0.1119 0.3104 0.0037 0.0347 130.06 14.56 RTHX-222 Staggered 1 0.6217 0.4663 0.9344 1.0857 4 246 100 0.0992 0.2660 0.0037 0.0264 98.67 12.92 160 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-223 Staggered 1 0.6202 0.4652 0.9394 1.1159 4 231 100 0.1052 0.2567 0.0038 0.0270 101.49 12.80 RTHX-224 Staggered 1 0.6202 0.4652 0.9304 1.2587 4 246 100 0.1119 0.3084 0.0037 0.0345 128.39 14.49 RTHX-225 Staggered 1 0.6217 0.4663 0.9326 1.2671 4 246 100 0.1119 0.3104 0.0037 0.0347 129.55 14.56 RTHX-226 Staggered 1 0.6217 0.4663 0.9453 1.1212 4 231 100 0.1052 0.2579 0.0038 0.0271 102.61 12.86 RTHX-227 Staggered 1 0.6217 0.4663 0.9362 1.1477 4 236 100 0.1046 0.2697 0.0037 0.0282 105.61 13.05 RTHX-228 Staggered 1 0.6217 0.4663 0.9453 1.1194 4 231 100 0.1052 0.2575 0.0038 0.0271 102.45 12.86 RTHX-229 Staggered 1 0.5938 0.4454 0.8951 0.9543 4 231 100 0.0786 0.2195 0.0036 0.0173 61.80 8.77 RTHX-230 Staggered 1 0.5938 0.4454 0.8942 0.9883 4 231 100 0.0833 0.2273 0.0036 0.0189 67.72 9.29 RTHX-231 Staggered 1 0.6217 0.4663 0.9326 1.2024 4 251 100 0.1066 0.3006 0.0037 0.0320 119.48 14.15 RTHX-232 Staggered 1 0.6202 0.4652 0.9322 1.0868 4 236 100 0.0999 0.2554 0.0037 0.0255 95.14 12.41 RTHX-233 Staggered 1 0.6393 0.4795 0.9646 1.3180 4 246 100 0.1105 0.3229 0.0039 0.0357 137.72 15.21 RTHX-234 Staggered 1 0.6202 0.4652 0.9340 1.0831 4 246 100 0.0999 0.2654 0.0037 0.0265 99.05 12.94 RTHX-235 Staggered 1 0.6202 0.4652 0.9358 1.0868 4 241 100 0.0999 0.2608 0.0037 0.0261 97.55 12.68 RTHX-236 Staggered 1 0.6202 0.4652 0.9340 1.0868 4 246 100 0.0966 0.2663 0.0037 0.0257 96.08 12.51 RTHX-237 Staggered 1 0.6217 0.4663 0.9326 1.1796 4 241 100 0.1099 0.2831 0.0037 0.0311 116.04 14.01 RTHX-238 Staggered 1 0.5968 0.4476 0.8969 1.0037 4 246 100 0.0886 0.2459 0.0036 0.0218 78.17 10.63 RTHX-239 Staggered 1 0.6202 0.4652 0.9304 1.1768 4 241 100 0.1105 0.2824 0.0037 0.0312 116.19 14.03 RTHX-240 Staggered 1 0.5938 0.4454 0.8942 0.9953 4 231 100 0.0806 0.2289 0.0036 0.0185 66.02 8.99 RTHX-241 Staggered 1 0.6173 0.4630 0.9296 1.2292 4 251 100 0.1119 0.3073 0.0037 0.0344 127.83 14.65 RTHX-242 Staggered 1 0.6202 0.4652 0.9358 1.0868 4 246 100 0.0946 0.2663 0.0037 0.0252 94.28 12.25 RTHX-243 Staggered 1 0.5938 0.4454 0.8942 0.9865 4 236 100 0.0833 0.2318 0.0036 0.0193 69.07 9.49 RTHX-244 Staggered 1 0.5953 0.4465 0.8973 0.9977 4 236 100 0.0886 0.2345 0.0036 0.0208 74.57 10.14 RTHX-245 Staggered 1 0.6672 0.5004 1.0066 1.3754 4 241 100 0.1105 0.3301 0.0040 0.0365 146.93 16.23 RTHX-246 Staggered 1 0.6217 0.4663 0.9362 1.2088 4 246 100 0.1119 0.2961 0.0037 0.0331 124.07 14.56 RTHX-247 Staggered 1 0.6217 0.4663 0.9326 1.1440 4 236 100 0.1046 0.2688 0.0037 0.0281 104.86 13.05 RTHX-248 Staggered 1 0.5938 0.4454 0.8942 0.9822 4 246 100 0.0747 0.2406 0.0036 0.0180 64.26 8.87 RTHX-249 Staggered 1 0.5938 0.4454 0.8942 0.9987 4 246 100 0.0747 0.2447 0.0036 0.0183 65.34 8.87 RTHX-250 Staggered 1 0.5982 0.4487 0.8991 1.0061 4 231 100 0.0833 0.2314 0.0036 0.0193 69.32 9.42 RTHX-251 Staggered 1 0.6217 0.4663 0.9380 1.0893 4 236 100 0.1046 0.2560 0.0038 0.0268 100.44 13.05 RTHX-252 Staggered 1 0.6173 0.4630 0.9296 1.1649 4 241 100 0.1079 0.2796 0.0037 0.0302 112.16 13.56 RTHX-253 Staggered 1 0.5938 0.4454 0.8942 0.9317 4 231 100 0.0786 0.2143 0.0036 0.0169 60.28 8.77 RTHX-254 Staggered 1 0.6202 0.4652 0.9358 1.0868 4 246 100 0.0966 0.2663 0.0037 0.0257 96.27 12.51 RTHX-255 Staggered 1 0.6393 0.4795 0.9646 1.2973 4 246 100 0.1099 0.3178 0.0039 0.0349 134.75 15.12 RTHX-256 Staggered 1 0.5938 0.4454 0.8908 0.9857 4 236 100 0.0886 0.2316 0.0036 0.0205 73.13 10.09 RTHX-257 Staggered 1 0.6217 0.4663 0.9362 1.2088 4 251 100 0.1119 0.3022 0.0037 0.0338 126.60 14.86 RTHX-258 Staggered 1 0.5938 0.4454 0.8925 0.9987 4 246 100 0.0886 0.2447 0.0036 0.0217 77.41 10.52 RTHX-259 Staggered 1 0.5938 0.4454 0.8942 0.9987 4 241 100 0.0893 0.2397 0.0036 0.0214 76.54 10.39 RTHX-260 Staggered 1 0.5982 0.4487 0.8991 1.0061 4 246 100 0.0886 0.2465 0.0036 0.0218 78.56 10.68 RTHX-261 Staggered 1 0.5953 0.4465 0.8965 1.0160 4 246 100 0.0886 0.2489 0.0036 0.0221 79.10 10.57 RTHX-262 Staggered 1 0.5938 0.4454 0.8942 0.9317 4 231 100 0.0780 0.2143 0.0036 0.0167 59.77 8.69 RTHX-263 Staggered 1 0.6393 0.4795 0.9646 1.3330 4 246 100 0.1105 0.3266 0.0039 0.0361 139.29 15.21 RTHX-264 Staggered 1 0.5938 0.4454 0.8942 0.9953 4 246 100 0.0747 0.2438 0.0036 0.0182 65.11 8.87 RTHX-265 Staggered 1 0.6276 0.4707 0.9450 1.2202 4 241 100 0.1105 0.2928 0.0038 0.0324 122.37 14.36 RTHX-266 Staggered 1 0.6217 0.4663 0.9362 1.2088 4 241 100 0.1105 0.2901 0.0037 0.0321 120.10 14.09 161 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-267 Staggered 1 0.5938 0.4454 0.8942 0.9874 4 236 100 0.0833 0.2320 0.0036 0.0193 69.14 9.49 RTHX-268 Staggered 1 0.5938 0.4454 0.8942 0.9874 4 231 100 0.0886 0.2271 0.0036 0.0201 71.98 9.88 RTHX-269 Staggered 1 0.6202 0.4652 0.9358 1.0868 4 231 100 0.0999 0.2500 0.0037 0.0250 93.48 12.15 RTHX-270 Staggered 1 0.6305 0.4729 0.9559 1.0779 4 246 100 0.0893 0.2641 0.0038 0.0236 90.15 11.95 RTHX-271 Staggered 1 0.6202 0.4652 0.9304 1.2514 4 251 100 0.1099 0.3128 0.0037 0.0344 127.93 14.52 RTHX-272 Staggered 1 0.5938 0.4454 0.8942 0.9987 4 241 100 0.0886 0.2397 0.0036 0.0212 75.97 10.31 RTHX-273 Staggered 1 0.6202 0.4652 0.9358 1.0604 4 231 100 0.0999 0.2439 0.0037 0.0244 91.21 12.15 RTHX-274 Staggered 1 0.6202 0.4652 0.9304 1.2587 4 251 100 0.1119 0.3147 0.0037 0.0352 131.01 14.79 RTHX-275 Staggered 1 0.6217 0.4663 0.9362 1.2088 4 246 100 0.1112 0.2961 0.0037 0.0329 123.34 14.47 RTHX-276 Staggered 1 0.6217 0.4663 0.9326 1.1732 4 241 100 0.1079 0.2816 0.0037 0.0304 113.32 13.76 RTHX-277 Staggered 1 0.6217 0.4663 0.9362 1.0629 4 246 100 0.0893 0.2604 0.0037 0.0232 87.06 11.62 RTHX-278 Staggered 1 0.5938 0.4454 0.8925 0.9987 4 246 100 0.0946 0.2447 0.0036 0.0231 82.63 11.23 RTHX-279 Staggered 1 0.6217 0.4663 0.9362 1.0629 4 236 100 0.0999 0.2498 0.0037 0.0250 93.46 12.47 RTHX-280 Staggered 1 0.6804 0.5103 1.0205 1.4186 4 246 100 0.1099 0.3475 0.0041 0.0382 155.89 17.13 RTHX-281 Staggered 1 0.6188 0.4641 0.9318 1.0543 4 236 100 0.0999 0.2478 0.0037 0.0248 92.26 12.36 RTHX-282 Staggered 1 0.6202 0.4652 0.9322 1.0831 4 246 100 0.0992 0.2654 0.0037 0.0263 98.20 12.86 RTHX-283 Staggered 1 0.6217 0.4663 0.9326 1.2024 4 246 100 0.1066 0.2946 0.0037 0.0314 117.09 13.87 RTHX-284 Staggered 1 0.6202 0.4652 0.9358 1.0831 4 246 100 0.0999 0.2654 0.0037 0.0265 99.25 12.94 RTHX-285 Staggered 1 0.6217 0.4663 0.9326 1.0456 4 246 100 0.0899 0.2562 0.0037 0.0230 85.94 11.71 RTHX-286 Staggered 1 0.5938 0.4454 0.8942 0.9813 4 231 100 0.0786 0.2257 0.0036 0.0177 63.49 8.77 RTHX-287 Staggered 1 0.5953 0.4465 0.8965 0.9977 4 231 100 0.0893 0.2295 0.0036 0.0205 73.46 10.00 RTHX-288 Staggered 1 0.6202 0.4652 0.9304 1.1768 4 241 100 0.1099 0.2824 0.0037 0.0310 115.49 13.94 RTHX-289 Staggered 1 0.5938 0.4454 0.8942 0.9813 4 231 100 0.0780 0.2257 0.0036 0.0176 62.95 8.69 RTHX-290 Staggered 1 0.5953 0.4465 0.8965 1.0012 4 241 100 0.0886 0.2403 0.0036 0.0213 76.35 10.36 RTHX-291 Staggered 1 0.5938 0.4454 0.8925 0.9317 4 231 100 0.0786 0.2143 0.0036 0.0169 60.16 8.77 RTHX-292 Staggered 1 0.6393 0.4795 0.9646 1.2964 4 246 100 0.1119 0.3176 0.0039 0.0355 137.10 15.40 RTHX-293 Staggered 1 0.6202 0.4652 0.9358 1.2587 4 246 100 0.1119 0.3084 0.0037 0.0345 129.14 14.49 RTHX-294 Staggered 1 0.5953 0.4465 0.8930 0.9977 4 246 100 0.0800 0.2444 0.0036 0.0195 69.82 9.54 RTHX-295 Staggered 1 0.6217 0.4663 0.9362 1.2024 4 241 100 0.1099 0.2886 0.0037 0.0317 118.74 14.01 RTHX-296 Staggered 1 0.6202 0.4652 0.9358 1.0868 4 246 100 0.0999 0.2663 0.0037 0.0266 99.58 12.94 RTHX-297 Staggered 1 0.5938 0.4454 0.8916 0.9857 4 231 100 0.0886 0.2267 0.0036 0.0201 71.65 9.88 RTHX-298 Staggered 1 0.5938 0.4454 0.8942 0.9326 4 231 100 0.0786 0.2145 0.0036 0.0169 60.34 8.77 RTHX-299 Staggered 1 0.5968 0.4476 0.8987 0.9870 4 231 100 0.0786 0.2270 0.0036 0.0179 64.18 8.85 RTHX-300 Staggered 1 0.5953 0.4465 0.8930 0.9977 4 231 100 0.0893 0.2295 0.0036 0.0205 73.17 10.00 RTHX-301 Staggered 1 0.5953 0.4465 0.8965 1.0012 4 236 100 0.0893 0.2353 0.0036 0.0210 75.32 10.22 RTHX-302 Staggered 1 0.5938 0.4454 0.8908 0.9822 4 236 100 0.0786 0.2308 0.0036 0.0182 64.67 8.96 RTHX-303 Staggered 1 0.6217 0.4663 0.9326 1.1468 4 241 100 0.1086 0.2752 0.0037 0.0299 111.45 13.84 RTHX-304 Staggered 1 0.6672 0.5004 1.0066 1.3754 4 246 100 0.1119 0.3370 0.0040 0.0377 151.79 16.77 RTHX-305 Staggered 1 0.5938 0.4454 0.8916 0.9987 4 246 100 0.0906 0.2447 0.0036 0.0222 79.07 10.76 RTHX-306 Staggered 1 0.5938 0.4454 0.8925 0.9839 4 231 100 0.0886 0.2263 0.0036 0.0201 71.59 9.88 RTHX-307 Staggered 1 0.5938 0.4454 0.8908 0.9874 4 231 100 0.0886 0.2271 0.0036 0.0201 71.70 9.88 RTHX-308 Staggered 1 0.5938 0.4454 0.8908 0.9874 4 241 100 0.0860 0.2370 0.0036 0.0204 72.58 10.00 RTHX-309 Staggered 1 0.5938 0.4454 0.8942 0.9317 4 231 100 0.0793 0.2143 0.0036 0.0170 60.79 8.84 RTHX-310 Staggered 1 0.6202 0.4652 0.9322 1.0868 4 241 100 0.0999 0.2608 0.0037 0.0261 97.17 12.68 162 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-311 Staggered 1 0.6393 0.4795 0.9721 1.2973 4 246 100 0.1105 0.3178 0.0039 0.0351 136.62 15.21 RTHX-312 Staggered 1 0.6202 0.4652 0.9322 1.1995 4 251 100 0.1066 0.2999 0.0037 0.0320 119.15 14.09 RTHX-313 Staggered 1 0.5938 0.4454 0.8916 0.9953 4 231 100 0.0806 0.2289 0.0036 0.0185 65.83 8.99 RTHX-314 Staggered 1 0.5938 0.4454 0.8942 0.9953 4 246 100 0.0800 0.2438 0.0036 0.0195 69.75 9.50 RTHX-315 Staggered 1 0.5938 0.4454 0.8942 0.9874 4 231 100 0.0833 0.2271 0.0036 0.0189 67.66 9.29 RTHX-316 Staggered 1 0.5938 0.4454 0.8925 0.9865 4 236 100 0.0833 0.2318 0.0036 0.0193 68.94 9.49 RTHX-317 Staggered 1 0.6393 0.4795 0.9646 1.2973 4 246 100 0.1119 0.3178 0.0039 0.0356 137.20 15.40 RTHX-318 Staggered 1 0.6202 0.4652 0.9322 1.0431 4 246 100 0.0899 0.2556 0.0037 0.0230 85.71 11.65 RTHX-319 Staggered 1 0.5968 0.4476 0.9004 0.9590 4 231 100 0.0786 0.2206 0.0036 0.0173 62.48 8.85 RTHX-320 In-line 1 0.7999 0.5999 0.9599 1.0628 11 131 100 0.1422 0.1388 0.0092 0.0197 181.67 45.07 RTHX-321 In-line 1 0.7999 0.5999 0.9599 1.0628 11 113 100 0.1645 0.1200 0.0092 0.0197 181.67 44.98 RTHX-322 In-line 1 0.8000 0.6000 0.9621 1.0629 11 112 100 0.1634 0.1188 0.0092 0.0194 178.68 44.26 RTHX-323 In-line 1 0.7999 0.5999 0.9620 1.0627 11 165 100 0.1107 0.1752 0.0092 0.0194 178.66 44.20 RTHX-324 In-line 1 0.7999 0.5999 0.9620 1.0627 11 165 100 0.1107 0.1752 0.0092 0.0194 178.66 44.20 RTHX-325 In-line 1 0.7999 0.5999 0.9620 1.0627 11 165 100 0.1107 0.1752 0.0092 0.0194 178.66 44.20 RTHX-326 In-line 1 0.7999 0.5999 0.9599 1.0628 11 112 100 0.1614 0.1188 0.0092 0.0192 176.28 43.72 RTHX-327 In-line 1 0.7999 0.5999 0.9598 1.0627 11 129 100 0.1376 0.1376 0.0092 0.0189 174.10 42.93 RTHX-328 In-line 1 0.7999 0.5999 0.9598 1.0627 11 129 100 0.1374 0.1376 0.0092 0.0189 173.83 42.86 RTHX-329 In-line 1 0.7999 0.5999 0.9598 1.0627 11 129 100 0.1374 0.1376 0.0092 0.0189 173.83 42.86 RTHX-330 In-line 1 0.7999 0.5999 0.9620 1.0627 11 112 100 0.1584 0.1188 0.0092 0.0188 173.18 42.91 RTHX-331 In-line 1 0.7999 0.5999 0.9598 1.0452 11 114 100 0.1579 0.1191 0.0092 0.0188 173.03 43.55 RTHX-332 In-line 1 0.8000 0.6000 0.9688 1.0454 11 133 100 0.1346 0.1391 0.0092 0.0187 172.89 43.31 RTHX-333 In-line 1 0.8001 0.6001 0.9623 1.0456 11 113 100 0.1588 0.1179 0.0092 0.0187 172.45 43.41 RTHX-334 In-line 1 0.8001 0.6000 0.9601 1.0455 11 113 100 0.1569 0.1179 0.0092 0.0185 170.20 42.89 RTHX-335 In-line 1 0.8000 0.6000 0.9601 1.0455 11 114 100 0.1553 0.1192 0.0092 0.0185 170.20 42.81 RTHX-336 In-line 1 0.7999 0.6000 0.9599 1.0453 11 113 100 0.1569 0.1179 0.0092 0.0185 170.18 42.89 RTHX-337 In-line 1 0.7999 0.5999 0.9599 1.0453 11 114 100 0.1553 0.1191 0.0092 0.0185 170.18 42.82 RTHX-338 In-line 1 0.7999 0.5999 0.9599 1.0453 11 114 100 0.1553 0.1191 0.0092 0.0185 170.17 42.82 RTHX-339 In-line 1 0.7999 0.5999 0.9598 1.0452 11 113 100 0.1569 0.1179 0.0092 0.0185 170.16 42.90 RTHX-340 In-line 1 0.7999 0.5999 0.9599 1.0365 11 114 100 0.1554 0.1187 0.0092 0.0184 169.66 42.85 RTHX-341 In-line 1 0.8000 0.6000 0.9621 1.0366 11 115 100 0.1549 0.1187 0.0092 0.0184 169.32 43.10 RTHX-342 In-line 1 0.7999 0.5999 0.9621 1.0365 11 114 100 0.1549 0.1187 0.0092 0.0184 169.30 42.73 RTHX-343 In-line 1 0.7999 0.5999 0.9620 1.0365 11 167 100 0.1061 0.1733 0.0092 0.0184 169.29 42.87 RTHX-344 In-line 1 0.7999 0.5999 0.9621 1.0365 11 114 100 0.1540 0.1187 0.0092 0.0183 168.29 42.47 RTHX-345 In-line 1 0.8000 0.6000 0.9600 1.0125 11 158 100 0.1118 0.1605 0.0092 0.0179 164.96 42.71 RTHX-346 In-line 1 0.7999 0.5999 0.9599 1.0124 11 171 100 0.1038 0.1727 0.0092 0.0179 164.95 42.95 RTHX-347 In-line 1 0.7999 0.5999 0.9599 1.0124 11 171 100 0.1038 0.1727 0.0092 0.0179 164.95 42.95 RTHX-348 In-line 1 0.7999 0.5999 0.9621 1.0124 11 114 100 0.1557 0.1150 0.0092 0.0179 164.86 42.94 RTHX-349 In-line 1 0.7999 0.5999 0.9599 1.0124 11 152 100 0.1159 0.1543 0.0092 0.0179 164.47 42.61 RTHX-350 In-line 1 0.7999 0.5999 0.9598 1.0124 11 151 100 0.1168 0.1531 0.0092 0.0179 164.46 42.67 RTHX-351 In-line 1 0.8001 0.6001 0.9601 1.0127 11 152 100 0.1157 0.1543 0.0092 0.0179 164.27 42.53 RTHX-352 In-line 1 0.7999 0.5999 0.9599 1.0124 11 116 100 0.1520 0.1175 0.0092 0.0179 164.23 42.65 RTHX-353 In-line 1 0.7999 0.5999 0.9599 1.0124 11 152 100 0.1157 0.1543 0.0092 0.0179 164.23 42.55 RTHX-354 In-line 1 0.7999 0.5999 0.9599 1.0124 11 115 100 0.1536 0.1162 0.0092 0.0179 164.23 42.73 163 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-355 In-line 1 0.7999 0.5999 0.9599 1.0125 11 115 100 0.1527 0.1162 0.0092 0.0178 163.29 42.48 RTHX-356 In-line 1 0.7999 0.5999 0.9599 1.0125 11 115 100 0.1527 0.1162 0.0092 0.0178 163.29 42.48 RTHX-357 In-line 1 0.7999 0.5999 0.9599 1.0124 11 115 100 0.1527 0.1162 0.0092 0.0178 163.28 42.48 RTHX-358 In-line 1 0.7999 0.5999 0.9598 1.0124 11 115 100 0.1527 0.1162 0.0092 0.0178 163.27 42.49 RTHX-359 In-line 1 0.7999 0.5999 0.9598 1.0124 11 115 100 0.1527 0.1162 0.0092 0.0178 163.27 42.49 RTHX-360 In-line 1 0.8000 0.6000 0.9600 0.9972 11 126 100 0.1415 0.1252 0.0092 0.0177 163.06 43.14 RTHX-361 In-line 1 0.7999 0.5999 0.9599 0.9971 11 126 100 0.1415 0.1252 0.0092 0.0177 163.04 43.14 RTHX-362 In-line 1 0.7999 0.5999 0.9599 0.9971 11 126 100 0.1416 0.1252 0.0092 0.0177 163.04 43.14 RTHX-363 In-line 1 0.7999 0.5999 0.9599 0.9971 11 126 100 0.1407 0.1252 0.0092 0.0176 162.11 42.90 RTHX-364 In-line 1 0.7999 0.5999 0.9643 0.9971 11 116 100 0.1522 0.1155 0.0092 0.0176 161.94 42.70 RTHX-365 In-line 1 0.7999 0.5999 0.9621 0.9971 11 117 100 0.1506 0.1167 0.0092 0.0176 161.79 42.63 RTHX-366 In-line 1 0.7999 0.5999 0.9599 0.9971 11 116 100 0.1518 0.1155 0.0092 0.0175 161.18 42.58 RTHX-367 In-line 1 0.7999 0.5999 0.9599 0.9971 11 116 100 0.1518 0.1155 0.0092 0.0175 161.18 42.58 RTHX-368 In-line 1 0.7999 0.5999 0.9599 0.9949 11 116 100 0.1519 0.1153 0.0092 0.0175 161.18 42.63 RTHX-369 In-line 1 0.7999 0.5999 0.9599 0.9949 11 116 100 0.1519 0.1153 0.0092 0.0175 161.18 42.63 RTHX-370 In-line 1 0.7999 0.5999 0.9599 0.9971 11 126 100 0.1393 0.1252 0.0092 0.0174 160.50 42.47 RTHX-371 In-line 1 0.7999 0.5999 0.9599 0.9949 11 117 100 0.1497 0.1166 0.0092 0.0174 160.49 42.36 RTHX-372 In-line 1 0.7999 0.5999 0.9599 0.9949 11 116 100 0.1513 0.1153 0.0092 0.0174 160.49 42.44 RTHX-373 In-line 1 0.7999 0.5999 0.9599 0.9949 11 116 100 0.1513 0.1153 0.0092 0.0174 160.49 42.44 RTHX-374 In-line 1 0.7999 0.5999 0.9621 0.9927 11 116 100 0.1512 0.1152 0.0092 0.0174 160.41 42.42 RTHX-375 In-line 1 0.7999 0.5999 0.9620 0.9927 11 134 100 0.1305 0.1335 0.0092 0.0174 160.40 42.31 RTHX-376 In-line 1 0.7999 0.5999 0.9620 0.9927 11 116 100 0.1512 0.1152 0.0092 0.0174 160.40 42.43 RTHX-377 In-line 1 0.7999 0.5999 0.9599 0.9840 11 155 100 0.1140 0.1524 0.0092 0.0174 159.81 42.75 RTHX-378 In-line 1 0.7999 0.5999 0.9643 0.9883 11 110 100 0.1584 0.1089 0.0092 0.0173 158.97 42.14 RTHX-379 In-line 1 0.7999 0.5999 0.9642 0.9883 11 110 100 0.1584 0.1089 0.0092 0.0173 158.97 42.14 RTHX-380 In-line 1 0.8000 0.6000 0.9622 0.9797 11 117 100 0.1505 0.1146 0.0092 0.0173 158.85 42.61 RTHX-381 In-line 1 0.7999 0.5999 0.9621 0.9796 11 118 100 0.1490 0.1158 0.0092 0.0173 158.83 42.53 RTHX-382 In-line 1 0.7999 0.5999 0.9620 0.9795 11 173 100 0.1021 0.1690 0.0092 0.0173 158.82 42.71 RTHX-383 In-line 1 0.7999 0.5999 0.9621 0.9796 11 127 100 0.1386 0.1243 0.0092 0.0172 158.62 42.59 RTHX-384 In-line 1 0.7999 0.5999 0.9599 0.9796 11 155 100 0.1129 0.1521 0.0092 0.0172 158.02 42.35 RTHX-385 In-line 1 0.7999 0.5999 0.9598 0.9796 11 155 100 0.1129 0.1521 0.0092 0.0172 158.02 42.35 RTHX-386 In-line 1 0.7999 0.5999 0.9598 0.9795 11 173 100 0.1016 0.1690 0.0092 0.0172 158.02 42.53 RTHX-387 In-line 1 0.7999 0.5999 0.9620 0.9795 11 98 100 0.1779 0.0964 0.0092 0.0172 157.94 42.18 RTHX-388 In-line 1 0.7999 0.5999 0.9620 0.9795 11 117 100 0.1497 0.1146 0.0092 0.0172 157.94 42.38 RTHX-389 In-line 1 0.7999 0.5999 0.9620 0.9664 11 118 100 0.1506 0.1139 0.0092 0.0172 157.94 42.99 RTHX-390 Staggered 1 0.7921 0.5940 1.1939 1.4099 6 390 100 0.4599 0.5499 0.0072 0.2529 1811.36 236.65 RTHX-391 Staggered 1 0.7922 0.5941 1.1940 1.4101 6 390 100 0.4592 0.5499 0.0072 0.2525 1809.11 236.30 RTHX-392 Staggered 1 0.7921 0.5940 1.1939 1.4099 6 390 100 0.4592 0.5499 0.0072 0.2525 1808.67 236.30 RTHX-393 Staggered 1 0.7922 0.5941 1.1894 1.4101 6 390 100 0.4592 0.5499 0.0071 0.2525 1802.07 236.30 RTHX-394 Staggered 1 0.7921 0.5940 1.1892 1.4099 6 390 100 0.4592 0.5499 0.0071 0.2525 1801.63 236.30 RTHX-395 Staggered 1 0.7921 0.5940 1.1881 1.4099 6 390 100 0.4592 0.5499 0.0071 0.2525 1799.87 236.30 RTHX-396 Staggered 1 0.7922 0.5941 1.1894 1.4054 6 390 100 0.4592 0.5481 0.0071 0.2517 1796.14 236.30 RTHX-397 Staggered 1 0.7921 0.5940 1.1892 1.4053 6 390 100 0.4592 0.5480 0.0071 0.2517 1795.69 236.30 RTHX-398 Staggered 1 0.7922 0.5941 1.1894 1.4043 6 390 100 0.4592 0.5477 0.0071 0.2515 1794.65 236.30 164 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-399 Staggered 1 0.7920 0.5940 1.1892 1.4029 6 390 100 0.4592 0.5471 0.0071 0.2512 1792.64 236.30 RTHX-400 Staggered 1 0.7922 0.5941 1.1894 1.4043 6 390 100 0.4578 0.5477 0.0071 0.2507 1789.30 235.59 RTHX-401 Staggered 1 0.7997 0.5997 1.2007 1.4234 6 380 100 0.4517 0.5409 0.0072 0.2443 1759.98 226.46 RTHX-402 Staggered 1 0.7990 0.5993 1.1997 1.4223 6 380 100 0.4517 0.5405 0.0072 0.2441 1757.22 226.46 RTHX-403 Staggered 1 0.7950 0.5962 1.1936 1.4151 6 380 100 0.4544 0.5377 0.0072 0.2443 1749.92 227.83 RTHX-404 Staggered 1 0.7944 0.5958 1.1928 1.4141 6 380 100 0.4544 0.5374 0.0072 0.2442 1747.60 227.83 RTHX-405 Staggered 1 0.7944 0.5958 1.1928 1.4130 6 380 100 0.4537 0.5369 0.0072 0.2436 1743.53 227.49 RTHX-406 Staggered 1 0.7944 0.5958 1.1928 1.4141 6 380 100 0.4517 0.5374 0.0072 0.2427 1737.07 226.46 RTHX-407 Staggered 1 0.7950 0.5962 1.1983 1.4151 6 380 100 0.4489 0.5377 0.0072 0.2414 1735.59 225.09 RTHX-408 Staggered 1 0.7949 0.5962 1.1982 1.4150 6 380 100 0.4489 0.5377 0.0072 0.2414 1735.34 225.09 RTHX-409 Staggered 1 0.7949 0.5962 1.1982 1.4149 6 380 100 0.4489 0.5377 0.0072 0.2414 1735.25 225.09 RTHX-410 Staggered 1 0.7950 0.5962 1.1936 1.4151 6 380 100 0.4489 0.5377 0.0072 0.2414 1728.84 225.09 RTHX-411 Staggered 1 0.7950 0.5962 1.1924 1.4151 6 380 100 0.4489 0.5377 0.0072 0.2414 1727.15 225.09 RTHX-412 Staggered 1 0.7947 0.5960 1.1931 1.4145 6 380 100 0.4482 0.5375 0.0072 0.2409 1724.85 224.75 RTHX-413 Staggered 1 0.7944 0.5958 1.1928 1.4141 6 380 100 0.4482 0.5374 0.0072 0.2409 1723.91 224.75 RTHX-414 Staggered 1 0.7922 0.5941 1.1941 1.4101 6 380 100 0.4489 0.5358 0.0072 0.2406 1723.41 225.09 RTHX-415 Staggered 1 0.7922 0.5941 1.1883 1.4101 6 380 100 0.4489 0.5358 0.0071 0.2406 1715.03 225.09 RTHX-416 Staggered 1 0.7922 0.5941 1.1894 1.4101 6 380 100 0.4482 0.5358 0.0071 0.2402 1714.00 224.75 RTHX-417 Staggered 1 0.7920 0.5940 1.1892 1.4099 6 380 100 0.4482 0.5357 0.0071 0.2401 1713.49 224.75 RTHX-418 Staggered 1 0.7922 0.5941 1.1894 1.4101 6 380 100 0.4469 0.5358 0.0071 0.2394 1708.77 224.06 RTHX-419 Staggered 1 0.7915 0.5936 1.1884 1.4089 6 380 100 0.4462 0.5354 0.0071 0.2389 1703.37 223.72 RTHX-420 Staggered 1 0.7915 0.5936 1.1884 1.4089 6 380 100 0.4462 0.5354 0.0071 0.2389 1703.21 223.72 RTHX-421 Staggered 1 0.7915 0.5936 1.1872 1.4089 6 380 100 0.4462 0.5354 0.0071 0.2389 1701.54 223.72 RTHX-422 Staggered 1 0.7909 0.5932 1.1875 1.4078 6 380 100 0.4462 0.5350 0.0071 0.2387 1700.77 223.72 RTHX-423 Staggered 1 0.7909 0.5932 1.1875 1.4078 6 380 100 0.4462 0.5350 0.0071 0.2387 1700.68 223.72 RTHX-424 Staggered 1 0.7908 0.5931 1.1874 1.4077 6 380 100 0.4462 0.5349 0.0071 0.2387 1700.51 223.72 RTHX-425 Staggered 1 0.7915 0.5936 1.1884 1.4043 6 380 100 0.4469 0.5336 0.0071 0.2385 1700.45 224.06 RTHX-426 Staggered 1 0.7913 0.5934 1.1880 1.4038 6 380 100 0.4469 0.5335 0.0071 0.2384 1699.27 224.06 RTHX-427 Staggered 1 0.7921 0.5940 1.1881 1.4053 6 380 100 0.4462 0.5340 0.0071 0.2383 1698.45 223.72 RTHX-428 Staggered 1 0.7919 0.5939 1.1879 1.4050 6 380 100 0.4462 0.5339 0.0071 0.2382 1697.86 223.72 RTHX-429 Staggered 1 0.7915 0.5936 1.1884 1.4043 6 380 100 0.4462 0.5336 0.0071 0.2381 1697.76 223.72 RTHX-430 Staggered 1 0.7915 0.5936 1.1884 1.4042 6 380 100 0.4462 0.5336 0.0071 0.2381 1697.59 223.72 RTHX-431 Staggered 1 0.7914 0.5936 1.1883 1.4042 6 380 100 0.4462 0.5336 0.0071 0.2381 1697.51 223.72 RTHX-432 Staggered 1 0.7915 0.5936 1.1884 1.4042 6 380 100 0.4455 0.5336 0.0071 0.2377 1694.99 223.37 RTHX-433 Staggered 1 0.7914 0.5936 1.1883 1.4042 6 380 100 0.4455 0.5336 0.0071 0.2377 1694.91 223.37 RTHX-434 Staggered 1 0.7912 0.5934 1.1879 1.4037 6 380 100 0.4448 0.5334 0.0071 0.2373 1691.05 223.03 RTHX-435 Staggered 1 0.7909 0.5932 1.1875 1.4032 6 380 100 0.4448 0.5332 0.0071 0.2372 1690.05 223.03 RTHX-436 Staggered 1 0.7909 0.5932 1.1875 1.4032 6 380 100 0.4448 0.5332 0.0071 0.2372 1689.96 223.03 RTHX-437 Staggered 1 0.7908 0.5931 1.1874 1.4031 6 380 100 0.4448 0.5332 0.0071 0.2372 1689.71 223.03 RTHX-438 Staggered 1 0.7915 0.5936 1.1873 1.4031 6 380 100 0.4448 0.5332 0.0071 0.2372 1689.50 223.03 RTHX-439 Staggered 1 0.7909 0.5932 1.1875 1.4020 6 380 100 0.4448 0.5328 0.0071 0.2370 1688.57 223.03 RTHX-440 Staggered 1 0.7908 0.5931 1.1874 1.4019 6 380 100 0.4448 0.5327 0.0071 0.2370 1688.32 223.03 RTHX-441 Staggered 1 0.7908 0.5931 1.1874 1.4019 6 380 100 0.4448 0.5327 0.0071 0.2370 1688.23 223.03 RTHX-442 Staggered 1 0.7908 0.5931 1.1863 1.4019 6 380 100 0.4448 0.5327 0.0071 0.2370 1686.67 223.03 165 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-443 Staggered 1 0.7903 0.5927 1.1865 1.4009 6 380 100 0.4448 0.5323 0.0071 0.2368 1685.81 223.03 RTHX-444 Staggered 1 0.7909 0.5932 1.1863 1.4020 6 380 100 0.4441 0.5328 0.0071 0.2366 1684.32 222.69 RTHX-445 Staggered 1 0.7909 0.5932 1.1863 1.4020 6 380 100 0.4441 0.5328 0.0071 0.2366 1684.24 222.69 RTHX-446 Staggered 1 0.7908 0.5931 1.1863 1.4019 6 380 100 0.4441 0.5327 0.0071 0.2366 1684.07 222.69 RTHX-447 Staggered 1 0.7906 0.5929 1.1859 1.4015 6 380 100 0.4441 0.5326 0.0071 0.2365 1682.91 222.69 RTHX-448 Staggered 1 0.7909 0.5932 1.1875 1.3986 6 380 100 0.4441 0.5315 0.0071 0.2360 1681.79 222.69 RTHX-449 Staggered 1 0.7906 0.5929 1.1870 1.3980 6 380 100 0.4441 0.5312 0.0071 0.2359 1680.37 222.69 RTHX-450 Staggered 1 0.7903 0.5927 1.1866 1.3975 6 380 100 0.4441 0.5310 0.0071 0.2359 1679.13 222.69 RTHX-451 Staggered 1 0.7902 0.5927 1.1865 1.3974 6 380 100 0.4441 0.5310 0.0071 0.2358 1678.96 222.69 RTHX-452 Staggered 1 0.7907 0.5930 1.1872 1.3959 6 380 100 0.4441 0.5304 0.0071 0.2356 1678.17 222.69 RTHX-453 Staggered 1 0.7909 0.5932 1.1875 1.3940 6 380 100 0.4441 0.5297 0.0071 0.2353 1676.29 222.69 RTHX-454 Staggered 1 0.7908 0.5931 1.1874 1.3938 6 380 100 0.4441 0.5297 0.0071 0.2352 1675.96 222.69 RTHX-455 Staggered 1 0.7914 0.5936 1.1871 1.3937 6 380 100 0.4441 0.5296 0.0071 0.2352 1675.41 222.69 RTHX-456 Staggered 1 0.7909 0.5932 1.1875 1.3928 6 380 100 0.4441 0.5293 0.0071 0.2351 1674.90 222.69 RTHX-457 Staggered 1 0.7909 0.5932 1.1875 1.3928 6 380 100 0.4441 0.5293 0.0071 0.2351 1674.81 222.69 RTHX-458 Staggered 1 0.7908 0.5931 1.1874 1.3927 6 380 100 0.4441 0.5292 0.0071 0.2350 1674.56 222.69 RTHX-459 Staggered 1 0.7907 0.5930 1.1872 1.3925 6 380 100 0.4441 0.5291 0.0071 0.2350 1674.07 222.69 RTHX-460 Staggered 1 0.7907 0.5930 1.1872 1.3924 6 380 100 0.4441 0.5291 0.0071 0.2350 1673.99 222.69 RTHX-461 Staggered 1 0.7921 0.5940 1.1881 1.3913 6 380 100 0.4441 0.5287 0.0071 0.2348 1673.87 222.69 RTHX-462 Staggered 1 0.7909 0.5932 1.1875 1.3893 6 380 100 0.4448 0.5279 0.0071 0.2348 1673.12 223.03 RTHX-463 Staggered 1 0.7909 0.5932 1.1863 1.3893 6 380 100 0.4448 0.5279 0.0071 0.2348 1671.49 223.03 RTHX-464 Staggered 1 0.7914 0.5936 1.1871 1.3902 6 380 100 0.4441 0.5283 0.0071 0.2346 1671.23 222.69 RTHX-465 Staggered 1 0.7909 0.5932 1.1864 1.3893 6 380 100 0.4441 0.5279 0.0071 0.2345 1669.08 222.69 RTHX-466 Staggered 1 0.7909 0.5932 1.1863 1.3893 6 380 100 0.4441 0.5279 0.0071 0.2345 1668.92 222.69 RTHX-467 Staggered 1 0.7909 0.5932 1.1863 1.3881 6 380 100 0.4441 0.5275 0.0071 0.2343 1667.60 222.69 RTHX-468 Staggered 1 0.7909 0.5932 1.1863 1.3881 6 380 100 0.4441 0.5275 0.0071 0.2343 1667.52 222.69 RTHX-469 Staggered 1 0.7901 0.5926 1.1852 1.3868 6 380 100 0.4441 0.5270 0.0071 0.2340 1664.31 222.69 RTHX-470 Staggered 1 0.7901 0.5926 1.1852 1.3856 6 380 100 0.4441 0.5265 0.0071 0.2338 1662.92 222.69 RTHX-471 Staggered 1 0.7915 0.5936 1.1872 1.3810 6 380 100 0.4441 0.5248 0.0071 0.2331 1660.23 222.69 RTHX-472 Staggered 1 0.7909 0.5932 1.1864 1.3800 6 380 100 0.4441 0.5244 0.0071 0.2329 1657.93 222.69 RTHX-473 Staggered 1 0.7907 0.5930 1.1872 1.3774 6 380 100 0.4441 0.5234 0.0071 0.2325 1655.87 222.69 RTHX-474 Staggered 1 0.7909 0.5932 1.1875 1.3754 6 380 100 0.4441 0.5226 0.0071 0.2321 1653.90 222.69 RTHX-475 Staggered 1 0.7908 0.5931 1.1874 1.3753 6 380 100 0.4441 0.5226 0.0071 0.2321 1653.65 222.69 RTHX-476 Staggered 1 0.7907 0.5931 1.1873 1.3751 6 380 100 0.4441 0.5225 0.0071 0.2321 1653.24 222.69 RTHX-477 Staggered 1 0.7907 0.5930 1.1872 1.3751 6 380 100 0.4441 0.5225 0.0071 0.2321 1653.16 222.69 RTHX-478 Staggered 1 0.7907 0.5930 1.1872 1.3750 6 380 100 0.4441 0.5225 0.0071 0.2321 1653.08 222.69 RTHX-479 Staggered 1 0.7915 0.5936 1.1872 1.3717 6 380 100 0.4448 0.5213 0.0071 0.2319 1651.61 223.03 RTHX-480 Staggered 1 0.7914 0.5936 1.1871 1.3717 6 380 100 0.4448 0.5212 0.0071 0.2319 1651.45 223.03 RTHX-481 Staggered 1 0.7909 0.5932 1.1875 1.3708 6 380 100 0.4448 0.5209 0.0071 0.2317 1650.94 223.03 RTHX-482 Staggered 1 0.7909 0.5932 1.1875 1.3707 6 380 100 0.4448 0.5209 0.0071 0.2317 1650.86 223.03 RTHX-483 Staggered 1 0.7909 0.5932 1.1863 1.3707 6 380 100 0.4448 0.5209 0.0071 0.2317 1649.24 223.03 RTHX-484 Staggered 1 0.7908 0.5931 1.1863 1.3706 6 380 100 0.4448 0.5208 0.0071 0.2317 1649.00 223.03 RTHX-485 Staggered 1 0.7914 0.5936 1.1871 1.3717 6 380 100 0.4441 0.5212 0.0071 0.2315 1648.91 222.69 RTHX-486 Staggered 1 0.7909 0.5931 1.1874 1.3707 6 380 100 0.4441 0.5209 0.0071 0.2313 1648.15 222.69 166 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-487 Staggered 1 0.7908 0.5931 1.1874 1.3706 6 380 100 0.4441 0.5208 0.0071 0.2313 1647.99 222.69 RTHX-488 Staggered 1 0.7901 0.5926 1.1852 1.3694 6 380 100 0.4441 0.5204 0.0071 0.2311 1643.45 222.69 RTHX-489 Staggered 1 0.7909 0.5932 1.1863 1.3649 6 380 100 0.4448 0.5187 0.0071 0.2307 1642.27 223.03 RTHX-490 Staggered 1 0.7909 0.5932 1.1864 1.3650 6 380 100 0.4441 0.5187 0.0071 0.2304 1639.82 222.69 RTHX-491 Staggered 1 0.7909 0.5932 1.1863 1.3649 6 380 100 0.4441 0.5187 0.0071 0.2304 1639.66 222.69 RTHX-492 Staggered 1 0.7907 0.5931 1.1861 1.3647 6 380 100 0.4441 0.5186 0.0071 0.2303 1639.09 222.69 RTHX-493 Staggered 1 0.7903 0.5927 1.1854 1.3638 6 380 100 0.4441 0.5183 0.0071 0.2302 1637.07 222.69 RTHX-494 Staggered 1 0.7909 0.5931 1.1874 1.3614 6 380 100 0.4441 0.5173 0.0071 0.2298 1637.00 222.69 RTHX-495 Staggered 1 0.7908 0.5931 1.1874 1.3614 6 380 100 0.4441 0.5173 0.0071 0.2298 1636.92 222.69 RTHX-496 Staggered 1 0.7906 0.5929 1.1859 1.3609 6 380 100 0.4441 0.5171 0.0071 0.2297 1634.19 222.69 RTHX-497 Staggered 1 0.7915 0.5936 1.1872 1.3578 6 380 100 0.4441 0.5160 0.0071 0.2292 1632.33 222.69 RTHX-498 Staggered 1 0.7914 0.5936 1.1871 1.3577 6 380 100 0.4441 0.5159 0.0071 0.2291 1632.17 222.69 RTHX-499 Staggered 1 0.7909 0.5932 1.1864 1.3569 6 380 100 0.4441 0.5156 0.0071 0.2290 1630.07 222.69 RTHX-500 Staggered 1 0.7909 0.5932 1.1863 1.3568 6 380 100 0.4441 0.5156 0.0071 0.2290 1629.91 222.69 RTHX-501 Staggered 1 0.7915 0.5936 1.1872 1.3532 6 380 100 0.4448 0.5142 0.0071 0.2287 1629.25 223.03 RTHX-502 Staggered 1 0.7909 0.5932 1.1863 1.3522 6 380 100 0.4448 0.5138 0.0071 0.2286 1626.92 223.03 RTHX-503 Staggered 1 0.7908 0.5931 1.1863 1.3521 6 380 100 0.4448 0.5138 0.0071 0.2285 1626.68 223.03 RTHX-504 Staggered 1 0.7909 0.5932 1.1875 1.3522 6 380 100 0.4441 0.5138 0.0071 0.2282 1626.01 222.69 RTHX-505 Staggered 1 0.7909 0.5932 1.1863 1.3522 6 380 100 0.4441 0.5138 0.0071 0.2282 1624.42 222.69 RTHX-506 Staggered 1 0.7906 0.5929 1.1859 1.3516 6 380 100 0.4441 0.5136 0.0071 0.2281 1623.05 222.69 RTHX-507 Staggered 1 0.7905 0.5929 1.1857 1.3515 6 380 100 0.4441 0.5136 0.0071 0.2281 1622.73 222.69 RTHX-508 Staggered 1 0.7906 0.5929 1.1859 1.3493 6 380 100 0.4441 0.5127 0.0071 0.2277 1620.27 222.69 RTHX-509 Staggered 1 0.7906 0.5929 1.1859 1.3470 6 380 100 0.4441 0.5119 0.0071 0.2273 1617.48 222.69 RTHX-510 Staggered 1 0.7915 0.5936 1.1884 1.3439 6 380 100 0.4441 0.5107 0.0071 0.2268 1617.17 222.69 RTHX-511 Staggered 1 0.7915 0.5936 1.1872 1.3439 6 380 100 0.4441 0.5107 0.0071 0.2268 1615.59 222.69 RTHX-512 Staggered 1 0.7909 0.5932 1.1875 1.3429 6 380 100 0.4441 0.5103 0.0071 0.2266 1614.85 222.69 RTHX-513 Staggered 1 0.7909 0.5932 1.1863 1.3429 6 380 100 0.4441 0.5103 0.0071 0.2266 1613.27 222.69 RTHX-514 Staggered 1 0.7909 0.5932 1.1863 1.3429 6 380 100 0.4441 0.5103 0.0071 0.2266 1613.19 222.69 RTHX-515 Staggered 1 0.7909 0.5932 1.1864 1.3406 6 380 100 0.4441 0.5094 0.0071 0.2263 1610.57 222.69 RTHX-516 Staggered 1 0.7909 0.5932 1.1863 1.3383 6 380 100 0.4448 0.5085 0.0071 0.2262 1610.18 223.03 RTHX-517 Staggered 1 0.7908 0.5931 1.1863 1.3382 6 380 100 0.4448 0.5085 0.0071 0.2262 1609.94 223.03 RTHX-518 Staggered 1 0.7909 0.5932 1.1863 1.3382 6 380 100 0.4441 0.5085 0.0071 0.2259 1607.62 222.69 RTHX-519 Staggered 1 0.7493 0.5620 1.7461 2.4639 11 478 67/5/28 1.6647 1.1785 0.0182 1.9618 35724.23 1688.45 RTHX-520 Staggered 1 0.7493 0.5620 1.7276 2.4639 11 471 67/5/28 1.6894 1.1612 0.0180 1.9618 35362.15 1688.44 RTHX-521 Staggered 1 0.7478 0.5609 1.7263 2.4590 11 478 67/22/11 1.6679 1.1762 0.0180 1.9618 35333.10 1685.15 RTHX-522 Staggered 1 0.7463 0.5598 1.7229 2.4542 11 477 66/17/17 1.6747 1.1714 0.0180 1.9618 35263.82 1681.84 RTHX-523 Staggered 1 0.7287 0.5466 1.6823 2.3964 11 478 67/22/11 1.7116 1.1462 0.0176 1.9618 34432.45 1642.19 RTHX-524 Staggered 1 0.7229 0.5422 1.6589 2.3771 11 471 67/5/28 1.7511 1.1203 0.0173 1.9618 33961.26 1628.96 RTHX-525 Staggered 1 0.6994 0.5246 1.6146 2.2999 11 474 61/23/16 1.7984 1.0909 0.0168 1.9618 33046.84 1576.10 RTHX-526 Staggered 1 0.7331 0.5499 1.5821 2.4108 11 477 66/17/17 1.7049 1.1507 0.0166 1.9618 32475.19 1652.10 RTHX-527 Staggered 1 0.7331 0.5499 1.5781 2.4108 11 477 66/17/17 1.7049 1.1507 0.0165 1.9618 32396.46 1652.10 RTHX-528 Staggered 1 0.7302 0.5477 1.5558 2.4072 11 477 66/23/11 1.7074 1.1490 0.0163 1.9618 31953.20 1641.40 RTHX-529 Staggered 1 0.7126 0.5345 1.5202 2.3433 11 477 66/17/17 1.7540 1.1185 0.0159 1.9618 31221.51 1605.85 RTHX-530 Staggered 1 0.7111 0.5334 1.5152 2.3385 11 471 84/8/8 1.7800 1.1021 0.0159 1.9618 31119.08 1602.53 167 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-531 Staggered 1 0.7126 0.5345 1.5124 2.3297 11 478 67/20/13 1.7605 1.1143 0.0158 1.9618 31068.46 1615.25 RTHX-532 Staggered 1 0.7126 0.5345 1.5124 2.3297 11 477 22/47/31 1.7642 1.1120 0.0158 1.9618 31068.46 1615.25 RTHX-533 Staggered 1 0.7302 0.5477 1.4858 2.4012 11 477 66/17/17 1.7117 1.1461 0.0156 1.9618 30580.92 1645.50 RTHX-534 Staggered 1 0.7126 0.5345 1.4500 2.3433 11 477 66/23/11 1.7540 1.1185 0.0152 1.9618 29844.03 1605.85 RTHX-535 Staggered 1 0.7229 0.5422 1.4313 2.3850 11 471 84/8/8 1.7453 1.1241 0.0150 1.9618 29497.59 1623.56 RTHX-536 Staggered 1 0.7009 0.5257 1.4261 2.3048 11 478 67/29/4 1.7796 1.1024 0.0150 1.9618 29352.77 1579.41 RTHX-537 Staggered 1 0.7229 0.5422 1.4076 2.3771 11 486 45/33/22 1.6971 1.1560 0.0148 1.9618 29031.82 1628.99 RTHX-538 Staggered 1 0.7170 0.5378 1.4021 2.3578 11 477 66/17/17 1.7432 1.1254 0.0147 1.9618 28911.77 1615.76 RTHX-539 Staggered 1 0.7111 0.5334 1.3906 2.3385 11 478 64/22/14 1.7539 1.1185 0.0146 1.9618 28675.27 1602.54 RTHX-540 Staggered 1 0.6994 0.5246 1.3677 2.2999 11 478 67/29/4 1.7833 1.1001 0.0144 1.9618 28202.28 1576.11 RTHX-541 Staggered 1 0.7126 0.5345 1.3642 2.3297 11 478 67/22/11 1.7605 1.1143 0.0144 1.9618 28160.44 1615.25 RTHX-542 Staggered 1 0.6994 0.5246 1.3849 2.3076 11 477 66/20/14 1.7555 1.1014 0.0145 1.9336 28129.83 1548.29 RTHX-543 Staggered 1 0.7126 0.5345 1.3622 2.3277 11 478 67/22/11 1.7620 1.1134 0.0143 1.9618 28122.18 1616.61 RTHX-544 Staggered 1 0.7302 0.5477 1.3199 2.4092 11 478 67/17/16 1.7025 1.1523 0.0139 1.9618 27326.65 1640.04 RTHX-545 Staggered 1 0.7302 0.5477 1.3199 2.4012 11 567 66/19/15 1.4401 1.3622 0.0139 1.9618 27326.65 1645.66 RTHX-546 Staggered 1 0.7287 0.5466 1.3093 2.3964 11 474 22/52/26 1.7260 1.1366 0.0138 1.9618 27115.26 1642.19 RTHX-547 Staggered 1 0.7331 0.5499 1.3252 2.4108 11 478 90/6/4 1.6768 1.1531 0.0140 1.9336 27041.83 1628.35 RTHX-548 Staggered 1 0.7214 0.5411 1.3040 2.3723 11 478 90/5/5 1.7041 1.1347 0.0138 1.9336 26609.16 1602.29 RTHX-549 Staggered 1 0.7302 0.5477 1.1740 2.4092 11 567 66/23/11 1.4354 1.3667 0.0125 1.9618 24464.46 1640.20 RTHX-550 Staggered 1 0.7302 0.5477 1.1720 2.4072 11 567 66/23/11 1.4366 1.3656 0.0125 1.9618 24425.25 1641.57 RTHX-551 Staggered 1 0.7067 0.5301 1.1499 2.3240 11 477 66/5/29 1.7685 1.1093 0.0122 1.9618 23944.09 1592.63 RTHX-552 Staggered 1 0.7111 0.5334 1.1414 2.3385 11 477 66/23/11 1.7576 1.1162 0.0121 1.9618 23787.64 1602.54 RTHX-553 Staggered 1 0.7111 0.5334 1.1356 2.3385 11 461 2/48/50 1.8185 1.0788 0.0121 1.9618 23673.09 1602.51 RTHX-554 Staggered 1 0.6877 0.5158 1.1038 2.2614 11 465 66/23/11 1.8644 1.0522 0.0117 1.9618 23002.89 1549.65 RTHX-555 Staggered 1 0.7302 0.5477 1.0641 2.4092 11 477 21/52/27 1.7060 1.1499 0.0114 1.9618 22308.01 1640.04 RTHX-556 Staggered 1 0.7111 0.5334 1.0091 2.3346 11 461 2/48/50 1.8216 1.0770 0.0108 1.9618 21191.09 1605.18 RTHX-557 Staggered 1 0.6994 0.5246 0.9944 2.2827 11 496 66/17/17 1.7316 1.1329 0.0106 1.9618 20879.10 1588.04 RTHX-558 Staggered 1 0.6994 0.5246 1.0020 2.2616 11 567 32/34/34 1.5070 1.2831 0.0107 1.9336 20726.89 1579.88 RTHX-559 Staggered 1 0.6994 0.5246 0.9944 2.2616 11 567 32/34/34 1.5070 1.2831 0.0106 1.9336 20578.84 1579.88 RTHX-560 In-line 1 0.5293 0.3970 0.8293 1.2828 21 1160 36/54/10 1.1801 1.4886 0.0171 1.7567 30067.74 2767.71 RTHX-561 In-line 1 0.5191 0.3893 0.8132 1.2579 21 1160 36/54/10 1.2035 1.4597 0.0168 1.7567 29484.71 2714.04 RTHX-562 In-line 1 0.5059 0.3794 0.7926 1.2259 21 1160 90/9/1 1.2349 1.4226 0.0164 1.7567 28735.10 2645.04 RTHX-563 In-line 1 0.5000 0.3750 0.7834 1.2008 21 1167 8/56/36 1.2532 1.4018 0.0162 1.7567 28401.94 2638.21 RTHX-564 In-line 1 0.5015 0.3761 0.7802 1.1933 21 1160 87/7/6 1.2686 1.3848 0.0161 1.7567 28292.34 2670.28 RTHX-565 In-line 1 0.5000 0.3750 0.7779 1.1898 21 1160 89/9/2 1.2723 1.3807 0.0161 1.7567 28209.61 2662.47 RTHX-566 In-line 1 0.5015 0.3761 0.7857 1.1796 20 978 8/46/46 1.4739 1.1541 0.0162 1.7011 27584.21 2491.16 RTHX-567 In-line 1 0.5000 0.3750 0.7834 1.1761 20 985 64/30/6 1.4678 1.1590 0.0162 1.7011 27503.55 2483.88 RTHX-568 In-line 1 0.5000 0.3750 0.7779 1.2008 20 1160 90/9/1 1.1414 1.3934 0.0161 1.5905 25540.01 2274.80 RTHX-569 In-line 1 0.5059 0.3794 0.7926 1.1927 21 1160 87/11/2 1.0972 1.3841 0.0164 1.5186 24840.39 2350.22 RTHX-570 In-line 1 0.5000 0.3750 0.7779 1.1789 21 1160 81/10/9 1.0977 1.3680 0.0161 1.5017 24113.76 2297.03 RTHX-571 In-line 1 0.5088 0.3816 0.7972 1.2080 20 1348 66/28/6 0.8920 1.6289 0.0165 1.4530 23904.40 2139.18 RTHX-572 In-line 1 0.5000 0.3750 0.7779 1.1885 22 1160 90/5/5 1.0258 1.3791 0.0168 1.4147 23818.77 2248.87 RTHX-573 In-line 1 0.5000 0.3750 0.7943 1.1789 21 1160 87/11/2 1.0621 1.3680 0.0164 1.4530 23809.22 2222.56 RTHX-574 In-line 1 0.5073 0.3805 0.7935 1.1795 21 1160 84/14/2 1.0615 1.3687 0.0164 1.4530 23795.16 2286.99 168 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-575 Staggered 2 0.6188 0.4641 1.9094 1.9873 15 404 43/57 0.4568 0.8035 0.0274 0.3670 10038.86 364.19 RTHX-576 Staggered 2 0.6188 0.4641 1.9094 1.9873 15 392 40/60 0.4719 0.7778 0.0273 0.3670 10015.07 363.32 RTHX-577 Staggered 2 0.6173 0.4630 1.9049 1.9826 14 409 42/58 0.4516 0.8127 0.0273 0.3670 10004.05 340.21 RTHX-578 Staggered 2 0.6188 0.4641 1.9026 1.9856 14 392 43/57 0.4708 0.7796 0.0254 0.3670 9307.83 339.91 RTHX-579 Staggered 2 0.6188 0.4641 1.7671 1.9873 15 409 37/63 0.4512 0.8134 0.0251 0.3670 9220.80 364.20 RTHX-580 Staggered 2 0.6188 0.4641 1.7502 1.9873 14 403 20/80 0.4579 0.8015 0.0247 0.3670 9081.55 339.91 RTHX-581 Staggered 2 0.6188 0.4641 1.7231 1.9873 15 409 42/58 0.4512 0.8134 0.0244 0.3670 8942.31 364.20 RTHX-582 Staggered 2 0.6188 0.4641 1.6960 1.9873 14 407 20/80 0.4534 0.8095 0.0243 0.3670 8924.90 339.92 RTHX-583 Staggered 2 0.6188 0.4641 1.6926 1.9873 15 409 43/57 0.4523 0.8115 0.0241 0.3670 8860.34 363.33 RTHX-584 Staggered 2 0.6173 0.4630 1.6802 1.9826 14 403 42/58 0.4579 0.8015 0.0240 0.3670 8803.07 339.91 RTHX-585 Staggered 2 0.6188 0.4641 1.6689 1.9873 14 400 43/57 0.4618 0.7949 0.0238 0.3670 8750.85 340.20 RTHX-586 Staggered 2 0.6188 0.4641 1.6588 1.9856 15 403 88/12 0.4583 0.8008 0.0237 0.3670 8707.34 364.50 RTHX-587 Staggered 2 0.6188 0.4641 1.6503 1.9856 15 410 20/80 0.4501 0.8154 0.0236 0.3670 8646.42 364.20 RTHX-588 Staggered 2 0.6188 0.4641 1.6384 1.9873 15 403 43/57 0.4590 0.7996 0.0235 0.3670 8625.93 363.33 RTHX-589 Staggered 2 0.6173 0.4630 1.6346 1.9826 15 410 20/80 0.4501 0.8154 0.0234 0.3670 8594.20 364.20 RTHX-590 Staggered 2 0.6188 0.4641 1.6283 1.9873 14 392 42/58 0.4943 0.7425 0.0232 0.3670 8531.96 328.73 RTHX-591 Staggered 2 0.5938 0.4454 1.6179 1.8926 15 409 42/58 0.4468 0.8134 0.0234 0.3634 8509.56 360.61 RTHX-592 Staggered 2 0.6188 0.4641 1.6283 1.9873 14 392 42/58 0.4943 0.7425 0.0227 0.3670 8331.51 328.73 RTHX-593 Staggered 2 0.5938 0.4454 1.5789 1.8926 13 404 20/80 0.4780 0.7678 0.0227 0.3670 8329.30 342.94 RTHX-594 Staggered 2 0.6305 0.4729 1.6971 1.8990 13 409 43/57 0.4811 0.7629 0.0227 0.3670 8319.80 336.56 RTHX-595 Staggered 2 0.6188 0.4641 1.6960 1.8637 13 397 42/58 0.4968 0.7387 0.0227 0.3670 8316.21 335.75 RTHX-596 Staggered 2 0.6173 0.4630 1.6954 1.8593 14 409 43/57 0.4789 0.7665 0.0226 0.3670 8310.51 364.17 RTHX-597 Staggered 2 0.6217 0.4663 1.6938 1.8725 13 404 20/80 0.4871 0.7535 0.0226 0.3670 8303.63 336.56 RTHX-598 Staggered 2 0.6188 0.4641 1.6926 1.8637 13 410 20/80 0.4800 0.7647 0.0225 0.3670 8271.31 336.56 RTHX-599 Staggered 2 0.6188 0.4641 1.6859 1.8637 13 409 43/57 0.4823 0.7611 0.0225 0.3670 8251.71 335.76 RTHX-600 Staggered 2 0.6173 0.4630 1.6819 1.8593 13 409 44/56 0.4789 0.7665 0.0225 0.3670 8245.55 338.15 RTHX-601 Staggered 2 0.6217 0.4663 1.6802 1.8725 13 404 42/58 0.4825 0.7607 0.0224 0.3670 8219.19 339.75 RTHX-602 Staggered 2 0.6246 0.4685 1.6745 1.8813 13 409 43/57 0.4811 0.7629 0.0224 0.3670 8206.66 336.56 RTHX-603 Staggered 2 0.6188 0.4641 1.6723 1.8637 13 409 42/58 0.4811 0.7629 0.0222 0.3670 8142.01 336.56 RTHX-604 Staggered 2 0.6188 0.4641 1.6588 1.8637 13 404 42/58 0.4825 0.7607 0.0222 0.3670 8137.61 339.75 RTHX-605 Staggered 2 0.6246 0.4685 1.6574 1.8813 13 404 88/12 0.4871 0.7535 0.0219 0.3670 8045.04 336.56 RTHX-606 Staggered 2 0.6188 0.4641 1.6384 1.8637 13 409 43/57 0.4811 0.7629 0.0219 0.3670 8036.96 336.56 RTHX-607 Staggered 2 0.6188 0.4641 1.6367 1.8637 14 409 43/57 0.4811 0.7629 0.0218 0.3670 8012.71 362.45 RTHX-608 Staggered 2 0.6188 0.4641 1.6317 1.8637 13 409 42/58 0.4811 0.7629 0.0216 0.3670 7939.98 336.56 RTHX-609 Staggered 2 0.6188 0.4641 1.6164 1.8637 14 409 20/80 0.4396 0.8349 0.0168 0.3670 6174.83 331.17 RTHX-610 In-line 2 0.6158 0.4619 0.7424 1.1688 24 306 85/15 0.4368 0.8200 0.0177 0.3581 6335.63 784.74 RTHX-611 In-line 2 0.6276 0.4707 0.7531 1.1705 22 307 85/15 0.4377 0.8223 0.0172 0.3599 6188.33 751.59 RTHX-612 In-line 2 0.6158 0.4619 0.7390 1.1486 22 313 85/15 0.4460 0.8069 0.0169 0.3599 6072.66 724.10 RTHX-613 In-line 2 0.5748 0.4311 0.6897 1.0736 24 339 62/38 0.4277 0.8498 0.0164 0.3634 5974.31 784.86 RTHX-614 In-line 2 0.6158 0.4619 0.7390 1.1486 22 302 85/15 0.4292 0.8069 0.0169 0.3464 5844.66 698.66 RTHX-615 In-line 2 0.6158 0.4619 0.7424 1.1587 23 291 85/15 0.4144 0.8129 0.0169 0.3369 5709.57 708.99 RTHX-616 In-line 2 0.5777 0.4333 0.6933 1.0459 23 338 85/15 0.4264 0.8279 0.0158 0.3530 5587.75 738.06 RTHX-617 In-line 2 0.5748 0.4311 0.6929 1.0406 24 324 74/26 0.4116 0.8185 0.0165 0.3369 5562.35 722.47 RTHX-618 In-line 2 0.5748 0.4311 0.6897 1.0185 22 343 85/15 0.4209 0.8307 0.0157 0.3497 5506.70 711.58 169 Design Tag Arrangement Slabs Do Di Pl Pt Nr Nt Pass Config. l H d Af V Vmat’l - - mm mm mm mm - - % m m m m² cm³ cm³ RTHX-619 In-line 2 0.5733 0.4300 0.6880 1.0159 22 344 85/15 0.4220 0.8286 0.0157 0.3497 5492.66 708.20 Table 31. Optimum RTHX performance and operating conditions. Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-001 DP I Water Radiator 0.03 1.32 25.00 300.00 342.00 200.00 Liquid 308.77 27.25 1.035 1.000 RTHX-002 DP I Water Radiator 0.03 1.41 25.00 300.00 342.00 200.00 Liquid 323.42 34.92 1.449 1.005 RTHX-003 DP I Water Radiator 0.03 1.41 25.00 300.00 342.00 200.00 Liquid 323.02 34.84 1.442 1.005 RTHX-004 DP I Water Radiator 0.03 1.41 25.00 300.00 342.00 200.00 Liquid 322.73 34.78 1.437 1.005 RTHX-005 DP I Water Radiator 0.03 1.40 25.00 300.00 342.00 200.00 Liquid 322.30 34.41 1.442 1.004 RTHX-006 DP I Water Radiator 0.03 1.40 25.00 300.00 342.00 200.00 Liquid 321.59 33.98 1.442 1.003 RTHX-007 DP I Water Radiator 0.03 1.40 25.00 300.00 342.00 200.00 Liquid 322.41 33.68 1.451 1.004 RTHX-008 DP I Water Radiator 0.03 1.40 25.00 300.00 342.00 200.00 Liquid 321.60 33.65 1.451 1.003 RTHX-009 DP I Water Radiator 0.03 1.38 25.00 300.00 342.00 200.00 Liquid 320.24 33.61 1.464 1.008 RTHX-010 DP I Water Radiator 0.03 1.38 25.00 300.00 342.00 200.00 Liquid 321.74 30.87 0.422 1.004 RTHX-011 DP I Water Radiator 0.03 1.38 25.00 300.00 342.00 200.00 Liquid 321.71 30.87 0.422 1.004 RTHX-012 DP I Water Radiator 0.03 1.35 25.00 300.00 342.00 200.00 Liquid 315.74 28.04 0.385 1.001 RTHX-013 DP I Water Radiator 0.03 1.35 25.00 300.00 342.00 200.00 Liquid 315.65 28.04 0.385 1.001 RTHX-014 DP I Water Radiator 0.03 1.33 25.00 300.00 342.00 200.00 Liquid 313.71 27.41 0.391 1.005 RTHX-015 DP I Water Radiator 0.03 1.33 25.00 300.00 342.00 200.00 Liquid 313.71 27.41 0.391 1.005 RTHX-016 DP I Water Radiator 0.03 1.33 25.00 300.00 342.00 200.00 Liquid 308.80 27.25 1.035 1.000 RTHX-017 DP I Water Radiator 0.03 1.33 25.00 300.00 342.00 200.00 Liquid 312.91 27.09 0.391 1.004 RTHX-018 DP I Water Radiator 0.03 1.32 25.00 300.00 342.00 200.00 Liquid 309.91 25.95 0.412 1.001 RTHX-019 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 308.50 25.47 0.396 1.005 RTHX-020 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 308.19 25.33 0.396 1.004 RTHX-021 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 304.81 25.24 0.396 1.000 RTHX-022 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 305.70 25.23 0.395 1.001 RTHX-023 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 305.69 25.22 0.395 1.001 RTHX-024 DP I Water Radiator 0.03 1.29 25.00 300.00 342.00 200.00 Liquid 307.09 24.99 0.467 1.006 RTHX-025 DP I Water Radiator 0.03 1.29 25.00 300.00 342.00 200.00 Liquid 306.50 24.65 0.470 1.005 RTHX-026 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 305.65 24.34 0.468 1.004 RTHX-027 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 305.65 24.33 0.468 1.004 RTHX-028 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 305.61 24.33 0.468 1.004 RTHX-029 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 305.61 24.33 0.468 1.004 RTHX-030 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 305.43 24.30 0.467 1.004 RTHX-031 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 305.39 24.29 0.467 1.004 RTHX-032 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 302.48 23.93 1.386 1.000 RTHX-033 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 302.48 23.93 1.386 1.000 RTHX-034 DP I Water Radiator 0.03 1.27 25.00 300.00 342.00 200.00 Liquid 304.30 23.83 0.472 1.005 RTHX-035 DP I Water Radiator 0.03 1.27 25.00 300.00 342.00 200.00 Liquid 303.33 23.77 0.457 1.004 170 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-036 DP I Water Radiator 0.03 1.27 25.00 300.00 342.00 200.00 Liquid 303.10 23.73 0.455 1.004 RTHX-037 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 300.36 22.29 0.470 1.001 RTHX-038 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 300.32 22.29 0.470 1.001 RTHX-039 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 300.29 22.28 0.469 1.001 RTHX-040 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 299.93 22.25 0.469 1.000 RTHX-041 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 299.91 22.25 0.469 1.000 RTHX-042 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 299.87 22.25 0.469 1.000 RTHX-043 DP I Water Radiator 0.03 1.25 25.00 300.00 342.00 200.00 Liquid 299.30 22.09 0.393 1.001 RTHX-044 DP I Water Radiator 0.03 1.25 25.00 300.00 342.00 200.00 Liquid 299.21 22.08 0.393 1.001 RTHX-045 DP I Water Radiator 0.03 1.24 25.00 300.00 342.00 200.00 Liquid 298.83 21.76 0.478 1.007 RTHX-046 DP I Water Radiator 0.03 1.23 25.00 300.00 342.00 200.00 Liquid 297.37 21.14 0.481 1.004 RTHX-047 DP I Water Radiator 0.03 1.23 25.00 300.00 342.00 200.00 Liquid 296.87 21.11 0.480 1.004 RTHX-048 DP I Water Radiator 0.03 1.23 25.00 300.00 342.00 200.00 Liquid 297.15 21.10 0.480 1.004 RTHX-049 DP I Water Radiator 0.03 1.23 25.00 300.00 342.00 200.00 Liquid 296.97 21.08 0.478 1.004 RTHX-050 DP I Water Radiator 0.03 1.22 25.00 300.00 342.00 200.00 Liquid 296.49 20.92 0.457 1.007 RTHX-051 DP I Water Radiator 0.03 1.22 25.00 300.00 342.00 200.00 Liquid 295.92 20.88 0.448 1.005 RTHX-052 DP I Water Radiator 0.03 1.22 25.00 300.00 342.00 200.00 Liquid 295.67 20.79 0.451 1.007 RTHX-053 DP I Water Radiator 0.03 1.22 25.00 300.00 342.00 200.00 Liquid 295.48 20.79 0.451 1.007 RTHX-054 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 293.13 20.77 0.443 1.011 RTHX-055 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 292.83 20.56 0.443 1.011 RTHX-056 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 292.68 20.54 0.442 1.011 RTHX-057 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 292.84 20.26 0.442 1.011 RTHX-058 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 291.77 20.21 0.442 1.010 RTHX-059 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 293.20 20.12 0.469 1.013 RTHX-060 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 293.15 20.12 0.469 1.013 RTHX-061 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 293.14 20.12 0.469 1.013 RTHX-062 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 293.15 20.02 0.447 1.014 RTHX-063 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 293.11 20.01 0.447 1.014 RTHX-064 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 289.98 19.88 0.431 1.010 RTHX-065 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 289.97 19.88 0.431 1.010 RTHX-066 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 289.92 19.87 0.431 1.010 RTHX-067 DP I Water Radiator 0.03 1.18 25.00 300.00 342.00 200.00 Liquid 286.29 18.30 0.445 1.002 RTHX-068 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 285.95 18.25 0.443 1.002 RTHX-069 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 285.93 18.25 0.442 1.002 RTHX-070 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 286.80 18.04 0.444 1.003 RTHX-071 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 286.02 18.02 0.444 1.002 RTHX-072 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 286.58 18.01 0.442 1.003 RTHX-073 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 285.93 18.00 0.443 1.002 RTHX-074 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 286.36 17.90 0.470 1.004 RTHX-075 DP I Water Radiator 0.03 1.16 25.00 300.00 342.00 200.00 Liquid 286.04 17.86 0.446 1.005 RTHX-076 DP I Water Radiator 0.03 1.16 25.00 300.00 342.00 200.00 Liquid 284.21 17.79 0.445 1.002 RTHX-077 DP I Water Radiator 0.03 1.16 25.00 300.00 342.00 200.00 Liquid 284.11 17.79 0.445 1.002 RTHX-078 DP I Water Radiator 0.03 1.16 25.00 300.00 342.00 200.00 Liquid 284.19 17.78 0.431 1.002 RTHX-079 DP I Water Radiator 0.03 1.16 25.00 300.00 342.00 200.00 Liquid 284.14 17.77 0.431 1.002 171 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-080 DP I Water Radiator 0.03 1.16 25.00 300.00 342.00 200.00 Liquid 285.22 17.76 0.436 1.006 RTHX-081 DP I Water Radiator 0.03 1.16 25.00 300.00 342.00 200.00 Liquid 283.38 17.60 0.434 1.004 RTHX-082 DP I Water Radiator 0.03 1.15 25.00 300.00 342.00 200.00 Liquid 284.51 17.49 0.436 1.010 RTHX-083 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 284.44 17.44 0.433 1.011 RTHX-084 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 284.37 17.43 0.432 1.011 RTHX-085 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 282.16 17.31 0.455 1.007 RTHX-086 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 282.69 17.29 0.431 1.008 RTHX-087 DP I Water Radiator 0.03 1.13 25.00 300.00 342.00 200.00 Liquid 280.31 16.62 0.431 1.005 RTHX-088 DP I Water Radiator 0.03 1.12 25.00 300.00 342.00 200.00 Liquid 277.94 15.65 0.432 1.002 RTHX-089 DP I Water Radiator 0.03 1.12 25.00 300.00 342.00 200.00 Liquid 276.71 15.61 0.432 1.000 RTHX-090 DP I Water Radiator 0.03 1.12 25.00 300.00 342.00 200.00 Liquid 276.57 15.49 0.423 1.002 RTHX-091 DP I Water Radiator 0.03 1.11 25.00 300.00 342.00 200.00 Liquid 275.71 15.43 0.420 1.001 RTHX-092 DP I Water Radiator 0.03 1.11 25.00 300.00 342.00 200.00 Liquid 275.15 15.43 0.422 1.000 RTHX-093 DP I Water Radiator 0.03 1.11 25.00 300.00 342.00 200.00 Liquid 274.90 15.40 0.420 1.000 RTHX-094 DP I Water Radiator 0.03 1.09 25.00 300.00 342.00 200.00 Liquid 272.37 14.48 0.439 1.002 RTHX-095 DP I Water Radiator 0.03 1.08 25.00 300.00 342.00 200.00 Liquid 271.89 14.28 0.442 1.004 RTHX-096 DP I Water Radiator 0.03 1.08 25.00 300.00 342.00 200.00 Liquid 271.79 14.27 0.443 1.004 RTHX-097 DP I Water Radiator 0.03 1.08 25.00 300.00 342.00 200.00 Liquid 271.63 14.26 0.443 1.004 RTHX-098 DP I Water Radiator 0.03 1.08 25.00 300.00 342.00 200.00 Liquid 271.19 14.23 0.442 1.003 RTHX-099 DP I Water Radiator 0.03 1.08 25.00 300.00 342.00 200.00 Liquid 271.13 14.23 0.443 1.003 RTHX-100 DP I Water Radiator 0.03 1.06 25.00 300.00 342.00 200.00 Liquid 268.84 13.76 0.410 1.010 RTHX-101 DP I Water Radiator 0.03 1.05 25.00 300.00 342.00 200.00 Liquid 268.34 13.67 0.434 1.013 RTHX-102 DP I Water Radiator 0.03 1.05 25.00 300.00 342.00 200.00 Liquid 268.49 13.67 0.404 1.011 RTHX-103 DP I Water Radiator 0.03 1.05 25.00 300.00 342.00 200.00 Liquid 268.62 13.62 0.434 1.013 RTHX-104 DP I Water Radiator 0.03 1.04 25.00 300.00 342.00 200.00 Liquid 264.52 13.29 0.409 1.008 RTHX-105 DP I Water Radiator 0.03 1.04 25.00 300.00 342.00 200.00 Liquid 263.52 12.72 0.411 1.002 RTHX-106 DP I Water Radiator 0.03 1.04 25.00 300.00 342.00 200.00 Liquid 264.13 12.67 0.410 1.004 RTHX-107 DP I Water Radiator 0.03 1.04 25.00 300.00 342.00 200.00 Liquid 264.11 12.67 0.410 1.004 RTHX-108 DP I Water Radiator 0.03 1.03 25.00 300.00 342.00 200.00 Liquid 263.01 12.27 0.412 1.001 RTHX-109 DP I Water Radiator 0.03 1.03 25.00 300.00 342.00 200.00 Liquid 262.96 12.26 0.412 1.001 RTHX-110 DP I Water Radiator 0.03 1.03 25.00 300.00 342.00 200.00 Liquid 262.77 12.25 0.411 1.001 RTHX-111 DP I Water Radiator 0.03 1.03 25.00 300.00 342.00 200.00 Liquid 262.08 12.22 0.410 1.001 RTHX-112 DP I Water Radiator 0.03 1.03 25.00 300.00 342.00 200.00 Liquid 262.48 12.22 0.410 1.001 RTHX-113 DP I Water Radiator 0.03 1.01 25.00 300.00 342.00 200.00 Liquid 260.09 11.73 1.337 1.008 RTHX-114 DP I Water Radiator 0.03 1.00 25.00 300.00 342.00 200.00 Liquid 254.67 11.19 1.340 1.000 RTHX-115 DP I Water Radiator 0.03 1.00 25.00 300.00 342.00 200.00 Liquid 254.62 11.19 1.339 1.000 RTHX-116 DP I Water Radiator 0.03 1.00 25.00 300.00 342.00 200.00 Liquid 254.57 11.18 1.338 1.000 RTHX-117 DP I Water Radiator 0.03 1.00 25.00 300.00 342.00 200.00 Liquid 254.32 11.16 1.332 1.000 RTHX-118 DP I Water Radiator 0.03 0.98 25.00 300.00 342.00 200.00 Liquid 253.72 10.96 1.357 1.005 RTHX-119 DP I Water Radiator 0.03 0.98 25.00 300.00 342.00 200.00 Liquid 253.72 10.96 1.357 1.005 RTHX-120 DP I Water Radiator 0.03 0.98 25.00 300.00 342.00 200.00 Liquid 253.71 10.96 1.357 1.005 RTHX-121 DP I Water Radiator 0.03 0.98 25.00 300.00 342.00 200.00 Liquid 253.28 10.95 1.357 1.004 RTHX-122 DP I Water Radiator 0.03 0.97 25.00 300.00 342.00 200.00 Liquid 251.99 10.67 1.370 1.005 RTHX-123 DP I Water Radiator 0.03 0.97 25.00 300.00 342.00 200.00 Liquid 251.73 10.65 1.364 1.005 172 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-124 DP I Water Radiator 0.03 0.97 25.00 300.00 342.00 200.00 Liquid 252.43 10.31 1.357 1.003 RTHX-125 DP I Water Radiator 0.03 0.97 25.00 300.00 342.00 200.00 Liquid 250.90 10.10 1.359 1.000 RTHX-126 DP I Water Radiator 0.03 0.94 25.00 300.00 342.00 200.00 Liquid 249.39 9.66 0.403 1.012 RTHX-127 DP I Water Radiator 0.03 0.94 25.00 300.00 342.00 200.00 Liquid 249.30 9.66 0.402 1.012 RTHX-128 DP I Water Radiator 0.03 0.93 25.00 300.00 342.00 200.00 Liquid 246.75 9.48 0.403 1.008 RTHX-129 DP I Water Radiator 0.03 0.93 25.00 300.00 342.00 200.00 Liquid 246.66 9.48 0.402 1.008 RTHX-130 DP I Water Radiator 0.03 0.93 25.00 300.00 342.00 200.00 Liquid 244.85 9.30 0.402 1.005 RTHX-131 DP I Water Radiator 0.03 0.93 25.00 300.00 342.00 200.00 Liquid 246.48 9.15 0.402 1.008 RTHX-132 DP I Water Radiator 0.03 0.93 25.00 300.00 342.00 200.00 Liquid 246.47 9.15 0.402 1.008 RTHX-133 DP I Water Radiator 0.03 0.93 25.00 300.00 342.00 200.00 Liquid 243.16 9.07 0.402 1.002 RTHX-134 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 245.51 8.97 0.402 1.006 RTHX-135 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 245.22 8.95 0.401 1.006 RTHX-136 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 242.72 8.93 0.403 1.001 RTHX-137 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 242.62 8.90 1.546 1.003 RTHX-138 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 242.09 8.88 0.397 1.002 RTHX-139 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 242.00 8.87 0.398 1.002 RTHX-140 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 241.94 8.85 1.528 1.004 RTHX-141 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 240.90 8.81 0.392 1.001 RTHX-142 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 240.89 8.64 0.394 1.008 RTHX-143 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 241.18 8.64 0.393 1.009 RTHX-144 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 240.83 8.58 1.586 1.011 RTHX-145 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 240.76 8.57 1.583 1.011 RTHX-146 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 240.72 8.57 1.583 1.011 RTHX-147 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 240.71 8.57 1.583 1.011 RTHX-148 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 240.62 8.56 1.580 1.011 RTHX-149 DP I Water Radiator 0.03 0.89 25.00 300.00 342.00 200.00 Liquid 240.47 8.55 1.576 1.011 RTHX-150 DP I Water Radiator 0.03 0.89 25.00 300.00 342.00 200.00 Liquid 239.55 7.95 0.393 1.006 RTHX-151 DP I Water Radiator 0.03 0.88 25.00 300.00 342.00 200.00 Liquid 238.60 7.89 0.387 1.006 RTHX-152 DP I Water Radiator 0.03 0.88 25.00 300.00 342.00 200.00 Liquid 239.11 7.79 0.396 1.008 RTHX-153 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 237.11 7.49 0.393 1.002 RTHX-154 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 237.11 7.49 0.393 1.002 RTHX-155 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 236.45 7.40 0.393 1.001 RTHX-156 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 236.28 7.39 0.392 1.001 RTHX-157 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 236.06 7.33 0.396 1.003 RTHX-158 DP I Water Radiator 0.03 0.86 25.00 300.00 342.00 200.00 Liquid 235.13 7.21 0.394 1.002 RTHX-159 DP I Water Radiator 0.03 0.85 25.00 300.00 342.00 200.00 Liquid 230.90 7.05 0.632 1.000 RTHX-160 DP I Water Radiator 0.03 0.85 25.00 300.00 342.00 200.00 Liquid 232.70 6.97 0.387 1.004 RTHX-161 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 229.91 6.89 1.486 1.003 RTHX-162 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 229.59 6.83 1.498 1.005 RTHX-163 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 229.50 6.83 1.496 1.005 RTHX-164 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 228.86 6.79 1.479 1.005 RTHX-165 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 228.68 6.76 1.479 1.004 RTHX-166 DP I Water Radiator 0.03 0.83 25.00 300.00 342.00 200.00 Liquid 228.59 6.76 1.462 1.005 RTHX-167 DP I Water Radiator 0.03 0.83 25.00 300.00 342.00 200.00 Liquid 228.62 6.70 1.511 1.009 173 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-168 DP I Water Radiator 0.03 0.83 25.00 300.00 342.00 200.00 Liquid 228.49 6.69 1.511 1.009 RTHX-169 DP I Water Radiator 0.03 0.83 25.00 300.00 342.00 200.00 Liquid 228.21 6.68 1.503 1.009 RTHX-170 DP I Water Radiator 0.03 0.83 25.00 300.00 342.00 200.00 Liquid 228.20 6.68 1.503 1.009 RTHX-171 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 228.76 6.65 1.527 1.011 RTHX-172 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 228.56 6.64 1.522 1.011 RTHX-173 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 228.32 6.63 1.516 1.011 RTHX-174 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 227.86 6.60 1.504 1.011 RTHX-175 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 227.89 6.60 1.499 1.012 RTHX-176 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 227.60 6.59 1.497 1.011 RTHX-177 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 227.57 6.59 1.504 1.011 RTHX-178 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 227.57 6.59 1.504 1.011 RTHX-179 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 227.39 6.56 1.504 1.010 RTHX-180 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 227.20 6.55 1.499 1.010 RTHX-181 DP I Water Radiator 0.03 0.81 25.00 300.00 342.00 200.00 Liquid 227.39 6.51 0.604 1.017 RTHX-182 DP I Water Radiator 0.03 0.80 25.00 300.00 342.00 200.00 Liquid 226.89 6.44 0.596 1.017 RTHX-183 DP I Water Radiator 0.03 0.80 25.00 300.00 342.00 200.00 Liquid 226.86 6.44 0.596 1.017 RTHX-184 DP I Water Radiator 0.03 0.80 25.00 300.00 342.00 200.00 Liquid 226.91 6.44 0.595 1.018 RTHX-185 DP I Water Radiator 0.03 0.80 25.00 300.00 342.00 200.00 Liquid 231.30 6.42 1.577 1.028 RTHX-186 DP I Water Radiator 0.03 0.80 25.00 300.00 342.00 200.00 Liquid 226.20 6.35 1.574 1.020 RTHX-187 DP I Water Radiator 0.03 0.80 25.00 300.00 342.00 200.00 Liquid 225.69 6.33 1.560 1.020 RTHX-188 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 226.28 6.30 0.617 1.023 RTHX-189 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 226.17 6.29 0.616 1.023 RTHX-190 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 226.07 6.29 0.616 1.023 RTHX-191 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 225.61 6.24 1.460 1.024 RTHX-192 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 224.99 6.22 1.583 1.023 RTHX-193 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 224.92 6.22 1.453 1.023 RTHX-194 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 224.55 6.20 1.443 1.023 RTHX-195 DP I Water Radiator 0.03 0.78 25.00 300.00 342.00 200.00 Liquid 224.79 6.16 0.585 1.027 RTHX-196 DP I Water Radiator 0.03 0.78 25.00 300.00 342.00 200.00 Liquid 222.24 6.10 1.380 1.022 RTHX-197 DP I Water Radiator 0.03 0.78 25.00 300.00 342.00 200.00 Liquid 222.16 6.10 1.379 1.022 RTHX-198 DP I Water Radiator 0.03 0.78 25.00 300.00 342.00 200.00 Liquid 222.14 6.10 1.378 1.022 RTHX-199 DP I Water Radiator 0.03 0.78 25.00 300.00 342.00 200.00 Liquid 222.20 6.09 1.380 1.022 RTHX-200 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 223.17 5.97 1.509 1.032 RTHX-201 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 223.15 5.96 0.566 1.033 RTHX-202 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.87 5.96 1.642 1.034 RTHX-203 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.77 5.94 1.642 1.034 RTHX-204 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.93 5.93 0.571 1.034 RTHX-205 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.51 5.91 1.642 1.033 RTHX-206 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.09 5.90 0.566 1.033 RTHX-207 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.26 5.89 0.569 1.036 RTHX-208 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.55 5.89 0.575 1.035 RTHX-209 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.54 5.89 0.575 1.035 RTHX-210 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.53 5.88 1.407 1.035 RTHX-211 DP I Water Radiator 0.03 0.76 25.00 300.00 342.00 200.00 Liquid 222.31 5.87 1.402 1.035 174 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-212 DP I Water Radiator 0.03 0.75 25.00 300.00 342.00 200.00 Liquid 222.21 5.82 0.585 1.038 RTHX-213 DP I Water Radiator 0.03 0.75 25.00 300.00 342.00 200.00 Liquid 221.67 5.78 0.646 1.039 RTHX-214 DP I Water Radiator 0.03 0.88 25.00 300.00 342.00 200.00 Liquid 255.21 6.40 0.968 1.000 RTHX-215 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 259.84 6.79 0.989 1.018 RTHX-216 DP I Water Radiator 0.03 0.97 25.00 300.00 342.00 200.00 Liquid 273.17 9.20 0.983 1.015 RTHX-217 DP I Water Radiator 0.03 0.81 25.00 300.00 342.00 200.00 Liquid 240.70 5.26 0.730 1.005 RTHX-218 DP I Water Radiator 0.03 1.07 25.00 300.00 342.00 200.00 Liquid 284.57 11.41 0.955 1.002 RTHX-219 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 323.28 20.05 0.797 1.000 RTHX-220 DP I Water Radiator 0.03 1.05 25.00 300.00 342.00 200.00 Liquid 284.15 10.81 0.868 1.003 RTHX-221 DP I Water Radiator 0.03 0.86 25.00 300.00 342.00 200.00 Liquid 254.02 6.19 0.980 1.003 RTHX-222 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 304.91 15.23 0.871 1.024 RTHX-223 DP I Water Radiator 0.03 1.11 25.00 300.00 342.00 200.00 Liquid 294.23 13.16 0.992 1.007 RTHX-224 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 255.51 6.34 0.990 1.005 RTHX-225 DP I Water Radiator 0.03 0.86 25.00 300.00 342.00 200.00 Liquid 259.30 6.28 0.981 1.012 RTHX-226 DP I Water Radiator 0.03 1.11 25.00 300.00 342.00 200.00 Liquid 292.52 12.92 0.982 1.006 RTHX-227 DP I Water Radiator 0.03 1.06 25.00 300.00 342.00 200.00 Liquid 283.86 11.28 0.955 1.001 RTHX-228 DP I Water Radiator 0.03 1.11 25.00 300.00 342.00 200.00 Liquid 293.04 13.02 0.982 1.007 RTHX-229 DP I Water Radiator 0.03 1.74 25.00 300.00 342.00 200.00 Liquid 425.66 41.91 0.882 1.010 RTHX-230 DP I Water Radiator 0.03 1.58 25.00 300.00 342.00 200.00 Liquid 389.88 30.99 0.934 1.001 RTHX-231 DP I Water Radiator 0.03 0.94 25.00 300.00 342.00 200.00 Liquid 270.89 8.19 0.916 1.016 RTHX-232 DP I Water Radiator 0.03 1.18 25.00 300.00 342.00 200.00 Liquid 305.54 15.72 0.922 1.009 RTHX-233 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 248.66 5.71 0.866 1.001 RTHX-234 DP I Water Radiator 0.03 1.13 25.00 300.00 342.00 200.00 Liquid 304.83 15.14 0.885 1.025 RTHX-235 DP I Water Radiator 0.03 1.15 25.00 300.00 342.00 200.00 Liquid 305.70 15.34 0.903 1.018 RTHX-236 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 306.93 15.65 0.855 1.014 RTHX-237 DP I Water Radiator 0.03 0.96 25.00 300.00 342.00 200.00 Liquid 271.81 8.98 0.983 1.013 RTHX-238 DP I Water Radiator 0.03 1.38 25.00 300.00 342.00 200.00 Liquid 340.57 23.73 0.914 1.003 RTHX-239 DP I Water Radiator 0.03 0.96 25.00 300.00 342.00 200.00 Liquid 272.39 8.95 0.999 1.016 RTHX-240 DP I Water Radiator 0.03 1.63 25.00 300.00 342.00 200.00 Liquid 405.20 31.61 0.904 1.002 RTHX-241 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 259.37 6.73 0.989 1.017 RTHX-242 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 308.84 16.13 0.837 1.008 RTHX-243 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 383.01 30.23 0.914 1.003 RTHX-244 DP I Water Radiator 0.03 1.44 25.00 300.00 342.00 200.00 Liquid 362.81 26.15 0.963 1.009 RTHX-245 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 245.03 5.46 0.746 1.003 RTHX-246 DP I Water Radiator 0.03 0.91 25.00 300.00 342.00 200.00 Liquid 264.24 7.60 0.981 1.019 RTHX-247 DP I Water Radiator 0.03 1.07 25.00 300.00 342.00 200.00 Liquid 284.92 11.47 0.955 1.002 RTHX-248 DP I Water Radiator 0.03 1.67 25.00 300.00 342.00 200.00 Liquid 418.43 34.91 0.786 1.008 RTHX-249 DP I Water Radiator 0.03 1.64 25.00 300.00 342.00 200.00 Liquid 409.51 31.78 0.786 1.000 RTHX-250 DP I Water Radiator 0.03 1.56 25.00 300.00 342.00 200.00 Liquid 390.39 29.04 0.907 1.004 RTHX-251 DP I Water Radiator 0.03 1.12 25.00 300.00 342.00 200.00 Liquid 302.79 14.72 0.956 1.025 RTHX-252 DP I Water Radiator 0.03 0.99 25.00 300.00 342.00 200.00 Liquid 277.10 9.61 0.993 1.011 RTHX-253 DP I Water Radiator 0.03 1.78 25.00 300.00 342.00 200.00 Liquid 421.96 48.09 0.882 1.006 RTHX-254 DP I Water Radiator 0.03 1.17 25.00 300.00 342.00 200.00 Liquid 306.84 15.64 0.855 1.014 RTHX-255 DP I Water Radiator 0.03 0.86 25.00 300.00 342.00 200.00 Liquid 250.41 6.12 0.861 1.001 175 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-256 DP I Water Radiator 0.03 1.46 25.00 300.00 342.00 200.00 Liquid 361.66 27.55 0.972 1.007 RTHX-257 DP I Water Radiator 0.03 0.89 25.00 300.00 342.00 200.00 Liquid 264.05 7.39 0.962 1.027 RTHX-258 DP I Water Radiator 0.03 1.38 25.00 300.00 342.00 200.00 Liquid 342.34 23.95 0.933 1.003 RTHX-259 DP I Water Radiator 0.03 1.40 25.00 300.00 342.00 200.00 Liquid 347.19 24.50 0.959 1.003 RTHX-260 DP I Water Radiator 0.03 1.37 25.00 300.00 342.00 200.00 Liquid 339.71 23.61 0.905 1.003 RTHX-261 DP I Water Radiator 0.03 1.36 25.00 300.00 342.00 200.00 Liquid 339.06 22.13 0.923 1.001 RTHX-262 DP I Water Radiator 0.03 1.80 25.00 300.00 342.00 200.00 Liquid 422.94 48.86 0.874 1.004 RTHX-263 DP I Water Radiator 0.03 0.83 25.00 300.00 342.00 200.00 Liquid 248.94 5.48 0.866 1.002 RTHX-264 DP I Water Radiator 0.03 1.65 25.00 300.00 342.00 200.00 Liquid 412.09 32.42 0.786 1.003 RTHX-265 DP I Water Radiator 0.03 0.93 25.00 300.00 342.00 200.00 Liquid 268.36 7.90 0.953 1.015 RTHX-266 DP I Water Radiator 0.03 0.94 25.00 300.00 342.00 200.00 Liquid 266.98 7.99 0.989 1.009 RTHX-267 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 382.42 30.08 0.914 1.002 RTHX-268 DP I Water Radiator 0.03 1.49 25.00 300.00 342.00 200.00 Liquid 366.21 28.17 0.993 1.003 RTHX-269 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 309.86 16.34 0.941 1.005 RTHX-270 DP I Water Radiator 0.03 1.27 25.00 300.00 342.00 200.00 Liquid 318.02 19.31 0.739 1.001 RTHX-271 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 257.47 6.49 0.953 1.009 RTHX-272 DP I Water Radiator 0.03 1.41 25.00 300.00 342.00 200.00 Liquid 354.28 24.92 0.952 1.008 RTHX-273 DP I Water Radiator 0.03 1.23 25.00 300.00 342.00 200.00 Liquid 318.46 18.58 0.942 1.016 RTHX-274 DP I Water Radiator 0.03 0.85 25.00 300.00 342.00 200.00 Liquid 254.91 6.16 0.970 1.012 RTHX-275 DP I Water Radiator 0.03 0.91 25.00 300.00 342.00 200.00 Liquid 266.10 7.69 0.975 1.019 RTHX-276 DP I Water Radiator 0.03 0.99 25.00 300.00 342.00 200.00 Liquid 274.20 9.45 0.965 1.009 RTHX-277 DP I Water Radiator 0.03 1.29 25.00 300.00 342.00 200.00 Liquid 321.98 19.86 0.782 1.000 RTHX-278 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 331.47 21.65 0.996 1.018 RTHX-279 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 313.03 17.79 0.913 1.019 RTHX-280 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 234.76 4.88 0.671 1.000 RTHX-281 DP I Water Radiator 0.03 1.21 25.00 300.00 342.00 200.00 Liquid 315.32 18.28 0.931 1.020 RTHX-282 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 305.44 15.30 0.879 1.023 RTHX-283 DP I Water Radiator 0.03 0.96 25.00 300.00 342.00 200.00 Liquid 271.46 8.43 0.934 1.009 RTHX-284 DP I Water Radiator 0.03 1.13 25.00 300.00 342.00 200.00 Liquid 304.74 15.13 0.885 1.025 RTHX-285 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 325.56 21.42 0.788 1.008 RTHX-286 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 419.05 35.71 0.882 1.004 RTHX-287 DP I Water Radiator 0.03 1.46 25.00 300.00 342.00 200.00 Liquid 367.31 26.73 0.991 1.008 RTHX-288 DP I Water Radiator 0.03 0.97 25.00 300.00 342.00 200.00 Liquid 272.68 9.03 0.993 1.014 RTHX-289 DP I Water Radiator 0.03 1.70 25.00 300.00 342.00 200.00 Liquid 419.31 36.20 0.874 1.001 RTHX-290 DP I Water Radiator 0.03 1.41 25.00 300.00 342.00 200.00 Liquid 352.73 24.79 0.943 1.007 RTHX-291 DP I Water Radiator 0.03 1.78 25.00 300.00 342.00 200.00 Liquid 422.23 48.10 0.882 1.007 RTHX-292 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 250.25 5.99 0.877 1.009 RTHX-293 DP I Water Radiator 0.03 0.87 25.00 300.00 342.00 200.00 Liquid 255.27 6.32 0.990 1.004 RTHX-294 DP I Water Radiator 0.03 1.53 25.00 300.00 342.00 200.00 Liquid 386.00 28.83 0.834 1.007 RTHX-295 DP I Water Radiator 0.03 0.95 25.00 300.00 342.00 200.00 Liquid 271.35 8.30 0.983 1.013 RTHX-296 DP I Water Radiator 0.03 1.13 25.00 300.00 342.00 200.00 Liquid 303.48 14.87 0.885 1.024 RTHX-297 DP I Water Radiator 0.03 1.49 25.00 300.00 342.00 200.00 Liquid 368.72 28.49 0.994 1.005 RTHX-298 DP I Water Radiator 0.03 1.78 25.00 300.00 342.00 200.00 Liquid 421.80 47.82 0.882 1.006 RTHX-299 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 414.49 35.12 0.864 1.002 176 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-300 DP I Water Radiator 0.03 1.46 25.00 300.00 342.00 200.00 Liquid 367.53 26.75 0.991 1.008 RTHX-301 DP I Water Radiator 0.03 1.43 25.00 300.00 342.00 200.00 Liquid 357.20 25.33 0.970 1.006 RTHX-302 DP I Water Radiator 0.03 1.65 25.00 300.00 342.00 200.00 Liquid 407.22 34.12 0.863 1.002 RTHX-303 DP I Water Radiator 0.03 1.00 25.00 300.00 342.00 200.00 Liquid 279.76 10.42 0.972 1.019 RTHX-304 DP I Water Radiator 0.03 0.80 25.00 300.00 342.00 200.00 Liquid 239.25 5.16 0.739 1.008 RTHX-305 DP I Water Radiator 0.03 1.35 25.00 300.00 342.00 200.00 Liquid 338.04 23.14 0.954 1.008 RTHX-306 DP I Water Radiator 0.03 1.50 25.00 300.00 342.00 200.00 Liquid 368.55 28.74 0.994 1.005 RTHX-307 DP I Water Radiator 0.03 1.49 25.00 300.00 342.00 200.00 Liquid 366.43 28.18 0.993 1.003 RTHX-308 DP I Water Radiator 0.03 1.47 25.00 300.00 342.00 200.00 Liquid 365.06 27.72 0.924 1.007 RTHX-309 DP I Water Radiator 0.03 1.77 25.00 300.00 342.00 200.00 Liquid 425.21 47.54 0.890 1.013 RTHX-310 DP I Water Radiator 0.03 1.15 25.00 300.00 342.00 200.00 Liquid 305.58 15.34 0.903 1.018 RTHX-311 DP I Water Radiator 0.03 0.85 25.00 300.00 342.00 200.00 Liquid 249.90 6.06 0.866 1.003 RTHX-312 DP I Water Radiator 0.03 0.94 25.00 300.00 342.00 200.00 Liquid 271.22 8.22 0.924 1.016 RTHX-313 DP I Water Radiator 0.03 1.63 25.00 300.00 342.00 200.00 Liquid 408.23 31.68 0.904 1.005 RTHX-314 DP I Water Radiator 0.03 1.54 25.00 300.00 342.00 200.00 Liquid 388.67 28.98 0.842 1.009 RTHX-315 DP I Water Radiator 0.03 1.59 25.00 300.00 342.00 200.00 Liquid 402.51 31.39 0.934 1.013 RTHX-316 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 383.12 30.24 0.914 1.003 RTHX-317 DP I Water Radiator 0.03 0.84 25.00 300.00 342.00 200.00 Liquid 249.82 5.97 0.877 1.008 RTHX-318 DP I Water Radiator 0.03 1.31 25.00 300.00 342.00 200.00 Liquid 326.08 21.51 0.796 1.007 RTHX-319 DP I Water Radiator 0.03 1.73 25.00 300.00 342.00 200.00 Liquid 424.97 41.50 0.865 1.011 RTHX-320 DP I Water Radiator 0.03 1.52 25.00 300.00 342.00 200.00 Liquid 177.22 39.76 0.563 1.018 RTHX-321 DP I Water Radiator 0.03 1.52 25.00 300.00 342.00 200.00 Liquid 177.13 39.76 0.753 1.018 RTHX-322 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 177.47 40.46 0.755 1.012 RTHX-323 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 177.52 40.46 0.347 1.012 RTHX-324 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 177.48 40.51 0.347 1.012 RTHX-325 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 177.49 40.51 0.347 1.012 RTHX-326 DP I Water Radiator 0.03 1.57 25.00 300.00 342.00 200.00 Liquid 177.81 41.01 0.745 1.008 RTHX-327 DP I Water Radiator 0.03 1.59 25.00 300.00 342.00 200.00 Liquid 178.09 41.59 0.549 1.003 RTHX-328 DP I Water Radiator 0.03 1.59 25.00 300.00 342.00 200.00 Liquid 178.12 41.66 0.548 1.003 RTHX-329 DP I Water Radiator 0.03 1.59 25.00 300.00 342.00 200.00 Liquid 178.12 41.66 0.548 1.003 RTHX-330 DP I Water Radiator 0.03 1.59 25.00 300.00 342.00 200.00 Liquid 177.63 42.28 0.732 1.001 RTHX-331 DP I Water Radiator 0.03 1.59 25.00 300.00 342.00 200.00 Liquid 179.95 43.44 0.722 1.008 RTHX-332 DP I Water Radiator 0.03 1.60 25.00 300.00 342.00 200.00 Liquid 179.61 43.73 0.527 1.006 RTHX-333 DP I Water Radiator 0.03 1.60 25.00 300.00 342.00 200.00 Liquid 179.40 44.14 0.733 1.005 RTHX-334 DP I Water Radiator 0.03 1.62 25.00 300.00 342.00 200.00 Liquid 180.44 44.23 0.724 1.003 RTHX-335 DP I Water Radiator 0.03 1.62 25.00 300.00 342.00 200.00 Liquid 180.41 44.23 0.709 1.003 RTHX-336 DP I Water Radiator 0.03 1.62 25.00 300.00 342.00 200.00 Liquid 180.45 44.23 0.724 1.003 RTHX-337 DP I Water Radiator 0.03 1.62 25.00 300.00 342.00 200.00 Liquid 180.43 44.23 0.709 1.003 RTHX-338 DP I Water Radiator 0.03 1.62 25.00 300.00 342.00 200.00 Liquid 180.43 44.23 0.710 1.003 RTHX-339 DP I Water Radiator 0.03 1.62 25.00 300.00 342.00 200.00 Liquid 180.47 44.24 0.725 1.003 RTHX-340 DP I Water Radiator 0.03 1.63 25.00 300.00 342.00 200.00 Liquid 181.47 45.13 0.710 1.005 RTHX-341 DP I Water Radiator 0.03 1.63 25.00 300.00 342.00 200.00 Liquid 181.20 45.50 0.708 1.004 RTHX-342 DP I Water Radiator 0.03 1.63 25.00 300.00 342.00 200.00 Liquid 181.21 45.50 0.708 1.004 RTHX-343 DP I Water Radiator 0.03 1.63 25.00 300.00 342.00 200.00 Liquid 181.28 45.50 0.333 1.003 177 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-344 DP I Water Radiator 0.03 1.64 25.00 300.00 342.00 200.00 Liquid 181.32 45.77 0.704 1.001 RTHX-345 DP I Water Radiator 0.03 1.67 25.00 300.00 342.00 200.00 Liquid 184.97 48.37 0.374 1.004 RTHX-346 DP I Water Radiator 0.03 1.67 25.00 300.00 342.00 200.00 Liquid 184.78 48.37 0.323 1.004 RTHX-347 DP I Water Radiator 0.03 1.67 25.00 300.00 342.00 200.00 Liquid 184.78 48.37 0.323 1.004 RTHX-348 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 184.65 48.46 0.727 1.004 RTHX-349 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 185.11 48.52 0.403 1.003 RTHX-350 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 185.13 48.52 0.410 1.003 RTHX-351 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 185.09 48.59 0.402 1.003 RTHX-352 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 185.24 48.59 0.695 1.003 RTHX-353 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 185.12 48.59 0.403 1.003 RTHX-354 DP I Water Radiator 0.03 1.68 25.00 300.00 342.00 200.00 Liquid 184.81 48.59 0.709 1.003 RTHX-355 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 184.86 48.89 0.705 1.001 RTHX-356 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 184.86 48.89 0.705 1.001 RTHX-357 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 184.86 48.89 0.705 1.001 RTHX-358 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 184.87 48.89 0.705 1.001 RTHX-359 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 184.87 48.89 0.705 1.001 RTHX-360 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 186.90 50.49 0.603 1.006 RTHX-361 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 186.92 50.49 0.603 1.006 RTHX-362 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 186.92 50.49 0.603 1.006 RTHX-363 DP I Water Radiator 0.03 1.70 25.00 300.00 342.00 200.00 Liquid 187.11 50.62 0.599 1.004 RTHX-364 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 186.97 50.87 0.703 1.003 RTHX-365 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 187.07 50.91 0.688 1.003 RTHX-366 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 187.14 51.22 0.701 1.002 RTHX-367 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 187.14 51.22 0.701 1.002 RTHX-368 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 187.37 51.40 0.701 1.003 RTHX-369 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 187.38 51.40 0.702 1.003 RTHX-370 DP I Water Radiator 0.03 1.72 25.00 300.00 342.00 200.00 Liquid 186.99 51.46 0.593 1.000 RTHX-371 DP I Water Radiator 0.03 1.72 25.00 300.00 342.00 200.00 Liquid 187.44 51.58 0.684 1.001 RTHX-372 DP I Water Radiator 0.03 1.72 25.00 300.00 342.00 200.00 Liquid 186.95 52.01 0.698 1.000 RTHX-373 DP I Water Radiator 0.03 1.72 25.00 300.00 342.00 200.00 Liquid 186.95 52.01 0.698 1.000 RTHX-374 DP I Water Radiator 0.03 1.72 25.00 300.00 342.00 200.00 Liquid 187.20 52.16 0.698 1.001 RTHX-375 DP I Water Radiator 0.03 1.72 25.00 300.00 342.00 200.00 Liquid 186.84 52.16 0.521 1.001 RTHX-376 DP I Water Radiator 0.03 1.72 25.00 300.00 342.00 200.00 Liquid 187.21 52.16 0.698 1.001 RTHX-377 DP I Water Radiator 0.03 1.73 25.00 300.00 342.00 200.00 Liquid 188.66 52.56 0.397 1.004 RTHX-378 DP I Water Radiator 0.03 1.74 25.00 300.00 342.00 200.00 Liquid 187.91 52.66 0.772 1.000 RTHX-379 DP I Water Radiator 0.03 1.74 25.00 300.00 342.00 200.00 Liquid 187.91 52.66 0.772 1.000 RTHX-380 DP I Water Radiator 0.03 1.74 25.00 300.00 342.00 200.00 Liquid 189.23 53.29 0.695 1.003 RTHX-381 DP I Water Radiator 0.03 1.74 25.00 300.00 342.00 200.00 Liquid 189.21 53.29 0.681 1.003 RTHX-382 DP I Water Radiator 0.03 1.74 25.00 300.00 342.00 200.00 Liquid 188.82 53.29 0.320 1.003 RTHX-383 DP I Water Radiator 0.03 1.74 25.00 300.00 342.00 200.00 Liquid 189.02 53.46 0.590 1.002 RTHX-384 DP I Water Radiator 0.03 1.75 25.00 300.00 342.00 200.00 Liquid 189.31 53.65 0.393 1.001 RTHX-385 DP I Water Radiator 0.03 1.75 25.00 300.00 342.00 200.00 Liquid 189.31 53.65 0.393 1.001 RTHX-386 DP I Water Radiator 0.03 1.75 25.00 300.00 342.00 200.00 Liquid 189.03 53.65 0.318 1.001 RTHX-387 DP I Water Radiator 0.03 1.75 25.00 300.00 342.00 200.00 Liquid 188.98 53.72 0.976 1.001 178 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-388 DP I Water Radiator 0.03 1.75 25.00 300.00 342.00 200.00 Liquid 189.34 53.78 0.692 1.001 RTHX-389 DP I Water Radiator 0.03 1.75 25.00 300.00 342.00 200.00 Liquid 189.41 55.43 0.696 1.003 RTHX-390 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 262.41 37.29 4.992 10.471 RTHX-391 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 262.48 37.37 4.982 10.467 RTHX-392 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 262.50 37.38 4.984 10.467 RTHX-393 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 262.52 37.38 4.982 10.467 RTHX-394 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 262.55 37.39 4.984 10.467 RTHX-395 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 262.56 37.39 4.984 10.467 RTHX-396 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 263.52 38.00 4.982 10.480 RTHX-397 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 263.57 38.01 4.984 10.480 RTHX-398 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 263.77 38.16 4.982 10.483 RTHX-399 DP II Water Radiator 0.30 1.19 250.00 300.00 342.00 200.00 Liquid 264.05 38.33 4.985 10.486 RTHX-400 DP II Water Radiator 0.30 1.20 250.00 300.00 342.00 200.00 Liquid 263.95 38.33 4.967 10.475 RTHX-401 DP II Water Radiator 0.30 1.23 250.00 300.00 342.00 200.00 Liquid 263.54 39.16 4.841 10.358 RTHX-402 DP II Water Radiator 0.30 1.23 250.00 300.00 342.00 200.00 Liquid 263.71 39.22 4.856 10.357 RTHX-403 DP II Water Radiator 0.30 1.23 250.00 300.00 342.00 200.00 Liquid 264.30 39.25 4.986 10.370 RTHX-404 DP II Water Radiator 0.30 1.23 250.00 300.00 342.00 200.00 Liquid 264.44 39.30 5.000 10.369 RTHX-405 DP II Water Radiator 0.30 1.23 250.00 300.00 342.00 200.00 Liquid 264.84 39.56 4.992 10.369 RTHX-406 DP II Water Radiator 0.30 1.24 250.00 300.00 342.00 200.00 Liquid 264.94 39.67 4.969 10.353 RTHX-407 DP II Water Radiator 0.30 1.24 250.00 300.00 342.00 200.00 Liquid 265.27 39.98 4.926 10.338 RTHX-408 DP II Water Radiator 0.30 1.24 250.00 300.00 342.00 200.00 Liquid 265.29 39.99 4.927 10.338 RTHX-409 DP II Water Radiator 0.30 1.24 250.00 300.00 342.00 200.00 Liquid 265.29 39.99 4.928 10.338 RTHX-410 DP II Water Radiator 0.30 1.24 250.00 300.00 342.00 200.00 Liquid 265.32 39.99 4.926 10.338 RTHX-411 DP II Water Radiator 0.30 1.24 250.00 300.00 342.00 200.00 Liquid 265.34 39.99 4.926 10.338 RTHX-412 DP II Water Radiator 0.30 1.25 250.00 300.00 342.00 200.00 Liquid 265.55 40.12 4.926 10.334 RTHX-413 DP II Water Radiator 0.30 1.25 250.00 300.00 342.00 200.00 Liquid 265.61 40.14 4.931 10.334 RTHX-414 DP II Water Radiator 0.30 1.25 250.00 300.00 342.00 200.00 Liquid 266.06 40.26 4.996 10.336 RTHX-415 DP II Water Radiator 0.30 1.25 250.00 300.00 342.00 200.00 Liquid 266.12 40.27 4.996 10.337 RTHX-416 DP II Water Radiator 0.30 1.25 250.00 300.00 342.00 200.00 Liquid 266.26 40.36 4.988 10.333 RTHX-417 DP II Water Radiator 0.30 1.25 250.00 300.00 342.00 200.00 Liquid 266.29 40.38 4.991 10.333 RTHX-418 DP II Water Radiator 0.30 1.25 250.00 300.00 342.00 200.00 Liquid 266.55 40.56 4.973 10.325 RTHX-419 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 266.88 40.72 4.982 10.321 RTHX-420 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 266.90 40.72 4.983 10.321 RTHX-421 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 266.91 40.72 4.983 10.321 RTHX-422 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 267.06 40.78 4.997 10.321 RTHX-423 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 267.07 40.78 4.997 10.321 RTHX-424 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 267.08 40.78 4.998 10.321 RTHX-425 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 267.89 41.30 4.989 10.339 RTHX-426 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 267.97 41.33 4.996 10.339 RTHX-427 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 267.91 41.35 4.968 10.336 RTHX-428 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 267.95 41.36 4.972 10.336 RTHX-429 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.06 41.40 4.982 10.336 RTHX-430 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.08 41.40 4.983 10.336 RTHX-431 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.08 41.41 4.983 10.336 179 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-432 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.22 41.50 4.975 10.332 RTHX-433 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.23 41.50 4.976 10.332 RTHX-434 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.49 41.63 4.975 10.328 RTHX-435 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.55 41.66 4.981 10.328 RTHX-436 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.56 41.66 4.982 10.328 RTHX-437 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.57 41.67 4.983 10.328 RTHX-438 DP II Water Radiator 0.30 1.26 250.00 300.00 342.00 200.00 Liquid 268.68 41.77 4.967 10.332 RTHX-439 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 268.86 41.83 4.982 10.332 RTHX-440 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 268.88 41.84 4.983 10.332 RTHX-441 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 268.88 41.84 4.984 10.332 RTHX-442 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 268.89 41.84 4.983 10.332 RTHX-443 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 269.06 41.90 4.998 10.332 RTHX-444 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 269.04 41.94 4.974 10.329 RTHX-445 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 269.04 41.94 4.975 10.329 RTHX-446 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 269.06 41.94 4.976 10.329 RTHX-447 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 269.14 41.97 4.982 10.328 RTHX-448 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 269.94 42.47 4.974 10.340 RTHX-449 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 270.04 42.50 4.983 10.340 RTHX-450 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 270.14 42.53 4.990 10.340 RTHX-451 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 270.15 42.54 4.991 10.340 RTHX-452 DP II Water Radiator 0.30 1.27 250.00 300.00 342.00 200.00 Liquid 270.62 42.85 4.979 10.348 RTHX-453 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.18 43.19 4.974 10.355 RTHX-454 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.20 43.20 4.976 10.355 RTHX-455 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.34 43.32 4.961 10.360 RTHX-456 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.49 43.37 4.974 10.359 RTHX-457 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.50 43.37 4.975 10.359 RTHX-458 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.52 43.38 4.976 10.359 RTHX-459 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.56 43.39 4.979 10.359 RTHX-460 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 271.56 43.40 4.980 10.359 RTHX-461 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.09 43.81 4.946 10.371 RTHX-462 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.28 43.83 4.983 10.374 RTHX-463 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.29 43.83 4.983 10.375 RTHX-464 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.30 43.88 4.962 10.371 RTHX-465 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.46 43.93 4.974 10.371 RTHX-466 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.48 43.94 4.975 10.371 RTHX-467 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.79 44.12 4.975 10.375 RTHX-468 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 272.80 44.13 4.975 10.375 RTHX-469 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 273.05 44.21 4.995 10.375 RTHX-470 DP II Water Radiator 0.30 1.28 250.00 300.00 342.00 200.00 Liquid 273.38 44.40 4.995 10.379 RTHX-471 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 274.91 45.42 4.961 10.403 RTHX-472 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 275.10 45.48 4.975 10.403 RTHX-473 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 275.83 45.90 4.981 10.411 RTHX-474 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 276.45 46.28 4.976 10.420 RTHX-475 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 276.47 46.29 4.977 10.420 180 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-476 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 276.51 46.30 4.980 10.420 RTHX-477 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 276.51 46.31 4.980 10.420 RTHX-478 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 276.52 46.31 4.981 10.420 RTHX-479 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 277.43 46.93 4.970 10.439 RTHX-480 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 277.45 46.94 4.970 10.439 RTHX-481 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 277.62 47.00 4.983 10.439 RTHX-482 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 277.62 47.00 4.984 10.439 RTHX-483 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 277.64 47.00 4.984 10.439 RTHX-484 DP II Water Radiator 0.30 1.29 250.00 300.00 342.00 200.00 Liquid 277.66 47.01 4.985 10.439 RTHX-485 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 277.67 47.05 4.963 10.436 RTHX-486 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 277.86 47.12 4.977 10.436 RTHX-487 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 277.87 47.12 4.978 10.436 RTHX-488 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 278.14 47.20 4.996 10.437 RTHX-489 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 279.41 48.06 4.984 10.460 RTHX-490 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 279.64 48.17 4.976 10.458 RTHX-491 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 279.65 48.18 4.977 10.458 RTHX-492 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 279.70 48.20 4.980 10.458 RTHX-493 DP II Water Radiator 0.30 1.30 250.00 300.00 342.00 200.00 Liquid 279.89 48.25 4.993 10.458 RTHX-494 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 280.74 48.84 4.978 10.470 RTHX-495 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 280.75 48.84 4.978 10.470 RTHX-496 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 280.87 48.87 4.985 10.471 RTHX-497 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 282.01 49.66 4.963 10.488 RTHX-498 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 282.02 49.66 4.964 10.488 RTHX-499 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 282.22 49.73 4.977 10.488 RTHX-500 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 282.24 49.73 4.978 10.488 RTHX-501 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 283.27 50.46 4.971 10.508 RTHX-502 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 283.50 50.53 4.985 10.508 RTHX-503 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 283.52 50.54 4.987 10.508 RTHX-504 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 283.74 50.65 4.977 10.505 RTHX-505 DP II Water Radiator 0.30 1.31 250.00 300.00 342.00 200.00 Liquid 283.76 50.65 4.977 10.506 RTHX-506 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 283.89 50.69 4.986 10.506 RTHX-507 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 283.92 50.70 4.988 10.506 RTHX-508 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 284.67 51.16 4.986 10.515 RTHX-509 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 285.46 51.64 4.986 10.524 RTHX-510 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 286.66 52.49 4.964 10.541 RTHX-511 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 286.67 52.50 4.964 10.541 RTHX-512 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 286.90 52.57 4.978 10.542 RTHX-513 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 286.92 52.57 4.978 10.542 RTHX-514 DP II Water Radiator 0.30 1.32 250.00 300.00 342.00 200.00 Liquid 286.92 52.57 4.979 10.542 RTHX-515 DP II Water Radiator 0.30 1.33 250.00 300.00 342.00 200.00 Liquid 287.72 53.06 4.978 10.551 RTHX-516 DP II Water Radiator 0.30 1.33 250.00 300.00 342.00 200.00 Liquid 288.26 53.44 4.986 10.562 RTHX-517 DP II Water Radiator 0.30 1.33 250.00 300.00 342.00 200.00 Liquid 288.28 53.45 4.988 10.562 RTHX-518 DP II Water Radiator 0.30 1.33 250.00 300.00 342.00 200.00 Liquid 288.56 53.57 4.979 10.560 RTHX-519 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 171.03 9.67 17.852 11.814 181 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-520 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 172.86 9.70 18.473 11.811 RTHX-521 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 172.89 9.70 18.036 11.816 RTHX-522 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 173.15 9.70 18.333 11.817 RTHX-523 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 175.67 9.75 20.866 11.823 RTHX-524 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 177.70 9.78 22.820 11.826 RTHX-525 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 180.32 9.83 27.160 11.833 RTHX-526 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 187.24 9.95 20.183 11.825 RTHX-527 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 187.72 9.96 20.182 11.825 RTHX-528 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 189.94 9.96 20.615 11.825 RTHX-529 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 192.80 10.04 23.794 11.833 RTHX-530 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 193.31 10.05 24.996 11.832 RTHX-531 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 194.36 10.16 23.614 11.838 RTHX-532 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 194.39 10.16 23.794 11.837 RTHX-533 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 199.20 10.16 20.551 11.829 RTHX-534 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 202.19 10.21 23.724 11.835 RTHX-535 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 205.78 10.23 22.484 11.834 RTHX-536 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 204.30 10.25 25.948 11.838 RTHX-537 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 209.61 10.35 20.637 11.835 RTHX-538 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 209.75 10.35 22.811 11.835 RTHX-539 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 210.72 10.37 23.772 11.837 RTHX-540 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 212.94 10.40 26.218 11.840 RTHX-541 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 215.62 10.55 23.486 11.842 RTHX-542 DP III R410A Condenser 1.84 0.95 58.30 308.15 339.75 2488.40 Vapor 211.27 10.57 26.216 11.833 RTHX-543 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 216.02 10.57 23.491 11.842 RTHX-544 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 224.00 10.58 20.283 11.833 RTHX-545 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 224.50 10.64 12.807 11.833 RTHX-546 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 226.18 10.67 21.022 11.835 RTHX-547 DP III R410A Condenser 1.84 0.95 58.30 308.15 339.75 2488.40 Vapor 225.21 10.91 19.702 11.828 RTHX-548 DP III R410A Condenser 1.84 0.95 58.30 308.15 339.75 2488.40 Vapor 227.49 10.95 21.585 11.832 RTHX-549 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 252.14 11.12 12.723 11.836 RTHX-550 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 252.68 11.14 12.711 11.836 RTHX-551 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 254.62 11.20 24.608 11.846 RTHX-552 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 257.04 11.25 23.721 11.845 RTHX-553 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 258.44 11.28 26.040 11.844 RTHX-554 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 262.45 11.32 30.934 11.850 RTHX-555 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 278.21 11.63 20.126 11.843 RTHX-556 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 291.22 11.94 25.873 11.851 RTHX-557 DP III R410A Condenser 1.84 0.94 58.30 308.15 339.75 2488.40 Vapor 294.30 12.08 23.079 11.860 RTHX-558 DP III R410A Condenser 1.84 0.95 58.30 308.15 339.75 2488.40 Vapor 295.23 12.54 15.890 11.863 RTHX-559 DP III R410A Condenser 1.84 0.95 58.30 308.15 339.75 2488.40 Vapor 297.51 12.58 15.889 11.863 RTHX-560 DP III R410A Condenser 1.84 1.05 58.30 308.15 339.75 2488.40 Vapor 100.21 6.03 12.380 11.826 RTHX-561 DP III R410A Condenser 1.84 1.05 58.30 308.15 339.75 2488.40 Vapor 101.47 6.05 13.902 11.820 RTHX-562 DP III R410A Condenser 1.84 1.05 58.30 308.15 339.75 2488.40 Vapor 103.19 6.07 16.155 11.825 RTHX-563 DP III R410A Condenser 1.84 1.05 58.30 308.15 339.75 2488.40 Vapor 105.52 6.33 17.182 11.837 182 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-564 DP III R410A Condenser 1.84 1.05 58.30 308.15 339.75 2488.40 Vapor 107.11 6.49 17.319 11.846 RTHX-565 DP III R410A Condenser 1.84 1.05 58.30 308.15 339.75 2488.40 Vapor 107.27 6.50 17.614 11.846 RTHX-566 DP III R410A Condenser 1.84 1.08 58.30 308.15 339.75 2488.40 Vapor 110.25 7.38 26.544 11.803 RTHX-567 DP III R410A Condenser 1.84 1.08 58.30 308.15 339.75 2488.40 Vapor 110.50 7.38 26.536 11.805 RTHX-568 DP III R410A Condenser 1.84 1.16 58.30 308.15 339.75 2488.40 Vapor 109.86 7.50 15.755 11.800 RTHX-569 DP III R410A Condenser 1.84 1.21 58.30 308.15 339.75 2488.40 Vapor 114.23 9.00 14.326 11.816 RTHX-570 DP III R410A Condenser 1.84 1.23 58.30 308.15 339.75 2488.40 Vapor 115.78 9.07 15.149 11.811 RTHX-571 DP III R410A Condenser 1.84 1.27 58.30 308.15 339.75 2488.40 Vapor 114.63 9.47 8.084 11.815 RTHX-572 DP III R410A Condenser 1.84 1.30 58.30 308.15 339.75 2488.40 Vapor 117.47 10.03 13.037 11.816 RTHX-573 DP III R410A Condenser 1.84 1.27 58.30 308.15 339.75 2488.40 Vapor 116.79 10.09 14.648 11.808 RTHX-574 DP III R410A Condenser 1.84 1.27 58.30 308.15 339.75 2488.40 Vapor 118.86 10.37 13.668 11.825 RTHX-575 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 170.88 28.16 10.992 10.002 RTHX-576 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 170.92 28.17 12.094 10.004 RTHX-577 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 171.47 28.21 10.572 10.004 RTHX-578 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 184.79 28.50 11.935 10.010 RTHX-579 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 186.76 28.55 10.570 10.013 RTHX-580 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 189.40 28.64 11.126 10.015 RTHX-581 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 192.92 28.73 10.572 10.014 RTHX-582 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 193.36 28.74 10.729 10.014 RTHX-583 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 194.61 28.79 10.717 10.019 RTHX-584 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 195.75 28.83 11.129 10.016 RTHX-585 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 197.13 28.91 11.348 10.020 RTHX-586 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 198.10 28.95 11.141 10.019 RTHX-587 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 199.90 28.95 10.541 10.017 RTHX-588 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 199.81 28.97 11.283 10.021 RTHX-589 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 201.19 29.00 10.542 10.018 RTHX-590 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 199.26 29.37 15.235 10.077 RTHX-591 DP III R410A Evaporator 0.51 1.39 58.30 299.82 285.93 1179.76 0.1924 202.04 29.52 10.459 10.008 RTHX-592 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 204.34 29.53 15.239 10.081 RTHX-593 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 200.19 29.85 11.845 10.005 RTHX-594 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 198.73 29.86 12.754 10.028 RTHX-595 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 198.41 29.87 14.117 10.029 RTHX-596 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 199.36 29.87 12.415 10.023 RTHX-597 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 198.77 29.87 13.182 10.029 RTHX-598 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 199.94 29.89 12.713 10.029 RTHX-599 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 200.26 29.91 12.929 10.030 RTHX-600 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 201.02 29.91 12.415 10.022 RTHX-601 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 202.22 29.93 12.491 10.017 RTHX-602 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 201.62 29.94 12.755 10.027 RTHX-603 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 203.32 29.99 12.756 10.028 RTHX-604 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 204.37 30.00 12.493 10.019 RTHX-605 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 205.53 30.07 13.186 10.030 RTHX-606 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 206.13 30.07 12.758 10.030 RTHX-607 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 206.79 30.09 12.758 10.031 183 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW RTHX-608 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 208.80 30.15 12.760 10.032 RTHX-609 DP III R410A Evaporator 0.51 1.38 58.30 299.82 285.93 1179.76 0.1924 283.80 31.19 10.294 10.008 RTHX-610 DP III R410A Evaporator 1.51 4.20 58.30 299.82 285.93 1179.76 0.1924 172.23 20.49 11.999 10.129 RTHX-611 DP III R410A Evaporator 2.51 6.96 58.30 299.82 285.93 1179.76 0.1924 174.10 21.69 11.859 10.108 RTHX-612 DP III R410A Evaporator 3.51 9.74 58.30 299.82 285.93 1179.76 0.1924 175.98 21.77 13.170 10.117 RTHX-613 DP III R410A Evaporator 4.51 12.40 58.30 299.82 285.93 1179.76 0.1924 183.15 21.80 13.124 10.196 RTHX-614 DP III R410A Evaporator 5.51 15.89 58.30 299.82 285.93 1179.76 0.1924 179.25 23.34 12.736 10.089 RTHX-615 DP III R410A Evaporator 6.51 19.31 58.30 299.82 285.93 1179.76 0.1924 178.52 23.64 12.338 10.066 RTHX-616 DP III R410A Evaporator 7.51 21.26 58.30 299.82 285.93 1179.76 0.1924 193.58 26.96 13.732 10.194 RTHX-617 DP III R410A Evaporator 8.51 25.25 58.30 299.82 285.93 1179.76 0.1924 199.53 30.16 12.864 10.211 RTHX-618 DP III R410A Evaporator 9.51 27.18 58.30 299.82 285.93 1179.76 0.1924 202.21 31.08 13.411 10.212 RTHX-619 DP III R410A Evaporator 10.51 30.04 58.30 299.82 285.93 1179.76 0.1924 202.51 31.09 13.610 10.213 FTHX Figure 130. Flat fin and tube HX (FTHX). oD tP lP pF f 184 Table 32. FTHX optimum designs dimensions. Design Tag Arrangement Do Di Pl Pt FPI δf Nr Nt Passes l H d Af V Vmat’l - mm mm mm mm in-1 mm - - % m m m m² cm³ cm³ FTHX-001 Staggered 1 0.4014 0.8067 1.3168 5.3226 0.115 6 245 100 0.0873 0.3226 0.0048 0.028 136.3 15.9 FTHX-002 Staggered 1 0.4014 0.8059 1.2485 5.0098 0.115 6 245 100 0.0820 0.3059 0.0048 0.025 121.2 14.6 FTHX-003 Staggered 1 0.4014 0.8051 1.1096 5.0098 0.115 6 230 100 0.0760 0.2552 0.0048 0.019 93.7 12.4 FTHX-004 Staggered 1 0.3838 0.7713 1.1052 5.3177 0.115 6 245 100 0.0766 0.2708 0.0046 0.021 96.1 12.5 FTHX-005 Staggered 1 0.4025 0.8089 1.1630 6.2708 0.115 6 230 100 0.0800 0.2675 0.0049 0.021 103.8 13.9 FTHX-006 Staggered 1 0.4014 0.8028 1.2430 5.3666 0.115 6 230 100 0.0873 0.2859 0.0048 0.025 120.2 14.8 FTHX-007 Staggered 1 0.3926 0.8013 1.0354 6.2610 0.115 6 230 100 0.0720 0.2381 0.0048 0.017 82.4 11.7 FTHX-008 Staggered 1 0.4014 0.8161 1.3231 5.0538 0.115 6 245 100 0.0873 0.3242 0.0049 0.028 138.5 15.8 FTHX-009 Staggered 1 0.4014 0.8067 1.1598 5.0489 0.115 6 230 100 0.0793 0.2668 0.0048 0.021 102.4 13.1 FTHX-010 Staggered 1 0.4014 0.8036 1.2289 5.6745 0.115 6 230 100 0.0873 0.2826 0.0048 0.025 118.9 14.9 FTHX-011 Staggered 1 0.4190 0.8519 1.3811 5.0489 0.115 6 245 100 0.1086 0.3384 0.0051 0.037 187.7 21.4 FTHX-012 Staggered 1 0.4014 0.8067 1.3231 5.3666 0.115 6 250 100 0.0873 0.3308 0.0048 0.029 139.7 16.3 FTHX-013 Staggered 1 0.4190 0.8519 1.3811 5.0489 0.115 6 245 100 0.0979 0.3384 0.0051 0.033 169.3 19.3 FTHX-014 Staggered 1 0.3937 0.7912 1.1376 5.3324 0.115 6 230 100 0.0800 0.2616 0.0047 0.021 99.3 12.8 FTHX-015 Staggered 1 0.3926 0.7875 1.0838 5.0391 0.115 6 230 100 0.0773 0.2493 0.0047 0.019 91.1 12.1 FTHX-016 Staggered 1 0.4014 0.8028 1.0586 5.0000 0.115 6 230 100 0.0773 0.2435 0.0048 0.019 90.7 12.6 FTHX-017 Staggered 1 0.4014 0.8051 1.1096 5.0000 0.115 6 230 100 0.0773 0.2552 0.0048 0.020 95.3 12.7 FTHX-018 Staggered 1 0.4014 0.8059 1.2360 5.0489 0.115 6 245 100 0.0873 0.3028 0.0048 0.026 127.8 15.5 FTHX-019 Staggered 1 0.4014 0.8161 1.3231 5.0098 0.115 6 245 100 0.0879 0.3242 0.0049 0.029 139.6 15.9 FTHX-020 Staggered 1 0.3926 0.8013 1.1713 5.3617 0.115 6 245 100 0.0806 0.2870 0.0048 0.023 111.2 13.9 FTHX-021 Staggered 1 0.4036 0.8072 1.0644 5.3226 0.115 6 230 100 0.0720 0.2448 0.0048 0.018 85.4 11.9 FTHX-022 Staggered 1 0.4410 0.8966 1.4768 5.4057 0.115 6 250 100 0.0886 0.3692 0.0054 0.033 176.0 20.1 FTHX-023 Staggered 1 0.4014 0.8067 1.3074 6.2610 0.115 6 245 100 0.0873 0.3203 0.0048 0.028 135.3 16.5 FTHX-024 Staggered 1 0.3926 0.8013 1.1713 5.0196 0.115 6 250 100 0.0813 0.2928 0.0048 0.024 114.5 14.1 FTHX-025 Staggered 1 0.4025 0.8050 1.1127 5.0000 0.115 6 230 100 0.0773 0.2559 0.0048 0.020 95.6 12.7 FTHX-026 Staggered 1 0.4014 0.8051 1.1096 5.0049 0.115 6 230 100 0.0766 0.2552 0.0048 0.020 94.5 12.6 FTHX-027 Staggered 1 0.4014 0.8161 1.1897 5.0098 0.115 6 230 100 0.0820 0.2736 0.0049 0.022 109.8 13.6 FTHX-028 Staggered 1 0.4014 0.8036 1.1912 5.0489 0.115 6 235 100 0.0820 0.2799 0.0048 0.023 110.6 13.9 FTHX-029 Staggered 1 0.4014 0.8036 1.3231 5.0880 0.115 6 245 100 0.0899 0.3242 0.0048 0.029 140.6 16.3 FTHX-030 Staggered 1 0.4014 0.8059 1.2485 5.3861 0.115 6 230 100 0.0873 0.2872 0.0048 0.025 121.2 14.8 FTHX-031 Staggered 1 0.3849 0.7758 0.9496 5.3275 0.115 6 230 100 0.0720 0.2184 0.0047 0.016 73.2 10.8 FTHX-032 Staggered 1 0.4190 0.8519 1.4138 5.0391 0.115 6 245 100 0.1072 0.3464 0.0051 0.037 189.8 21.2 FTHX-033 Staggered 1 0.4014 0.8059 1.2462 5.4448 0.115 6 245 100 0.0806 0.3053 0.0048 0.025 119.0 14.6 FTHX-034 Staggered 1 0.4025 0.8152 1.3283 5.0098 0.115 6 245 100 0.0899 0.3254 0.0049 0.029 143.2 16.3 FTHX-035 Staggered 1 0.4014 0.8067 1.0594 5.0196 0.115 6 230 100 0.0766 0.2437 0.0048 0.019 90.4 12.5 FTHX-036 Staggered 1 0.4014 0.8114 1.3231 5.0929 0.115 6 245 100 0.0873 0.3242 0.0049 0.028 137.7 15.8 FTHX-037 Staggered 1 0.4025 0.8089 1.3267 5.0489 0.115 6 245 100 0.0899 0.3250 0.0049 0.029 141.9 16.3 FTHX-038 Staggered 1 0.4014 0.8059 1.2462 5.3666 0.115 6 245 100 0.0873 0.3053 0.0048 0.027 128.9 15.8 FTHX-039 Staggered 1 0.4025 0.8050 1.1127 5.3226 0.115 6 230 100 0.0766 0.2559 0.0048 0.020 94.7 12.8 FTHX-040 Staggered 1 0.4014 0.8059 1.3097 5.1271 0.115 6 245 100 0.0873 0.3209 0.0048 0.028 135.4 15.8 FTHX-041 Staggered 1 0.4014 0.8193 1.1912 5.3226 0.115 6 230 100 0.0820 0.2740 0.0049 0.022 110.4 13.8 185 Design Tag Arrangement Do Di Pl Pt FPI δf Nr Nt Passes l H d Af V Vmat’l - mm mm mm mm in-1 mm - - % m m m m² cm³ cm³ FTHX-042 Staggered 1 0.4036 0.8103 1.3303 5.0147 0.115 6 245 100 0.0899 0.3259 0.0049 0.029 142.5 16.4 FTHX-043 Staggered 1 0.4366 0.8774 1.4391 5.0147 0.115 6 245 100 0.0899 0.3526 0.0053 0.032 166.9 19.2 FTHX-044 Staggered 1 0.4212 0.8564 1.4278 5.0196 0.115 6 245 100 0.1092 0.3498 0.0051 0.038 196.3 21.9 FTHX-045 Staggered 1 0.4014 0.8067 1.0657 5.0196 0.115 6 230 100 0.0766 0.2451 0.0048 0.019 90.9 12.5 FTHX-046 Staggered 1 0.4014 0.8067 1.2477 5.0098 0.115 6 245 100 0.0873 0.3057 0.0048 0.027 129.1 15.6 FTHX-047 Staggered 1 0.4014 0.8028 1.0335 9.1153 0.115 6 205 100 0.0773 0.2119 0.0048 0.016 78.9 12.6 FTHX-048 Staggered 1 0.4025 0.8058 1.3259 5.3275 0.115 6 250 100 0.0899 0.3315 0.0048 0.030 144.1 16.8 FTHX-049 Staggered 1 0.4014 0.8036 1.3231 5.3421 0.115 6 245 100 0.0873 0.3242 0.0048 0.028 136.4 15.9 FTHX-050 Staggered 1 0.4410 0.8966 1.4768 5.3617 0.115 6 250 100 0.0899 0.3692 0.0054 0.033 178.6 20.4 FTHX-051 Staggered 1 0.4014 0.8036 1.2226 5.6745 0.115 6 230 100 0.0873 0.2812 0.0048 0.025 118.3 14.9 FTHX-052 Staggered 1 0.4014 0.8028 1.0092 5.3226 0.115 6 205 100 0.0766 0.2069 0.0048 0.016 76.4 11.1 FTHX-053 Staggered 1 0.4047 0.8450 1.3640 5.0587 0.115 6 245 100 0.0906 0.3342 0.0051 0.030 153.5 16.8 FTHX-054 Staggered 1 0.4014 0.8059 1.2485 5.3812 0.115 6 245 100 0.0873 0.3059 0.0048 0.027 129.1 15.8 FTHX-055 Staggered 1 0.3926 0.8013 1.1713 5.0196 0.115 6 245 100 0.0766 0.2870 0.0048 0.022 105.7 13.0 FTHX-056 Staggered 1 0.4014 0.8114 1.3223 5.0098 0.115 6 245 100 0.0879 0.3240 0.0049 0.028 138.7 15.9 FTHX-057 Staggered 1 0.4014 0.8067 1.3113 5.3177 0.115 6 245 100 0.0873 0.3213 0.0048 0.028 135.7 15.9 FTHX-058 Staggered 1 0.3849 0.7758 0.9496 5.0147 0.115 6 230 100 0.0713 0.2184 0.0047 0.016 72.5 10.6 FTHX-059 Staggered 1 0.3926 0.8013 1.1713 5.3617 0.115 6 245 100 0.0813 0.2870 0.0048 0.023 112.2 14.0 FTHX-060 Staggered 1 0.4014 0.8161 1.3450 5.0489 0.115 6 245 100 0.0899 0.3295 0.0049 0.030 145.1 16.3 FTHX-061 Staggered 1 0.4014 0.8059 1.2360 5.0489 0.115 6 245 100 0.0899 0.3028 0.0048 0.027 131.7 16.0 FTHX-062 Staggered 1 0.4014 0.8028 1.0586 6.2610 0.115 6 230 100 0.0720 0.2435 0.0048 0.018 84.4 12.2 FTHX-063 Staggered 1 0.4014 0.8036 1.2289 5.3226 0.115 6 230 100 0.0860 0.2826 0.0048 0.024 117.1 14.5 FTHX-064 Staggered 1 0.4014 0.8028 1.0304 9.1153 0.115 6 205 100 0.0773 0.2112 0.0048 0.016 78.7 12.6 FTHX-065 Staggered 1 0.3926 0.7890 1.1651 5.0489 0.115 6 235 100 0.0820 0.2738 0.0047 0.022 106.2 13.3 FTHX-066 Staggered 1 0.4014 0.8059 1.2422 5.0489 0.115 6 245 100 0.0899 0.3043 0.0048 0.027 132.4 16.0 FTHX-067 Staggered 1 0.4014 0.8067 1.2477 5.0098 0.115 6 230 100 0.0879 0.2870 0.0048 0.025 122.2 14.7 FTHX-068 Staggered 1 0.4047 0.8133 1.1694 6.2708 0.115 6 230 100 0.0800 0.2690 0.0049 0.022 105.0 14.0 FTHX-069 Staggered 1 0.4014 0.8067 1.0586 6.2610 0.115 6 230 100 0.0720 0.2435 0.0048 0.018 84.8 12.2 FTHX-070 Staggered 1 0.4014 0.8059 1.2430 5.3666 0.115 6 245 100 0.0873 0.3045 0.0048 0.027 128.5 15.8 FTHX-071 Staggered 1 0.4212 0.8564 1.4147 5.3275 0.115 6 245 100 0.0899 0.3466 0.0051 0.031 160.2 18.2 FTHX-072 Staggered 1 0.4190 0.8421 1.3680 5.0489 0.115 6 245 100 0.1086 0.3351 0.0051 0.036 183.8 21.3 FTHX-073 Staggered 1 0.4025 0.8089 1.3574 5.3617 0.115 6 245 100 0.0899 0.3326 0.0049 0.030 145.2 16.6 FTHX-074 Staggered 1 0.4025 0.8089 1.3259 5.3275 0.115 6 250 100 0.0886 0.3315 0.0049 0.029 142.6 16.6 FTHX-075 Staggered 1 0.4014 0.8028 1.1096 5.3275 0.115 6 230 100 0.0766 0.2552 0.0048 0.020 94.2 12.7 FTHX-076 Staggered 1 0.4014 0.8059 1.2540 5.3666 0.115 6 245 100 0.0906 0.3072 0.0048 0.028 134.6 16.4 FTHX-077 Staggered 1 0.4014 0.8059 1.2485 5.9384 0.115 6 245 100 0.0899 0.3059 0.0048 0.028 133.0 16.6 FTHX-078 Staggered 1 0.4014 0.8059 1.2493 5.3617 0.115 6 245 100 0.0873 0.3061 0.0048 0.027 129.2 15.8 FTHX-079 Staggered 1 0.4069 0.8138 1.0731 6.2610 0.115 6 230 100 0.0720 0.2468 0.0049 0.018 86.8 12.5 FTHX-080 Staggered 1 0.4014 0.8028 1.0084 9.0762 0.115 6 205 100 0.0766 0.2067 0.0048 0.016 76.3 12.4 FTHX-081 Staggered 1 0.4366 0.8877 1.4391 5.3617 0.115 6 245 100 0.0899 0.3526 0.0053 0.032 168.9 19.5 FTHX-082 Staggered 1 0.4014 0.8067 1.2132 5.0489 0.115 6 230 100 0.0853 0.2790 0.0048 0.024 115.2 14.2 FTHX-083 Staggered 1 0.4025 0.8081 1.3259 5.0684 0.115 6 250 100 0.0873 0.3315 0.0048 0.029 140.3 16.2 FTHX-084 Staggered 1 0.4014 0.8036 1.2226 5.0196 0.115 6 245 100 0.0879 0.2995 0.0048 0.026 127.0 15.6 FTHX-085 Staggered 1 0.3926 0.7890 1.0838 5.0000 0.115 6 230 100 0.0773 0.2493 0.0047 0.019 91.2 12.1 186 Design Tag Arrangement Do Di Pl Pt FPI δf Nr Nt Passes l H d Af V Vmat’l - mm mm mm mm in-1 mm - - % m m m m² cm³ cm³ FTHX-086 Staggered 1 0.4014 0.8067 1.1096 5.0196 0.115 6 230 100 0.0766 0.2552 0.0048 0.020 94.7 12.6 FTHX-087 Staggered 1 0.4014 0.8059 1.2101 5.9384 0.115 6 245 100 0.0793 0.2965 0.0048 0.024 113.7 14.5 FTHX-088 Staggered 1 0.4025 0.8089 1.3519 5.3275 0.115 6 245 100 0.0899 0.3312 0.0049 0.030 144.6 16.6 FTHX-089 Staggered 1 0.4014 0.8059 1.2422 5.3666 0.115 6 245 100 0.0906 0.3043 0.0048 0.028 133.3 16.3 FTHX-090 Staggered 1 0.4047 0.8450 1.3656 5.0196 0.115 6 245 100 0.0906 0.3346 0.0051 0.030 153.7 16.8 FTHX-091 Staggered 1 0.4025 0.8404 1.3582 5.1271 0.115 6 245 100 0.0906 0.3328 0.0050 0.030 152.0 16.7 FTHX-092 Staggered 1 0.4036 0.8072 1.0936 5.0147 0.115 6 230 100 0.0713 0.2515 0.0048 0.018 86.9 11.8 FTHX-093 Staggered 1 0.4014 0.8059 1.2422 5.3617 0.115 6 245 100 0.0813 0.3043 0.0048 0.025 119.6 14.7 Table 33. Optimum FTHX performance and operating conditions. Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW FTHX-001 DP I Water Radiator 0.03 1.07 25.00 300.00 342.00 200.00 Liquid 210.38 13.19 0.926 1.003 FTHX-002 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 230.32 17.24 0.870 1.005 FTHX-003 DP I Water Radiator 0.03 1.55 25.00 300.00 342.00 200.00 Liquid 279.15 33.20 0.860 1.011 FTHX-004 DP I Water Radiator 0.03 1.45 25.00 300.00 342.00 200.00 Liquid 268.94 27.52 0.974 1.015 FTHX-005 DP I Water Radiator 0.03 1.40 25.00 300.00 342.00 200.00 Liquid 251.09 25.98 0.895 1.008 FTHX-006 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 228.96 17.70 0.987 1.005 FTHX-007 DP I Water Radiator 0.03 1.75 25.00 300.00 342.00 200.00 Liquid 297.84 45.69 0.890 1.013 FTHX-008 DP I Water Radiator 0.03 1.06 25.00 300.00 342.00 200.00 Liquid 210.55 12.94 0.926 1.001 FTHX-009 DP I Water Radiator 0.03 1.42 25.00 300.00 342.00 200.00 Liquid 260.52 26.14 0.897 1.006 FTHX-010 DP I Water Radiator 0.03 1.22 25.00 300.00 342.00 200.00 Liquid 231.17 18.45 0.987 1.011 FTHX-011 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 191.30 8.37 0.974 1.072 FTHX-012 DP I Water Radiator 0.03 1.04 25.00 300.00 342.00 200.00 Liquid 207.86 12.62 0.908 1.007 FTHX-013 DP I Water Radiator 0.03 0.91 25.00 300.00 342.00 200.00 Liquid 196.27 9.92 0.877 1.041 FTHX-014 DP I Water Radiator 0.03 1.43 25.00 300.00 342.00 200.00 Liquid 262.99 26.90 0.977 1.007 FTHX-015 DP I Water Radiator 0.03 1.56 25.00 300.00 342.00 200.00 Liquid 283.92 33.80 0.956 1.017 FTHX-016 DP I Water Radiator 0.03 1.59 25.00 300.00 342.00 200.00 Liquid 291.35 38.77 0.876 1.033 FTHX-017 DP I Water Radiator 0.03 1.52 25.00 300.00 342.00 200.00 Liquid 277.19 32.13 0.875 1.017 FTHX-018 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 229.05 16.23 0.928 1.028 FTHX-019 DP I Water Radiator 0.03 1.05 25.00 300.00 342.00 200.00 Liquid 210.43 12.70 0.934 1.004 FTHX-020 DP I Water Radiator 0.03 1.30 25.00 300.00 342.00 200.00 Liquid 246.91 21.37 0.936 1.018 FTHX-021 DP I Water Radiator 0.03 1.70 25.00 300.00 342.00 200.00 Liquid 296.83 43.20 0.797 1.016 FTHX-022 DP I Water Radiator 0.03 0.92 25.00 300.00 342.00 200.00 Liquid 184.85 9.81 0.633 1.013 FTHX-023 DP I Water Radiator 0.03 1.07 25.00 300.00 342.00 200.00 Liquid 206.28 13.68 0.927 1.005 FTHX-024 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 246.65 20.33 0.925 1.025 FTHX-025 DP I Water Radiator 0.03 1.52 25.00 300.00 342.00 200.00 Liquid 276.46 31.99 0.865 1.017 FTHX-026 DP I Water Radiator 0.03 1.53 25.00 300.00 342.00 200.00 Liquid 278.16 32.62 0.867 1.016 FTHX-027 DP I Water Radiator 0.03 1.34 25.00 300.00 342.00 200.00 Liquid 249.53 22.46 0.927 1.007 FTHX-028 DP I Water Radiator 0.03 1.31 25.00 300.00 342.00 200.00 Liquid 247.49 21.73 0.908 1.012 187 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW FTHX-029 DP I Water Radiator 0.03 1.03 25.00 300.00 342.00 200.00 Liquid 209.32 12.40 0.955 1.012 FTHX-030 DP I Water Radiator 0.03 1.20 25.00 300.00 342.00 200.00 Liquid 227.87 17.41 0.987 1.003 FTHX-031 DP I Water Radiator 0.03 1.91 25.00 300.00 342.00 200.00 Liquid 331.20 62.56 0.965 1.034 FTHX-032 DP I Water Radiator 0.03 0.81 25.00 300.00 342.00 200.00 Liquid 187.16 7.97 0.962 1.062 FTHX-033 DP I Water Radiator 0.03 1.22 25.00 300.00 342.00 200.00 Liquid 229.51 17.98 0.856 1.001 FTHX-034 DP I Water Radiator 0.03 1.02 25.00 300.00 342.00 200.00 Liquid 208.53 12.20 0.945 1.009 FTHX-035 DP I Water Radiator 0.03 1.61 25.00 300.00 342.00 200.00 Liquid 291.62 39.13 0.868 1.031 FTHX-036 DP I Water Radiator 0.03 1.06 25.00 300.00 342.00 200.00 Liquid 210.49 12.97 0.926 1.001 FTHX-037 DP I Water Radiator 0.03 1.03 25.00 300.00 342.00 200.00 Liquid 208.87 12.27 0.945 1.009 FTHX-038 DP I Water Radiator 0.03 1.13 25.00 300.00 342.00 200.00 Liquid 224.74 15.86 0.928 1.024 FTHX-039 DP I Water Radiator 0.03 1.53 25.00 300.00 342.00 200.00 Liquid 275.09 32.56 0.858 1.015 FTHX-040 DP I Water Radiator 0.03 1.07 25.00 300.00 342.00 200.00 Liquid 214.61 13.40 0.927 1.007 FTHX-041 DP I Water Radiator 0.03 1.34 25.00 300.00 342.00 200.00 Liquid 246.92 22.40 0.927 1.007 FTHX-042 DP I Water Radiator 0.03 1.02 25.00 300.00 342.00 200.00 Liquid 208.59 12.24 0.934 1.010 FTHX-043 DP I Water Radiator 0.03 0.95 25.00 300.00 342.00 200.00 Liquid 193.16 10.59 0.683 1.016 FTHX-044 DP I Water Radiator 0.03 0.79 25.00 300.00 342.00 200.00 Liquid 184.60 7.54 0.960 1.066 FTHX-045 DP I Water Radiator 0.03 1.60 25.00 300.00 342.00 200.00 Liquid 289.94 38.22 0.868 1.029 FTHX-046 DP I Water Radiator 0.03 1.12 25.00 300.00 342.00 200.00 Liquid 226.65 15.72 0.928 1.025 FTHX-047 DP I Water Radiator 0.03 1.83 25.00 300.00 342.00 200.00 Liquid 283.99 53.51 0.981 1.004 FTHX-048 DP I Water Radiator 0.03 1.01 25.00 300.00 342.00 200.00 Liquid 206.23 11.99 0.926 1.016 FTHX-049 DP I Water Radiator 0.03 1.06 25.00 300.00 342.00 200.00 Liquid 208.96 13.03 0.926 1.000 FTHX-050 DP I Water Radiator 0.03 0.90 25.00 300.00 342.00 200.00 Liquid 184.49 9.57 0.643 1.017 FTHX-051 DP I Water Radiator 0.03 1.22 25.00 300.00 342.00 200.00 Liquid 232.66 18.76 0.987 1.013 FTHX-052 DP I Water Radiator 0.03 1.89 25.00 300.00 342.00 200.00 Liquid 320.76 58.03 0.973 1.018 FTHX-053 DP I Water Radiator 0.03 0.99 25.00 300.00 342.00 200.00 Liquid 200.66 11.02 0.931 1.007 FTHX-054 DP I Water Radiator 0.03 1.12 25.00 300.00 342.00 200.00 Liquid 223.76 15.75 0.928 1.023 FTHX-055 DP I Water Radiator 0.03 1.36 25.00 300.00 342.00 200.00 Liquid 253.65 23.05 0.889 1.003 FTHX-056 DP I Water Radiator 0.03 1.05 25.00 300.00 342.00 200.00 Liquid 210.71 12.79 0.934 1.004 FTHX-057 DP I Water Radiator 0.03 1.07 25.00 300.00 342.00 200.00 Liquid 211.45 13.39 0.927 1.005 FTHX-058 DP I Water Radiator 0.03 1.93 25.00 300.00 342.00 200.00 Liquid 335.63 63.36 0.956 1.033 FTHX-059 DP I Water Radiator 0.03 1.29 25.00 300.00 342.00 200.00 Liquid 245.99 20.98 0.944 1.019 FTHX-060 DP I Water Radiator 0.03 1.01 25.00 300.00 342.00 200.00 Liquid 205.14 11.66 0.955 1.003 FTHX-061 DP I Water Radiator 0.03 1.10 25.00 300.00 342.00 200.00 Liquid 227.13 15.47 0.957 1.036 FTHX-062 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 291.33 43.97 0.814 1.013 FTHX-063 DP I Water Radiator 0.03 1.23 25.00 300.00 342.00 200.00 Liquid 234.43 18.86 0.972 1.007 FTHX-064 DP I Water Radiator 0.03 1.84 25.00 300.00 342.00 200.00 Liquid 284.74 54.31 0.981 1.005 FTHX-065 DP I Water Radiator 0.03 1.34 25.00 300.00 342.00 200.00 Liquid 253.02 22.60 0.992 1.011 FTHX-066 DP I Water Radiator 0.03 1.10 25.00 300.00 342.00 200.00 Liquid 225.75 15.19 0.956 1.034 FTHX-067 DP I Water Radiator 0.03 1.19 25.00 300.00 342.00 200.00 Liquid 230.31 17.14 0.995 1.007 FTHX-068 DP I Water Radiator 0.03 1.39 25.00 300.00 342.00 200.00 Liquid 249.72 25.73 0.875 1.009 FTHX-069 DP I Water Radiator 0.03 1.71 25.00 300.00 342.00 200.00 Liquid 291.34 43.93 0.815 1.013 FTHX-070 DP I Water Radiator 0.03 1.13 25.00 300.00 342.00 200.00 Liquid 225.44 15.99 0.928 1.025 FTHX-071 DP I Water Radiator 0.03 0.96 25.00 300.00 342.00 200.00 Liquid 193.29 10.62 0.788 1.006 FTHX-072 DP I Water Radiator 0.03 0.82 25.00 300.00 342.00 200.00 Liquid 193.85 8.74 0.975 1.076 188 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in hair ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW FTHX-073 DP I Water Radiator 0.03 1.00 25.00 300.00 342.00 200.00 Liquid 201.45 11.46 0.944 1.000 FTHX-074 DP I Water Radiator 0.03 1.02 25.00 300.00 342.00 200.00 Liquid 207.45 12.23 0.912 1.013 FTHX-075 DP I Water Radiator 0.03 1.53 25.00 300.00 342.00 200.00 Liquid 275.86 32.70 0.867 1.015 FTHX-076 DP I Water Radiator 0.03 1.08 25.00 300.00 342.00 200.00 Liquid 220.73 14.74 0.963 1.034 FTHX-077 DP I Water Radiator 0.03 1.09 25.00 300.00 342.00 200.00 Liquid 218.69 15.13 0.956 1.034 FTHX-078 DP I Water Radiator 0.03 1.12 25.00 300.00 342.00 200.00 Liquid 224.07 15.71 0.928 1.023 FTHX-079 DP I Water Radiator 0.03 1.69 25.00 300.00 342.00 200.00 Liquid 287.25 42.96 0.771 1.013 FTHX-080 DP I Water Radiator 0.03 1.89 25.00 300.00 342.00 200.00 Liquid 291.30 60.21 0.973 1.009 FTHX-081 DP I Water Radiator 0.03 0.95 25.00 300.00 342.00 200.00 Liquid 190.37 10.56 0.683 1.015 FTHX-082 DP I Water Radiator 0.03 1.26 25.00 300.00 342.00 200.00 Liquid 240.48 19.82 0.965 1.008 FTHX-083 DP I Water Radiator 0.03 1.04 25.00 300.00 342.00 200.00 Liquid 209.97 12.53 0.898 1.009 FTHX-084 DP I Water Radiator 0.03 1.14 25.00 300.00 342.00 200.00 Liquid 231.86 16.63 0.935 1.034 FTHX-085 DP I Water Radiator 0.03 1.56 25.00 300.00 342.00 200.00 Liquid 284.18 33.68 0.956 1.017 FTHX-086 DP I Water Radiator 0.03 1.53 25.00 300.00 342.00 200.00 Liquid 278.01 32.56 0.867 1.015 FTHX-087 DP I Water Radiator 0.03 1.28 25.00 300.00 342.00 200.00 Liquid 236.38 20.52 0.842 1.007 FTHX-088 DP I Water Radiator 0.03 1.01 25.00 300.00 342.00 200.00 Liquid 202.51 11.70 0.944 1.002 FTHX-089 DP I Water Radiator 0.03 1.09 25.00 300.00 342.00 200.00 Liquid 223.27 15.10 0.964 1.038 FTHX-090 DP I Water Radiator 0.03 0.99 25.00 300.00 342.00 200.00 Liquid 200.68 10.97 0.931 1.004 FTHX-091 DP I Water Radiator 0.03 1.00 25.00 300.00 342.00 200.00 Liquid 200.93 11.07 0.951 1.005 FTHX-092 DP I Water Radiator 0.03 1.67 25.00 300.00 342.00 200.00 Liquid 291.65 39.29 0.789 1.005 FTHX-093 DP I Water Radiator 0.03 1.21 25.00 300.00 342.00 200.00 Liquid 230.38 17.88 0.863 1.005 189 NTHX Figure 131. NTHX surface concept. Table 34. NTHX dimensions. Design Tag ht wt δt Pl Pt Nt Nr x1 x2 x3 y1 y2 y3 l H d Af V Vmat’l mm mm mm mm mm - - - - - - - - m m m m² cm³ cm³ NTHX-001 1.1000 3.0000 0.3000 2.4000 2.2000 7 45 0.00000 0.00000 0.00000 0.18000 0.36000 0.04500 0.1000 0.1000 0.0174 0.0100 174.00 46.90 NTHX-002 0.7053 1.7642 0.1411 1.5715 1.7229 5 70 0.42033 0.74194 0.07820 0.07234 0.58944 0.97752 0.1432 0.1179 0.0081 0.0169 135.90 21.78 NTHX-003 0.5684 1.4319 0.1137 1.1905 1.3886 5 79 0.81232 0.99218 0.08016 0.93255 0.67742 0.20332 0.1571 0.1075 0.0062 0.0169 104.56 17.76 NTHX-004 0.5489 1.3741 0.1098 1.1424 1.3408 5 79 0.43597 0.73998 0.06452 0.93255 0.73998 0.37537 0.1626 0.1038 0.0059 0.0169 100.33 17.81 NTHX-005 0.5489 1.3848 0.1098 1.1391 1.3408 5 79 0.42033 0.74194 0.33040 0.93255 0.74780 0.12610 0.1626 0.1038 0.0059 0.0169 100.30 17.54 NTHX-006 0.5489 1.3741 0.1098 1.1424 1.3408 5 79 0.43402 0.64614 0.06452 0.93255 0.73998 0.37537 0.1615 0.1038 0.0059 0.0168 99.62 17.67 NTHX-007 0.5684 1.4319 0.1137 1.1779 1.3886 5 79 0.93744 0.62463 0.08798 0.93255 0.73998 0.20332 0.1414 0.1075 0.0061 0.0152 93.36 15.75 NTHX-008 0.5489 1.3848 0.1098 1.1391 1.3408 5 79 0.93646 0.67742 0.08798 0.93255 0.74780 0.37537 0.1464 0.1038 0.0059 0.0152 90.29 15.74 NTHX-009 0.5489 1.4159 0.1098 1.1273 1.3408 5 79 0.93646 0.67742 0.08798 0.93255 0.74780 0.37537 0.1464 0.1038 0.0059 0.0152 90.05 16.07 NTHX-010 0.5489 1.4159 0.1098 1.0775 1.3408 5 79 0.93646 0.67937 0.08798 0.93255 0.74780 0.40665 0.1464 0.1038 0.0057 0.0152 87.02 16.14 NTHX-011 0.5489 1.4159 0.1098 1.0775 1.3408 5 79 0.81232 0.99218 0.08016 0.93255 0.74780 0.37537 0.1450 0.1038 0.0057 0.0151 86.18 16.07 Uniform Air Flow l Pt Pl wt ht -1 -0.5 0 0.5 1 1.5 2 2.5 3 -1 0 1 2 3 4 5 6 7 tw th lP 2 tP  ,le lex y  ,te tex y  0 0,x y  1 1,x y  2 2,x y 0.2t th   tN rN u T 190 Design Tag ht wt δt Pl Pt Nt Nr x1 x2 x3 y1 y2 y3 l H d Af V Vmat’l mm mm mm mm mm - - - - - - - - m m m m² cm³ cm³ NTHX-012 0.5489 1.4159 0.1098 1.0651 1.3065 5 79 0.81232 0.99218 0.08016 0.93255 0.74780 0.40665 0.1488 0.1011 0.0057 0.0151 85.43 16.55 NTHX-013 0.5684 1.4319 0.1137 1.1779 1.3952 5 79 0.81232 0.99022 0.08016 0.93255 0.73998 0.37634 0.1265 0.1080 0.0061 0.0137 83.91 14.71 NTHX-014 0.5489 1.3741 0.1098 1.1786 1.3472 5 79 0.81232 0.89638 0.07820 0.93255 0.68524 0.40665 0.1310 0.1043 0.0061 0.0137 83.16 14.19 NTHX-015 0.5489 1.3848 0.1098 1.1391 1.3408 5 79 0.81232 0.99218 0.08016 0.93255 0.74780 0.37537 0.1316 0.1038 0.0059 0.0137 81.15 14.29 NTHX-016 0.5489 1.4170 0.1098 1.0783 1.3387 5 79 0.93744 0.99218 0.08016 0.93255 0.74780 0.37537 0.1318 0.1036 0.0057 0.0137 78.27 14.53 NTHX-017 0.5513 1.3802 0.1103 1.0503 1.3532 5 79 0.81232 0.67742 0.08798 0.93255 0.74780 0.37537 0.1304 0.1048 0.0056 0.0137 76.23 14.13 NTHX-018 0.5489 1.3741 0.1098 1.0336 1.3140 5 79 0.81232 0.99218 0.08016 0.93353 0.74780 0.28152 0.1327 0.1017 0.0055 0.0135 74.37 14.10 NTHX-019 0.5098 1.3160 0.1020 0.9899 1.2204 5 80 0.43500 0.71065 0.08016 0.93255 0.74780 0.37537 0.1427 0.0957 0.0053 0.0137 72.06 14.05 NTHX-020 0.5489 1.3741 0.1098 1.0457 1.3483 5 70 0.81232 0.99022 0.20528 0.93646 0.74780 0.42229 0.1355 0.0922 0.0056 0.0125 69.46 13.15 NTHX-021 0.5489 1.3848 0.1098 1.0416 1.3129 5 79 0.81134 0.87488 0.08798 0.93255 0.73998 0.37537 0.1230 0.1016 0.0056 0.0125 69.40 13.34 NTHX-022 0.5489 1.3741 0.1098 1.0336 1.3140 5 80 0.81036 0.71065 0.08016 0.93255 0.74780 0.37537 0.1213 0.1030 0.0055 0.0125 68.86 13.20 NTHX-023 0.5122 1.3224 0.1024 1.0034 1.2252 5 79 0.80450 0.86706 0.07820 0.91691 0.74780 0.65689 0.1318 0.0949 0.0053 0.0125 66.70 13.05 NTHX-024 0.5489 1.3741 0.1098 1.0336 1.3140 5 70 0.81232 0.67742 0.08798 0.91691 0.59140 0.40665 0.1307 0.0899 0.0055 0.0118 64.75 12.60 NTHX-025 0.5098 1.3160 0.1020 1.0015 1.2194 5 79 0.42620 0.64614 0.06549 0.93255 0.73998 0.37537 0.1245 0.0944 0.0053 0.0118 62.56 12.09 NTHX-026 0.5098 1.2842 0.1020 0.9772 1.2194 5 79 0.42033 0.67742 0.08798 0.41642 0.74780 0.40665 0.1245 0.0944 0.0052 0.0118 61.04 11.90 NTHX-027 0.5122 1.2823 0.1024 0.9758 1.2573 5 70 0.42131 0.37048 0.26979 0.38514 0.71065 0.97067 0.1367 0.0860 0.0052 0.0118 60.95 11.87 NTHX-028 0.5098 1.3160 0.1020 0.9986 1.1556 5 79 0.80352 0.71065 0.08016 0.93255 0.73216 0.37537 0.1195 0.0895 0.0053 0.0107 56.77 11.40 NTHX-029 0.5098 1.3160 0.1020 0.9986 1.1556 5 79 0.40860 0.62463 0.26979 0.93255 0.66960 0.40665 0.1158 0.0895 0.0053 0.0104 55.02 11.53 NTHX-030 0.6540 1.7394 0.1308 1.5073 1.5508 6 65 0.99707 0.98631 0.00293 0.99707 0.33822 0.00880 0.1019 0.0999 0.0093 0.0102 94.45 14.30 NTHX-031 0.6540 1.7394 0.1308 1.5035 1.5508 6 65 0.95112 0.99316 0.01075 0.99707 0.33040 0.01662 0.1019 0.0999 0.0093 0.0102 94.26 14.39 NTHX-032 0.6540 1.7381 0.1308 1.3801 1.5508 6 70 0.95112 0.98534 0.00293 0.99316 0.33822 0.00782 0.0960 0.1061 0.0086 0.0102 87.96 14.50 NTHX-033 0.6491 1.7315 0.1298 1.3748 1.5392 6 74 0.95112 0.98729 0.00098 0.99707 0.33822 0.00880 0.0901 0.1130 0.0086 0.0102 87.62 14.23 NTHX-034 0.6491 1.7264 0.1298 1.3708 1.5392 6 74 0.95112 0.96285 0.00098 0.99707 0.33822 0.00880 0.0901 0.1130 0.0086 0.0102 87.37 14.17 NTHX-035 0.6466 1.7187 0.1293 1.3041 1.5334 6 65 0.95112 0.96285 0.00098 0.99902 0.33822 0.00489 0.1031 0.0988 0.0082 0.0102 83.90 14.09 NTHX-036 0.6149 1.6354 0.1230 1.2985 1.4581 6 65 0.95112 0.98534 0.00293 0.99707 0.33822 0.00098 0.1084 0.0939 0.0081 0.0102 82.76 13.40 NTHX-037 0.6344 1.6862 0.1269 1.2795 1.5057 6 66 0.95112 0.96481 0.00098 0.99707 0.33822 0.01662 0.1050 0.0970 0.0081 0.0102 82.31 14.12 NTHX-038 0.6075 1.6207 0.1215 1.2868 1.4407 6 65 0.95112 0.98534 0.00098 0.99707 0.46334 0.01662 0.1114 0.0914 0.0081 0.0102 82.02 13.76 NTHX-039 0.6295 1.6744 0.1259 1.2742 1.4929 6 65 0.95112 0.96676 0.00098 0.99707 0.33822 0.00098 0.1059 0.0962 0.0080 0.0102 81.92 13.70 NTHX-040 0.6075 1.6159 0.1215 1.2262 1.4419 6 65 0.95112 0.96285 0.00098 0.99707 0.33822 0.00880 0.1096 0.0929 0.0077 0.0102 78.88 13.27 NTHX-041 0.5880 1.4995 0.1176 1.1411 1.3944 6 65 0.98240 0.98534 0.00293 0.99707 0.33822 0.00098 0.1134 0.0898 0.0072 0.0102 73.37 12.33 NTHX-042 0.5880 1.4984 0.1176 1.1403 1.3944 6 65 0.98240 0.73509 0.00293 0.99707 0.33822 0.00098 0.1134 0.0898 0.0072 0.0102 73.31 12.12 NTHX-043 0.5562 1.4783 0.1112 1.1218 1.3201 6 66 0.95112 0.98534 0.00293 0.99707 0.33822 0.01662 0.1197 0.0850 0.0071 0.0102 72.16 12.40 NTHX-044 0.5880 1.5639 0.1176 1.1901 1.3944 6 64 0.95112 0.98534 0.00098 0.99707 0.31476 0.00880 0.1103 0.0870 0.0075 0.0096 72.16 12.30 NTHX-045 0.5880 1.5639 0.1176 1.1867 1.3944 6 65 0.96872 0.98631 0.00098 0.99707 0.33822 0.00098 0.1060 0.0898 0.0075 0.0095 71.41 11.98 NTHX-046 0.5880 1.5639 0.1176 1.1867 1.3944 6 65 0.94721 0.96285 0.00293 0.99707 0.33822 0.00782 0.1052 0.0898 0.0075 0.0094 70.84 11.92 NTHX-047 0.5880 1.5639 0.1176 1.1901 1.3955 6 74 0.96285 0.98534 0.00098 0.99707 0.31476 0.00880 0.0928 0.1011 0.0075 0.0094 70.44 11.95 NTHX-048 0.5904 1.5058 0.1181 1.1426 1.4002 6 65 0.96676 0.98631 0.00098 0.99707 0.32258 0.12610 0.1073 0.0902 0.0072 0.0097 69.89 12.50 NTHX-049 0.5880 1.4995 0.1176 1.1411 1.3944 6 65 0.96676 0.98631 0.00098 0.99707 0.32258 0.12610 0.1078 0.0898 0.0072 0.0097 69.76 12.45 NTHX-050 0.5880 1.4995 0.1176 1.1378 1.3944 6 65 0.96676 0.98631 0.00098 0.99707 0.32258 0.12610 0.1078 0.0898 0.0072 0.0097 69.60 12.45 NTHX-051 1.0332 2.8688 0.2066 2.1958 2.3210 7 34 0.98925 0.47312 0.01369 1.00000 0.46823 0.00098 0.1309 0.0776 0.0160 0.0102 163.01 28.50 NTHX-052 1.0039 2.7945 0.2008 2.1389 2.2551 7 43 0.99316 0.72923 0.00978 1.00000 0.46823 0.00000 0.1062 0.0957 0.0156 0.0102 158.79 28.05 NTHX-053 1.0000 2.7836 0.2000 2.1305 2.2463 7 35 0.99218 0.47898 0.01466 1.00000 0.43597 0.00000 0.1313 0.0774 0.0156 0.0102 158.17 27.53 NTHX-054 1.0000 2.7765 0.2000 2.1252 2.2463 7 35 0.99218 0.47898 0.01466 1.00000 0.43597 0.00000 0.1313 0.0774 0.0155 0.0102 157.77 27.46 NTHX-055 1.0078 2.7344 0.2016 2.0628 2.2639 7 41 0.99022 0.47898 0.01369 0.99609 0.43597 0.00000 0.1110 0.0916 0.0151 0.0102 153.54 27.05 191 Design Tag ht wt δt Pl Pt Nt Nr x1 x2 x3 y1 y2 y3 l H d Af V Vmat’l mm mm mm mm mm - - - - - - - - m m m m² cm³ cm³ NTHX-056 1.0000 2.7109 0.2000 2.0391 2.2483 7 35 0.99707 0.23069 0.01369 1.00000 0.43402 0.00000 0.1312 0.0774 0.0149 0.0102 151.85 26.43 NTHX-057 1.0000 2.7132 0.2000 2.0349 2.2483 7 34 0.99707 0.23069 0.01369 0.99804 0.46823 0.00098 0.1351 0.0752 0.0149 0.0102 151.62 26.60 NTHX-058 1.0000 2.7015 0.2000 2.0320 2.2385 7 35 0.98631 0.47898 0.01466 0.99804 0.43695 0.01564 0.1357 0.0749 0.0149 0.0102 151.33 27.96 NTHX-059 1.0000 2.7109 0.2000 2.0331 2.2463 7 43 0.99707 0.73314 0.00978 1.00000 0.49853 0.00000 0.1052 0.0953 0.0149 0.0100 149.56 27.01 NTHX-060 1.0000 2.7109 0.2000 2.0749 2.2463 7 35 0.99022 0.47898 0.01369 0.99218 0.40567 0.00000 0.1313 0.0751 0.0152 0.0099 149.53 26.78 NTHX-061 1.0000 2.7109 0.2000 2.0629 2.2463 7 35 0.99022 0.47898 0.03030 0.99022 0.43695 0.00000 0.1313 0.0751 0.0151 0.0099 148.82 26.96 NTHX-062 1.0000 2.7109 0.2000 2.0391 2.2385 7 44 0.99022 0.47898 0.01369 1.00000 0.43597 0.00000 0.1038 0.0950 0.0149 0.0099 147.41 26.71 NTHX-063 1.0000 2.7120 0.2000 2.0340 2.2385 7 35 0.99022 0.47898 0.01369 0.98925 0.43695 0.00000 0.1317 0.0749 0.0149 0.0099 147.12 26.99 NTHX-064 1.0000 2.7109 0.2000 2.0331 2.2346 7 34 0.99022 0.47898 0.00978 1.00000 0.43402 0.00391 0.1320 0.0747 0.0149 0.0099 147.06 26.28 NTHX-065 1.0000 2.7109 0.2000 2.0331 2.2385 7 35 0.99707 0.23069 0.01369 0.99609 0.43597 0.00000 0.1312 0.0749 0.0149 0.0098 146.45 26.44 NTHX-066 1.0000 2.7132 0.2000 2.0468 2.2385 7 35 0.99218 0.47898 0.01369 0.99609 0.43695 0.00000 0.1296 0.0749 0.0150 0.0097 145.46 26.55 NTHX-067 1.0000 2.7132 0.2000 2.0349 2.2346 7 34 0.95894 0.47898 0.01369 1.00000 0.46725 0.00196 0.1298 0.0747 0.0149 0.0097 144.77 25.98 NTHX-068 1.0000 2.7413 0.2000 2.0681 2.2463 7 44 0.98925 0.47898 0.01369 0.99609 0.42033 0.00000 0.1001 0.0953 0.0151 0.0095 144.60 25.97 NTHX-069 1.0000 2.7109 0.2000 2.0451 2.2463 7 44 0.98925 0.47898 0.01369 1.00000 0.43597 0.00000 0.1001 0.0953 0.0150 0.0095 142.99 25.76 NTHX-070 1.0000 2.7132 0.2000 2.0468 2.2385 7 35 0.99022 0.48094 0.00684 1.00000 0.46823 0.00000 0.1235 0.0771 0.0150 0.0095 142.82 25.37 NTHX-071 1.0000 2.7132 0.2000 2.0409 2.2385 7 34 0.99022 0.47898 0.01369 1.00000 0.43695 0.00000 0.1272 0.0749 0.0150 0.0095 142.48 25.32 NTHX-072 1.0000 2.7097 0.2000 2.0323 2.2385 7 44 0.99022 0.47898 0.01369 1.00000 0.43597 0.00000 0.1002 0.0950 0.0149 0.0095 141.96 25.78 NTHX-073 1.0000 2.7132 0.2000 2.0468 2.2385 7 35 0.99022 0.48094 0.00684 1.00000 0.46823 0.00000 0.1225 0.0771 0.0150 0.0094 141.68 25.17 NTHX-074 1.0000 2.7765 0.2000 2.0885 2.2405 7 35 0.99022 0.47898 0.01369 0.99609 0.43402 0.00000 0.1198 0.0772 0.0153 0.0092 141.52 25.05 NTHX-075 1.0000 2.7015 0.2000 2.0261 2.1935 7 35 0.99218 0.47898 0.01466 1.00000 0.43597 0.00000 0.1290 0.0734 0.0149 0.0095 140.67 26.32 NTHX-076 1.0078 2.7628 0.2016 2.0721 2.2186 7 35 0.99022 0.47898 0.01369 1.00000 0.46823 0.00000 0.1209 0.0764 0.0152 0.0092 140.49 25.49 NTHX-077 1.0000 2.7413 0.2000 2.0620 2.2023 7 41 0.98925 0.22874 0.01369 1.00000 0.43597 0.00000 0.1038 0.0891 0.0151 0.0092 139.73 24.75 NTHX-078 1.0039 2.7244 0.2008 2.0433 2.2100 7 35 0.99022 0.47898 0.01369 1.00000 0.48094 0.00000 0.1214 0.0761 0.0150 0.0092 138.53 25.20 NTHX-079 1.0000 2.7132 0.2000 2.0349 2.2014 7 35 0.99022 0.47312 0.01369 1.00000 0.46823 0.00000 0.1219 0.0758 0.0149 0.0092 137.96 25.05 NTHX-080 1.0000 2.7109 0.2000 2.0331 2.2014 7 35 0.99022 0.47898 0.01369 0.99609 0.43695 0.00000 0.1255 0.0736 0.0149 0.0092 137.85 25.70 NTHX-081 1.0000 2.7132 0.2000 2.0349 2.2014 7 35 0.98436 0.73118 0.02933 1.00000 0.46823 0.00000 0.1217 0.0758 0.0149 0.0092 137.70 25.46 NTHX-082 1.0000 2.7109 0.2000 2.0331 2.2014 7 34 0.99022 0.47898 0.00978 1.00000 0.43402 0.00391 0.1253 0.0736 0.0149 0.0092 137.58 24.95 NTHX-083 1.0000 2.7015 0.2000 2.0261 2.1935 7 35 0.99022 0.47898 0.01369 1.00000 0.49267 0.00000 0.1223 0.0756 0.0149 0.0092 137.37 25.11 NTHX-084 1.0000 2.7132 0.2000 2.0349 2.1935 7 35 0.99022 0.47898 0.01369 0.99609 0.43402 0.00000 0.1214 0.0756 0.0149 0.0092 136.89 24.86 NTHX-085 1.0000 2.7015 0.2000 2.0261 2.1935 7 41 0.99218 0.47898 0.01466 1.00000 0.43597 0.00391 0.1034 0.0887 0.0149 0.0092 136.30 24.77 NTHX-086 1.0000 2.7015 0.2000 2.0261 2.1935 7 41 0.99218 0.47898 0.01466 1.00000 0.43402 0.01662 0.1032 0.0887 0.0149 0.0092 136.04 24.90 NTHX-087 1.0000 2.7132 0.2000 2.0349 2.1935 7 35 0.98925 0.47996 0.00587 0.99609 0.43402 0.00000 0.1191 0.0756 0.0149 0.0090 134.28 24.36 Table 35. NTHX performances and operating conditions. Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in h ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW NTHX-001 DP I Water Radiator 0.03 3.00 25.00 300.00 350.00 200.00 Liquid 201.00 64.10 0.650 1.072 NTHX-002 DP I Water Radiator 0.03 1.78 25.00 300.00 349.41 200.00 Liquid 232.14 18.20 0.495 1.072 NTHX-003 DP I Water Radiator 0.03 1.78 25.00 300.00 348.20 200.00 Liquid 246.46 18.50 0.894 1.080 NTHX-004 DP I Water Radiator 0.03 1.78 25.00 300.00 348.20 200.00 Liquid 257.39 21.05 0.889 1.100 192 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in h ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW NTHX-005 DP I Water Radiator 0.03 1.78 25.00 300.00 348.18 200.00 Liquid 255.05 21.09 0.942 1.098 NTHX-006 DP I Water Radiator 0.03 1.79 25.00 300.00 348.20 200.00 Liquid 257.12 21.43 0.905 1.096 NTHX-007 DP I Water Radiator 0.03 1.97 25.00 300.00 348.51 200.00 Liquid 250.04 21.93 0.974 1.041 NTHX-008 DP I Water Radiator 0.03 1.97 25.00 300.00 348.18 200.00 Liquid 258.15 22.84 0.984 1.051 NTHX-009 DP I Water Radiator 0.03 1.97 25.00 300.00 348.20 200.00 Liquid 257.14 23.15 0.936 1.060 NTHX-010 DP I Water Radiator 0.03 1.97 25.00 300.00 348.20 200.00 Liquid 259.53 23.57 0.911 1.064 NTHX-011 DP I Water Radiator 0.03 1.99 25.00 300.00 348.20 200.00 Liquid 260.98 23.79 0.805 1.063 NTHX-012 DP I Water Radiator 0.03 1.99 25.00 300.00 348.20 200.00 Liquid 267.00 25.22 0.810 1.086 NTHX-013 DP I Water Radiator 0.03 2.20 25.00 300.00 348.20 200.00 Liquid 261.83 26.22 0.640 1.002 NTHX-014 DP I Water Radiator 0.03 2.20 25.00 300.00 348.20 200.00 Liquid 264.44 26.42 0.763 1.005 NTHX-015 DP I Water Radiator 0.03 2.20 25.00 300.00 348.18 200.00 Liquid 266.01 26.73 0.766 1.013 NTHX-016 DP I Water Radiator 0.03 2.20 25.00 300.00 348.17 200.00 Liquid 266.09 26.82 0.773 1.025 NTHX-017 DP I Water Radiator 0.03 2.20 25.00 300.00 348.20 200.00 Liquid 267.58 27.73 0.824 1.010 NTHX-018 DP I Water Radiator 0.03 2.22 25.00 300.00 348.17 200.00 Liquid 272.30 28.18 0.836 1.025 NTHX-019 DP I Water Radiator 0.03 2.20 25.00 300.00 349.45 200.00 Liquid 282.45 31.79 0.950 1.094 NTHX-020 DP I Water Radiator 0.03 2.40 25.00 300.00 349.42 200.00 Liquid 279.28 32.20 0.807 1.013 NTHX-021 DP I Water Radiator 0.03 2.40 25.00 300.00 348.18 200.00 Liquid 278.88 32.67 0.733 1.002 NTHX-022 DP I Water Radiator 0.03 2.40 25.00 300.00 349.42 200.00 Liquid 278.21 32.95 0.755 1.023 NTHX-023 DP I Water Radiator 0.03 2.40 25.00 300.00 348.20 200.00 Liquid 290.51 35.35 0.829 1.035 NTHX-024 DP I Water Radiator 0.03 2.55 25.00 300.00 349.42 200.00 Liquid 284.82 36.65 0.880 1.005 NTHX-025 DP I Water Radiator 0.03 2.55 25.00 300.00 348.20 200.00 Liquid 290.12 38.90 0.867 1.006 NTHX-026 DP I Water Radiator 0.03 2.55 25.00 300.00 348.20 200.00 Liquid 295.74 41.81 0.875 1.001 NTHX-027 DP I Water Radiator 0.03 2.55 25.00 300.00 348.19 200.00 Liquid 308.25 45.80 0.972 1.008 NTHX-028 DP I Water Radiator 0.03 2.81 25.00 300.00 348.20 200.00 Liquid 306.29 46.61 0.952 1.009 NTHX-029 DP I Water Radiator 0.03 2.90 25.00 300.00 348.20 200.00 Liquid 324.31 58.00 0.693 1.024 NTHX-030 DP I Water Radiator 0.03 2.95 25.00 300.00 349.99 200.00 Liquid 256.14 44.95 0.400 1.006 NTHX-031 DP I Water Radiator 0.03 2.95 25.00 300.00 349.99 200.00 Liquid 256.51 45.26 0.393 1.007 NTHX-032 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 256.76 45.27 0.353 1.009 NTHX-033 DP I Water Radiator 0.03 2.95 25.00 300.00 349.83 200.00 Liquid 261.06 45.30 0.316 1.014 NTHX-034 DP I Water Radiator 0.03 2.95 25.00 300.00 349.84 200.00 Liquid 261.08 45.37 0.322 1.013 NTHX-035 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 263.05 45.53 0.429 1.015 NTHX-036 DP I Water Radiator 0.03 2.95 25.00 300.00 349.13 200.00 Liquid 267.15 45.84 0.550 1.011 NTHX-037 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 261.38 45.94 0.467 1.019 NTHX-038 DP I Water Radiator 0.03 2.95 25.00 300.00 348.50 200.00 Liquid 263.55 46.09 0.568 1.001 NTHX-039 DP I Water Radiator 0.03 2.95 25.00 300.00 349.21 200.00 Liquid 265.71 46.10 0.495 1.010 NTHX-040 DP I Water Radiator 0.03 2.95 25.00 300.00 349.13 200.00 Liquid 269.93 46.34 0.587 1.016 NTHX-041 DP I Water Radiator 0.03 2.95 25.00 300.00 349.13 200.00 Liquid 278.92 46.37 0.764 1.013 NTHX-042 DP I Water Radiator 0.03 2.95 25.00 300.00 349.13 200.00 Liquid 276.96 47.38 0.892 1.008 NTHX-043 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 275.45 47.46 0.892 1.048 NTHX-044 DP I Water Radiator 0.03 3.12 25.00 300.00 349.76 200.00 Liquid 275.11 51.39 0.691 1.017 NTHX-045 DP I Water Radiator 0.03 3.15 25.00 300.00 349.13 200.00 Liquid 279.77 51.57 0.646 1.000 NTHX-046 DP I Water Radiator 0.03 3.17 25.00 300.00 349.72 200.00 Liquid 280.47 52.60 0.636 1.010 NTHX-047 DP I Water Radiator 0.03 3.20 25.00 300.00 349.76 200.00 Liquid 277.88 52.71 0.502 1.007 NTHX-048 DP I Water Radiator 0.03 3.10 25.00 300.00 349.13 200.00 Liquid 288.14 53.04 0.640 1.003 193 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in h ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW NTHX-049 DP I Water Radiator 0.03 3.10 25.00 300.00 349.13 200.00 Liquid 288.51 53.06 0.654 1.004 NTHX-050 DP I Water Radiator 0.03 3.10 25.00 300.00 349.13 200.00 Liquid 288.62 53.09 0.654 1.004 NTHX-051 DP I Water Radiator 0.03 2.95 25.00 300.00 349.60 200.00 Liquid 206.57 42.22 0.158 1.012 NTHX-052 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 212.66 42.30 0.097 1.030 NTHX-053 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 210.74 42.55 0.176 1.027 NTHX-054 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 210.91 42.55 0.178 1.026 NTHX-055 DP I Water Radiator 0.03 2.95 25.00 300.00 349.76 200.00 Liquid 211.58 42.59 0.131 1.015 NTHX-056 DP I Water Radiator 0.03 2.95 25.00 300.00 349.74 200.00 Liquid 208.73 42.70 0.224 1.007 NTHX-057 DP I Water Radiator 0.03 2.95 25.00 300.00 349.60 200.00 Liquid 208.60 42.74 0.231 1.005 NTHX-058 DP I Water Radiator 0.03 2.95 25.00 300.00 349.73 200.00 Liquid 207.74 43.34 0.198 1.021 NTHX-059 DP I Water Radiator 0.03 2.99 25.00 300.00 349.74 200.00 Liquid 216.38 43.52 0.103 1.019 NTHX-060 DP I Water Radiator 0.03 3.04 25.00 300.00 349.76 200.00 Liquid 208.25 44.94 0.197 1.007 NTHX-061 DP I Water Radiator 0.03 3.04 25.00 300.00 349.73 200.00 Liquid 208.39 45.10 0.191 1.007 NTHX-062 DP I Water Radiator 0.03 3.04 25.00 300.00 349.92 200.00 Liquid 211.25 45.20 0.121 1.015 NTHX-063 DP I Water Radiator 0.03 3.04 25.00 300.00 349.76 200.00 Liquid 209.76 45.30 0.193 1.012 NTHX-064 DP I Water Radiator 0.03 3.04 25.00 300.00 349.68 200.00 Liquid 216.84 45.40 0.194 1.014 NTHX-065 DP I Water Radiator 0.03 3.05 25.00 300.00 349.91 200.00 Liquid 206.55 45.73 0.229 1.005 NTHX-066 DP I Water Radiator 0.03 3.09 25.00 300.00 349.76 200.00 Liquid 211.11 46.55 0.190 1.007 NTHX-067 DP I Water Radiator 0.03 3.09 25.00 300.00 349.76 200.00 Liquid 217.44 46.76 0.186 1.009 NTHX-068 DP I Water Radiator 0.03 3.14 25.00 300.00 349.77 200.00 Liquid 212.82 47.43 0.114 1.001 NTHX-069 DP I Water Radiator 0.03 3.14 25.00 300.00 349.92 200.00 Liquid 213.35 47.45 0.116 1.000 NTHX-070 DP I Water Radiator 0.03 3.15 25.00 300.00 349.92 200.00 Liquid 218.98 47.84 0.174 1.004 NTHX-071 DP I Water Radiator 0.03 3.15 25.00 300.00 349.68 200.00 Liquid 219.11 47.91 0.187 1.000 NTHX-072 DP I Water Radiator 0.03 3.15 25.00 300.00 349.92 200.00 Liquid 214.52 47.94 0.116 1.003 NTHX-073 DP I Water Radiator 0.03 3.17 25.00 300.00 349.92 200.00 Liquid 219.67 48.45 0.172 1.002 NTHX-074 DP I Water Radiator 0.03 3.24 25.00 300.00 349.81 200.00 Liquid 220.52 50.00 0.162 1.001 NTHX-075 DP I Water Radiator 0.03 3.17 25.00 300.00 349.72 200.00 Liquid 218.09 50.41 0.192 1.018 NTHX-076 DP I Water Radiator 0.03 3.24 25.00 300.00 349.76 200.00 Liquid 224.06 51.68 0.161 1.010 NTHX-077 DP I Water Radiator 0.03 3.24 25.00 300.00 349.76 200.00 Liquid 220.97 51.82 0.147 1.002 NTHX-078 DP I Water Radiator 0.03 3.24 25.00 300.00 349.83 200.00 Liquid 224.83 51.85 0.167 1.009 NTHX-079 DP I Water Radiator 0.03 3.24 25.00 300.00 349.92 200.00 Liquid 225.37 51.90 0.172 1.012 NTHX-080 DP I Water Radiator 0.03 3.24 25.00 300.00 349.74 200.00 Liquid 219.21 51.95 0.184 1.008 NTHX-081 DP I Water Radiator 0.03 3.25 25.00 300.00 349.44 200.00 Liquid 228.37 51.99 0.146 1.008 NTHX-082 DP I Water Radiator 0.03 3.25 25.00 300.00 349.68 200.00 Liquid 226.12 52.12 0.184 1.007 NTHX-083 DP I Water Radiator 0.03 3.24 25.00 300.00 349.88 200.00 Liquid 226.17 52.36 0.171 1.012 NTHX-084 DP I Water Radiator 0.03 3.27 25.00 300.00 349.44 200.00 Liquid 227.10 52.97 0.174 1.004 NTHX-085 DP I Water Radiator 0.03 3.27 25.00 300.00 349.72 200.00 Liquid 227.42 53.07 0.126 1.007 NTHX-086 DP I Water Radiator 0.03 3.28 25.00 300.00 349.72 200.00 Liquid 227.86 53.54 0.125 1.007 NTHX-087 DP I Water Radiator 0.03 3.33 25.00 300.00 349.60 200.00 Liquid 228.92 54.49 0.171 1.001 194 WTHX Figure 132. WTHX concept. Table 36. WTHX dimensions. Design Tag ht wt δt Pl Pt Nr Nt x1 x2 x3 x4 y1 y2 y3 y4 l H d Af V mm mm mm mm mm - - - - - - - - - - m m m m² cm³ WTHX-001 0.5000 1.4228 0.1000 2.2583 1.1065 6 114 0.97067 0.88270 0.07625 0.09189 0.92375 0.99218 0.8651 0.0391 0.0804 0.1266 0.0135 0.0102 137.97 WTHX-002 0.5000 1.4228 0.1000 1.8428 1.0510 6 108 0.97067 0.53861 0.07625 0.00978 0.98631 0.95894 0.8651 0.0391 0.0890 0.1140 0.0111 0.0101 112.18 δt (xtoi,ytoi) (xtii,ytii) γi δa ≥ δt δb ≥ δt (x2,y2) (x1,y1) (xle,yle) (x3,y3) (x4,y4) (xte,yte) wt = xte - xle wt / 4 wt / 4 wt / 4 wt / 4 ht x y δt/2 Pl/2 wt Pl / 2 Pt Uniform Air Flow Uniform Water Flow l d 195 Design Tag ht wt δt Pl Pt Nr Nt x1 x2 x3 x4 y1 y2 y3 y4 l H d Af V mm mm mm mm mm - - - - - - - - - - m m m m² cm³ WTHX-003 0.5264 1.5411 0.1053 2.5365 1.1722 6 108 0.97067 0.57771 0.07625 0.01760 0.92375 0.99218 0.8495 0.0391 0.0801 0.1271 0.0152 0.0102 155.01 WTHX-004 0.5029 1.3977 0.1006 2.1911 1.0993 6 108 0.97067 0.57771 0.07625 0.02933 0.92766 0.99022 0.8651 0.0547 0.0860 0.1192 0.0131 0.0103 134.78 WTHX-005 0.5000 1.4247 0.1000 1.8436 1.0518 6 108 0.97067 0.50244 0.07625 0.09189 0.99316 0.99218 0.8495 0.1017 0.0891 0.1141 0.0111 0.0102 112.41 WTHX-006 0.5000 1.3895 0.1000 2.1784 1.0929 6 124 0.97067 0.82796 0.07625 0.02542 0.92375 0.99218 0.8651 0.0078 0.0739 0.1360 0.0131 0.0101 131.46 WTHX-007 0.5000 1.3895 0.1000 2.1784 1.0929 6 110 0.97067 0.57771 0.07625 0.01760 0.92375 0.99218 0.8651 0.0078 0.0833 0.1207 0.0131 0.0101 131.45 WTHX-008 0.5000 1.3895 0.1000 2.1784 1.0920 6 108 0.98631 0.88270 0.07625 0.02542 0.89247 0.99218 0.8651 0.0078 0.0859 0.1184 0.0131 0.0102 133.03 WTHX-009 0.5264 1.5411 0.1053 2.5666 1.1722 6 108 0.97067 0.88563 0.00587 0.09189 0.93060 0.99218 0.8495 0.0391 0.0806 0.1271 0.0154 0.0103 157.88 WTHX-010 0.5000 1.3895 0.1000 2.1801 1.0929 6 109 0.98631 0.88563 0.10753 0.02542 0.92375 0.95894 0.8495 0.0078 0.0857 0.1196 0.0131 0.0103 134.10 WTHX-011 0.5264 1.5411 0.1053 2.5666 1.1722 6 108 0.97067 0.53372 0.03030 0.08407 0.93060 0.99218 0.8495 0.0391 0.0806 0.1271 0.0154 0.0102 157.74 WTHX-012 0.5000 1.4052 0.1000 1.7651 1.0373 6 111 0.99022 0.53372 0.07625 0.09189 0.99413 0.99218 0.8495 0.0391 0.0879 0.1156 0.0106 0.0102 107.66 WTHX-013 0.5000 1.4228 0.1000 1.8411 1.0501 6 108 0.97067 0.50244 0.07722 0.08016 0.93060 0.99218 0.8495 0.0391 0.0899 0.1139 0.0110 0.0102 113.13 WTHX-014 0.5000 1.4228 0.1000 1.8411 1.0510 6 108 0.97067 0.53372 0.03030 0.08407 0.99413 0.99218 0.8651 0.1017 0.0890 0.1140 0.0110 0.0101 112.07 WTHX-015 0.5000 1.4228 0.1000 1.8411 1.0510 6 108 0.97067 0.57283 0.10850 0.08407 0.92375 0.96090 0.8651 0.0391 0.0899 0.1140 0.0110 0.0102 113.15 WTHX-016 0.5000 1.4228 0.1000 2.2583 1.1065 6 108 0.98631 0.88563 0.07625 0.02933 0.92375 0.99218 0.8495 0.0078 0.0854 0.1200 0.0135 0.0103 138.91 WTHX-017 0.5000 1.4228 0.1000 1.8411 1.0510 6 108 0.99022 0.53372 0.07625 0.09189 0.99316 0.99218 0.8495 0.0391 0.0899 0.1140 0.0110 0.0103 113.24 WTHX-018 0.5000 1.3895 0.1000 2.1784 1.0929 6 114 0.97067 0.57771 0.07625 0.01760 0.92375 0.96090 0.9746 0.0000 0.0803 0.1251 0.0131 0.0101 131.36 WTHX-019 0.5000 1.3895 0.1000 2.1784 1.0929 6 120 0.97067 0.57771 0.24829 0.02639 0.92375 0.99022 0.8651 0.0391 0.0763 0.1316 0.0131 0.0100 131.34 WTHX-020 0.5000 1.4052 0.1000 1.7633 1.0373 6 123 0.98631 0.56891 0.07722 0.09189 0.92766 0.99022 0.8651 0.0391 0.0800 0.1281 0.0106 0.0102 108.36 WTHX-021 0.5000 1.4052 0.1000 1.7633 1.0373 6 111 0.99022 0.53372 0.07625 0.09189 0.99413 0.99218 0.8495 0.0391 0.0881 0.1156 0.0106 0.0102 107.73 WTHX-022 0.5000 1.4247 0.1000 1.8436 1.0518 6 108 0.97067 0.50244 0.07625 0.09189 0.99316 0.99218 0.8495 0.1017 0.0892 0.1141 0.0111 0.0102 112.64 WTHX-023 0.5000 1.3895 0.1000 2.1784 1.0929 6 172 0.99022 0.53372 0.07625 0.09189 0.92766 0.97458 0.8651 0.0391 0.0539 0.1885 0.0131 0.0102 132.76 WTHX-024 0.5000 1.4228 0.1000 2.2600 1.1065 6 196 0.98631 0.58553 0.07625 0.00978 0.92571 0.99022 0.8651 0.0391 0.0469 0.2174 0.0136 0.0102 138.11 WTHX-025 0.5000 1.4228 0.1000 1.8411 1.0510 6 108 0.97067 0.50244 0.07625 0.09189 0.99316 0.99218 0.8495 0.1017 0.0891 0.1140 0.0110 0.0102 112.26 WTHX-026 0.5029 1.4311 0.1006 1.8728 1.0571 6 108 0.97849 0.75269 0.07625 0.09189 0.92375 0.99022 0.8651 0.0391 0.0894 0.1147 0.0112 0.0103 115.24 WTHX-027 0.5264 1.4999 0.1053 2.5567 1.1722 6 126 0.97067 0.53372 0.03030 0.08407 0.92375 0.96090 0.8651 0.0391 0.0691 0.1482 0.0153 0.0102 157.14 WTHX-028 0.5000 1.3895 0.1000 2.1784 1.0929 6 148 0.97067 0.57771 0.07625 0.02933 0.92766 0.99218 0.8651 0.0078 0.0632 0.1622 0.0131 0.0103 133.99 WTHX-029 0.5000 1.3895 0.1000 2.1784 1.0929 6 108 0.97067 0.88563 0.10753 0.02542 0.92375 0.95894 0.8495 0.0391 0.0845 0.1185 0.0131 0.0100 130.95 WTHX-030 0.5000 1.3895 0.1000 2.1784 1.0929 6 110 0.97067 0.88563 0.00587 0.09189 0.93060 0.99218 0.8651 0.0078 0.0839 0.1207 0.0131 0.0101 132.30 WTHX-031 0.5000 1.4228 0.1000 1.8411 1.0510 6 109 0.97067 0.55034 0.07625 0.09189 0.99316 0.99218 0.8495 0.1017 0.0885 0.1151 0.0110 0.0102 112.48 WTHX-032 0.5000 1.3895 0.1000 2.1784 1.0929 6 109 0.93939 0.88270 0.07625 0.02542 0.89247 0.99218 0.9922 0.0078 0.0857 0.1196 0.0131 0.0103 133.99 WTHX-033 0.5000 1.4228 0.1000 1.8411 1.0518 6 108 0.98631 0.51026 0.24829 0.02639 0.99413 0.99218 0.8651 0.1017 0.0890 0.1141 0.0110 0.0102 112.12 WTHX-034 0.5000 1.3895 0.1000 1.7369 1.0176 6 108 0.97849 0.75269 0.07625 0.09189 0.92375 0.99022 0.8495 0.0391 0.0929 0.1104 0.0104 0.0103 106.88 WTHX-035 0.5029 1.4311 0.1006 1.8728 1.0571 6 161 0.97067 0.57771 0.07625 0.09189 0.92375 0.99218 0.8495 0.0000 0.0601 0.1707 0.0112 0.0103 115.20 WTHX-036 0.5000 1.4228 0.1000 2.2531 1.1065 6 109 0.97067 0.57771 0.07625 0.02933 0.92766 0.99022 0.8651 0.0391 0.0840 0.1211 0.0135 0.0102 137.58 WTHX-037 0.5000 1.3895 0.1000 2.1784 1.0929 6 109 0.97067 0.50244 0.07625 0.07625 0.99316 0.99218 0.8651 0.0078 0.0850 0.1196 0.0131 0.0102 132.83 WTHX-038 0.5000 1.4052 0.1000 1.7633 1.0373 6 170 0.97067 0.53177 0.07625 0.09189 0.98631 0.99022 0.8495 0.0391 0.0580 0.1768 0.0106 0.0103 108.46 WTHX-039 0.5000 1.4228 0.1000 1.8411 1.0518 6 108 0.97458 0.50049 0.07625 0.09189 0.99316 0.99218 0.8495 0.1017 0.0898 0.1141 0.0110 0.0103 113.23 WTHX-040 0.5000 1.3895 0.1000 2.1784 1.0929 6 172 0.97067 0.89834 0.07625 0.02542 0.89247 0.99218 0.8651 0.0391 0.0543 0.1885 0.0131 0.0102 133.87 WTHX-041 0.5000 1.3817 0.1000 2.1661 1.0929 6 172 0.97067 0.55034 0.07625 0.00978 0.99316 0.92962 0.8495 0.0391 0.0543 0.1885 0.0130 0.0102 133.12 WTHX-042 0.5000 1.4228 0.1000 2.2531 1.1065 6 109 0.97067 0.57771 0.07625 0.02542 0.92375 0.99218 0.8641 0.0078 0.0846 0.1211 0.0135 0.0102 138.46 WTHX-043 0.5337 1.5626 0.1067 2.6024 1.1885 6 108 0.97067 0.53372 0.02933 0.12317 0.93157 0.97458 0.8651 0.0391 0.0795 0.1289 0.0156 0.0103 160.08 WTHX-044 0.5000 1.4228 0.1000 1.8411 1.0501 6 120 0.98631 0.51026 0.24829 0.02639 0.92375 0.99022 0.8651 0.0391 0.0810 0.1265 0.0110 0.0102 113.13 WTHX-045 0.5000 1.4052 0.1000 1.7633 1.0373 6 123 0.98631 0.56891 0.07722 0.09189 0.92766 0.99022 0.8651 0.0391 0.0800 0.1281 0.0106 0.0103 108.47 WTHX-046 0.5000 1.3895 0.1000 2.1784 1.0929 6 161 0.97067 0.53372 0.03030 0.08016 0.92375 0.99218 0.8495 0.0000 0.0575 0.1765 0.0131 0.0101 132.61 196 Design Tag ht wt δt Pl Pt Nr Nt x1 x2 x3 x4 y1 y2 y3 y4 l H d Af V mm mm mm mm mm - - - - - - - - - - m m m m² cm³ WTHX-047 0.5000 1.3895 0.1000 1.7369 1.0176 6 120 0.98631 0.51026 0.20137 0.02542 0.89247 0.99022 0.8651 0.0391 0.0828 0.1226 0.0104 0.0102 105.78 WTHX-048 0.5000 1.3895 0.1000 2.1784 1.0929 6 108 0.97067 0.53861 0.07625 0.00978 0.98631 0.95894 0.8651 0.0401 0.0853 0.1185 0.0131 0.0101 132.19 WTHX-049 0.5000 1.3895 0.1000 2.1784 1.0929 6 108 0.97263 0.53372 0.03030 0.08016 0.92766 0.99022 0.8749 0.0391 0.0846 0.1185 0.0131 0.0100 131.05 Table 37. WTHX performance and operating conditions. Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in h ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW WTHX-001 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 137.21 40.89 0.745 1.001 WTHX-002 DP I Water Radiator 0.03 2.96 25.00 300.00 350.00 200.00 Liquid 159.11 46.09 0.890 1.000 WTHX-003 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 129.56 40.09 0.617 1.001 WTHX-004 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.94 41.05 0.882 1.002 WTHX-005 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 158.76 45.90 0.841 1.000 WTHX-006 DP I Water Radiator 0.03 2.98 25.00 300.00 350.00 200.00 Liquid 143.35 43.03 0.704 1.001 WTHX-007 DP I Water Radiator 0.03 2.98 25.00 300.00 350.00 200.00 Liquid 143.01 43.11 0.896 1.003 WTHX-008 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 140.75 41.64 0.933 1.001 WTHX-009 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 127.79 39.87 0.616 1.003 WTHX-010 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.87 41.07 0.903 1.002 WTHX-011 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 128.32 39.90 0.616 1.004 WTHX-012 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 163.76 47.22 0.878 1.001 WTHX-013 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 157.81 45.27 0.892 1.001 WTHX-014 DP I Water Radiator 0.03 2.96 25.00 300.00 350.00 200.00 Liquid 159.14 46.29 0.866 1.000 WTHX-015 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 157.65 45.05 0.867 1.000 WTHX-016 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 136.55 40.24 0.882 1.001 WTHX-017 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 157.61 44.88 0.895 1.000 WTHX-018 DP I Water Radiator 0.03 2.99 25.00 300.00 350.00 200.00 Liquid 143.32 43.39 0.809 1.004 WTHX-019 DP I Water Radiator 0.03 2.99 25.00 300.00 350.00 200.00 Liquid 143.03 43.66 0.687 1.004 WTHX-020 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 162.29 46.62 0.715 1.001 WTHX-021 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 163.58 47.21 0.879 1.001 WTHX-022 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 158.48 45.70 0.842 1.000 WTHX-023 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 141.27 42.10 0.355 1.002 WTHX-024 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 138.75 40.84 0.265 1.001 WTHX-025 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 158.93 45.99 0.844 1.000 WTHX-026 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 156.09 44.82 0.862 1.001 WTHX-027 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 128.58 40.06 0.480 1.000 WTHX-028 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 140.54 41.09 0.504 1.002 WTHX-029 DP I Water Radiator 0.03 2.99 25.00 300.00 350.00 200.00 Liquid 143.37 43.93 0.876 1.002 197 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in h ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW WTHX-030 DP I Water Radiator 0.03 2.96 25.00 300.00 350.00 200.00 Liquid 141.41 42.18 0.884 1.001 WTHX-031 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 158.53 45.77 0.838 1.000 WTHX-032 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 140.12 41.08 0.886 1.003 WTHX-033 DP I Water Radiator 0.03 2.96 25.00 300.00 350.00 200.00 Liquid 159.18 46.15 0.822 1.000 WTHX-034 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 166.58 49.39 0.963 1.016 WTHX-035 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 156.40 44.85 0.402 1.001 WTHX-036 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 137.89 40.92 0.837 1.001 WTHX-037 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 141.55 41.87 0.906 1.003 WTHX-038 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 162.63 46.46 0.376 1.001 WTHX-039 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 157.64 45.04 0.852 1.000 WTHX-040 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.73 41.11 0.362 1.000 WTHX-041 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 140.60 41.24 0.367 1.001 WTHX-042 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 137.19 40.39 0.863 1.002 WTHX-043 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 127.05 39.69 0.562 1.000 WTHX-044 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 157.68 45.41 0.694 1.001 WTHX-045 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 162.16 46.38 0.716 1.001 WTHX-046 DP I Water Radiator 0.03 2.96 25.00 300.00 350.00 200.00 Liquid 141.51 42.14 0.429 1.001 WTHX-047 DP I Water Radiator 0.03 2.96 25.00 300.00 350.00 200.00 Liquid 168.38 50.72 0.768 1.017 WTHX-048 DP I Water Radiator 0.03 2.97 25.00 300.00 350.00 200.00 Liquid 142.35 42.49 0.905 1.004 WTHX-049 DP I Water Radiator 0.03 2.99 25.00 300.00 350.00 200.00 Liquid 143.66 43.81 0.900 1.004 198 AFHX Figure 133. AFHX Concept. l Uniform Air Flow Uniform Water Flow 199 Table 38. AFHX dimensions. Design Tag r1 δ1 δ2 δt a Pt Ports/Nt Nt Nr l H d Af V mm mm mm mm - mm - - - m m m m² cm³ AFHX-001 23.6706 1.0450 0.5225 0.1045 2.9883 1.5674 3 2 51 0.12930 0.07929 0.01875 0.01025 192.28 AFHX-002 23.6706 1.0450 0.5225 0.1045 2.9902 1.5674 3 2 54 0.12215 0.08393 0.01875 0.01025 192.27 AFHX-003 23.6950 1.0450 0.5225 0.1045 2.9902 1.5674 3 2 54 0.12195 0.08393 0.01877 0.01024 192.15 AFHX-004 23.6950 1.0450 0.5225 0.1045 2.9902 1.5674 3 2 54 0.12195 0.08393 0.01877 0.01024 192.14 AFHX-005 23.6950 1.0450 0.5225 0.1045 2.9863 1.5674 3 2 54 0.12195 0.08393 0.01877 0.01024 192.13 AFHX-006 23.6950 1.0450 0.5225 0.1045 2.9589 1.5674 3 2 54 0.12198 0.08393 0.01877 0.01024 192.10 AFHX-007 23.6950 1.0450 0.5225 0.1045 2.9609 1.5674 3 2 54 0.12197 0.08393 0.01877 0.01024 192.09 AFHX-008 23.6950 1.0450 0.5225 0.1045 2.9589 1.5674 3 2 54 0.12195 0.08393 0.01877 0.01024 192.07 AFHX-009 23.6950 1.0450 0.5225 0.1045 2.9570 1.5674 3 2 54 0.12195 0.08393 0.01876 0.01024 192.06 AFHX-010 23.6950 1.0450 0.5225 0.1045 2.9570 1.5674 3 2 56 0.11762 0.08702 0.01876 0.01024 192.06 AFHX-011 23.6950 1.0450 0.5225 0.1045 2.9550 1.5674 3 2 54 0.12195 0.08393 0.01876 0.01024 192.06 AFHX-012 23.6950 1.0450 0.5225 0.1045 2.9550 1.5674 3 2 54 0.12195 0.08393 0.01876 0.01024 192.05 AFHX-013 23.6950 1.0450 0.5225 0.1045 2.9726 1.5674 3 2 54 0.12176 0.08393 0.01877 0.01022 191.80 AFHX-014 23.3284 1.0371 0.5186 0.1037 2.9883 1.5557 3 2 51 0.13000 0.07889 0.01854 0.01026 190.12 AFHX-015 23.3284 1.0371 0.5186 0.1037 2.9883 1.5557 3 2 51 0.12999 0.07889 0.01854 0.01026 190.12 AFHX-016 23.3284 1.0371 0.5186 0.1037 2.9922 1.5557 3 2 54 0.12276 0.08351 0.01854 0.01025 190.05 AFHX-017 23.3284 1.0371 0.5186 0.1037 2.9902 1.5557 3 2 54 0.12276 0.08351 0.01854 0.01025 190.04 AFHX-018 23.3284 1.0371 0.5186 0.1037 2.9883 1.5557 3 2 55 0.12045 0.08504 0.01854 0.01024 189.89 AFHX-019 23.3284 1.0371 0.5186 0.1037 2.9883 1.5557 3 2 51 0.12974 0.07889 0.01854 0.01024 189.75 AFHX-020 23.3284 1.0371 0.5186 0.1037 2.9863 1.5557 3 2 51 0.12974 0.07889 0.01854 0.01024 189.75 AFHX-021 23.3284 1.0371 0.5186 0.1037 2.9844 1.5557 3 2 51 0.12974 0.07889 0.01854 0.01024 189.74 AFHX-022 23.3284 1.0371 0.5186 0.1037 2.9902 1.5557 3 2 51 0.12970 0.07889 0.01854 0.01023 189.69 AFHX-023 23.3284 1.0371 0.5186 0.1037 2.9609 1.5557 3 2 51 0.12974 0.07889 0.01853 0.01024 189.68 AFHX-024 23.0841 1.0313 0.5156 0.1031 2.9550 1.5469 3 2 54 0.12327 0.08319 0.01838 0.01025 188.44 AFHX-025 23.0841 1.0313 0.5156 0.1031 2.9922 1.5469 3 2 51 0.13023 0.07860 0.01838 0.01024 188.17 AFHX-026 23.0841 1.0313 0.5156 0.1031 2.9922 1.5469 3 2 51 0.13023 0.07860 0.01838 0.01024 188.17 AFHX-027 23.3284 1.0332 0.5166 0.1033 2.9589 1.5499 3 2 51 0.12887 0.07870 0.01855 0.01014 188.11 AFHX-028 23.2796 1.0313 0.5156 0.1031 2.8944 1.5469 3 2 51 0.12930 0.07860 0.01850 0.01016 188.05 AFHX-029 23.3040 1.0313 0.5156 0.1031 2.9863 1.5469 3 2 51 0.12858 0.07860 0.01855 0.01011 187.42 AFHX-030 23.3040 1.0313 0.5156 0.1031 2.9550 1.5469 3 2 51 0.12858 0.07860 0.01854 0.01011 187.35 AFHX-031 21.9599 1.0020 0.5010 0.1002 3.0000 1.5029 3 2 54 0.12559 0.08161 0.01768 0.01025 181.22 AFHX-032 21.9599 1.0020 0.5010 0.1002 2.9980 1.5029 3 2 54 0.12548 0.08161 0.01768 0.01024 181.05 AFHX-033 21.9599 1.0020 0.5010 0.1002 3.0000 1.5029 3 2 54 0.12539 0.08161 0.01768 0.01023 180.93 AFHX-034 21.9599 1.0020 0.5010 0.1002 2.9883 1.5029 3 2 54 0.12539 0.08161 0.01768 0.01023 180.90 AFHX-035 21.8866 1.0000 0.5000 0.1000 2.9589 1.5000 3 2 54 0.12583 0.08150 0.01763 0.01025 180.75 AFHX-036 21.8866 1.0000 0.5000 0.1000 2.9550 1.5000 3 2 54 0.12583 0.08150 0.01762 0.01025 180.74 AFHX-037 21.8866 1.0000 0.5000 0.1000 2.9902 1.5000 3 2 54 0.12572 0.08150 0.01763 0.01025 180.68 AFHX-038 21.8866 1.0000 0.5000 0.1000 2.9550 1.5000 3 2 54 0.12578 0.08150 0.01762 0.01025 180.67 AFHX-039 21.8866 1.0000 0.5000 0.1000 2.9980 1.5000 3 2 54 0.12560 0.08150 0.01764 0.01024 180.52 AFHX-040 21.8866 1.0000 0.5000 0.1000 2.9980 1.5000 3 2 54 0.12557 0.08150 0.01764 0.01023 180.48 AFHX-041 21.8866 1.0000 0.5000 0.1000 2.9902 1.5000 3 2 54 0.12558 0.08150 0.01763 0.01024 180.48 200 Design Tag r1 δ1 δ2 δt a Pt Ports/Nt Nt Nr l H d Af V mm mm mm mm - mm - - - m m m m² cm³ AFHX-042 21.8866 1.0000 0.5000 0.1000 2.9589 1.5000 3 2 54 0.12564 0.08150 0.01763 0.01024 180.48 AFHX-043 21.8866 1.0000 0.5000 0.1000 2.9589 1.5000 3 2 54 0.12561 0.08150 0.01763 0.01024 180.44 AFHX-044 21.8866 1.0000 0.5000 0.1000 2.9609 1.5000 3 2 54 0.12560 0.08150 0.01763 0.01024 180.43 AFHX-045 21.8866 1.0000 0.5000 0.1000 2.9570 1.5000 3 2 54 0.12561 0.08150 0.01763 0.01024 180.43 AFHX-046 21.8866 1.0000 0.5000 0.1000 2.9589 1.5000 3 2 54 0.12560 0.08150 0.01763 0.01024 180.42 AFHX-047 21.8866 1.0000 0.5000 0.1000 2.9570 1.5000 3 2 54 0.12560 0.08150 0.01763 0.01024 180.42 AFHX-048 21.8866 1.0000 0.5000 0.1000 2.9609 1.5000 3 2 54 0.12559 0.08150 0.01763 0.01024 180.41 AFHX-049 21.8866 1.0000 0.5000 0.1000 2.9413 1.5000 3 2 54 0.12561 0.08150 0.01762 0.01024 180.39 AFHX-050 21.8866 1.0000 0.5000 0.1000 2.9609 1.5000 3 2 54 0.12555 0.08150 0.01763 0.01023 180.36 AFHX-051 21.8866 1.0000 0.5000 0.1000 2.9550 1.5000 3 2 54 0.12555 0.08150 0.01762 0.01023 180.34 AFHX-052 21.8866 1.0000 0.5000 0.1000 2.9550 1.5000 3 2 54 0.12555 0.08150 0.01762 0.01023 180.34 AFHX-053 21.9599 1.0000 0.5000 0.1000 2.9589 1.5000 3 2 54 0.12511 0.08150 0.01768 0.01020 180.28 AFHX-054 21.9599 1.0000 0.5000 0.1000 2.9589 1.5000 3 2 54 0.12506 0.08150 0.01768 0.01019 180.20 AFHX-055 21.9844 1.0000 0.5000 0.1000 2.9980 1.5000 3 2 54 0.12484 0.08150 0.01771 0.01017 180.17 AFHX-056 21.9844 1.0000 0.5000 0.1000 2.9902 1.5000 3 2 54 0.12484 0.08150 0.01771 0.01017 180.15 AFHX-057 21.9844 1.0000 0.5000 0.1000 2.9980 1.5000 3 2 54 0.12481 0.08150 0.01771 0.01017 180.13 AFHX-058 21.9844 1.0000 0.5000 0.1000 2.9883 1.5000 3 2 54 0.12483 0.08150 0.01771 0.01017 180.13 AFHX-059 21.9844 1.0000 0.5000 0.1000 2.9980 1.5000 3 2 54 0.12480 0.08150 0.01771 0.01017 180.11 AFHX-060 21.9844 1.0000 0.5000 0.1000 2.9980 1.5000 3 2 54 0.12479 0.08150 0.01771 0.01017 180.10 AFHX-061 21.9844 1.0000 0.5000 0.1000 2.9883 1.5000 3 2 54 0.12480 0.08150 0.01771 0.01017 180.09 AFHX-062 21.9844 1.0000 0.5000 0.1000 2.9883 1.5000 3 2 54 0.12479 0.08150 0.01771 0.01017 180.07 AFHX-063 21.9844 1.0000 0.5000 0.1000 2.9883 1.5000 3 2 54 0.12479 0.08150 0.01771 0.01017 180.07 AFHX-064 21.9844 1.0000 0.5000 0.1000 2.9570 1.5000 3 2 54 0.12484 0.08150 0.01770 0.01017 180.07 AFHX-065 21.9844 1.0000 0.5000 0.1000 2.9570 1.5000 3 2 54 0.12483 0.08150 0.01770 0.01017 180.06 AFHX-066 21.9844 1.0000 0.5000 0.1000 2.9883 1.5000 3 2 54 0.12475 0.08150 0.01771 0.01017 180.02 AFHX-067 21.9844 1.0000 0.5000 0.1000 2.9883 1.5000 3 2 54 0.12475 0.08150 0.01771 0.01017 180.02 AFHX-068 21.9844 1.0000 0.5000 0.1000 2.9726 1.5000 3 2 54 0.12477 0.08150 0.01770 0.01017 180.01 AFHX-069 21.9844 1.0000 0.5000 0.1000 2.9609 1.5000 3 2 54 0.12479 0.08150 0.01770 0.01017 180.00 AFHX-070 21.9844 1.0000 0.5000 0.1000 2.9609 1.5000 3 2 54 0.12479 0.08150 0.01770 0.01017 180.00 AFHX-071 21.9844 1.0000 0.5000 0.1000 2.9589 1.5000 3 2 54 0.12479 0.08150 0.01770 0.01017 179.99 AFHX-072 21.9844 1.0000 0.5000 0.1000 2.9570 1.5000 3 2 54 0.12479 0.08150 0.01770 0.01017 179.99 AFHX-073 21.9844 1.0000 0.5000 0.1000 2.9570 1.5000 3 2 54 0.12479 0.08150 0.01770 0.01017 179.99 201 Table 39. AFHX performance and operating conditions. Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in h ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW AFHX-001 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 133.94 57.11 0.850 1.001 AFHX-002 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.71 57.12 0.759 1.001 AFHX-003 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.77 57.29 0.757 1.001 AFHX-004 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.77 57.29 0.757 1.001 AFHX-005 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.77 57.30 0.757 1.001 AFHX-006 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.74 57.36 0.758 1.001 AFHX-007 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.75 57.36 0.758 1.001 AFHX-008 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.75 57.37 0.758 1.001 AFHX-009 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.75 57.38 0.758 1.001 AFHX-010 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.59 57.38 0.705 1.000 AFHX-011 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.75 57.38 0.758 1.001 AFHX-012 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.75 57.38 0.758 1.001 AFHX-013 DP I Water Radiator 0.03 2.94 25.00 300.00 350.00 200.00 Liquid 134.84 57.48 0.756 1.000 AFHX-014 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.78 57.51 0.868 1.001 AFHX-015 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.78 57.51 0.868 1.001 AFHX-016 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 135.56 57.54 0.775 1.001 AFHX-017 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 135.56 57.54 0.775 1.001 AFHX-018 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 135.52 57.62 0.746 1.000 AFHX-019 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.88 57.68 0.866 1.000 AFHX-020 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.88 57.69 0.866 1.000 AFHX-021 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.87 57.69 0.866 1.000 AFHX-022 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.90 57.71 0.866 1.000 AFHX-023 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 134.86 57.75 0.866 1.000 AFHX-024 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 136.14 57.95 0.787 1.000 AFHX-025 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 135.51 58.03 0.879 1.000 AFHX-026 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 135.51 58.03 0.879 1.000 AFHX-027 DP I Water Radiator 0.03 2.96 25.00 300.00 350.00 200.00 Liquid 135.66 59.08 0.860 1.000 AFHX-028 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 135.70 59.20 0.865 1.001 AFHX-029 DP I Water Radiator 0.03 2.97 25.00 300.00 350.00 200.00 Liquid 136.03 59.54 0.859 1.000 AFHX-030 DP I Water Radiator 0.03 2.97 25.00 300.00 350.00 200.00 Liquid 136.01 59.62 0.859 1.000 AFHX-031 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.19 59.96 0.843 1.001 AFHX-032 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.23 60.05 0.842 1.001 AFHX-033 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.26 60.11 0.842 1.000 AFHX-034 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.26 60.13 0.842 1.000 AFHX-035 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.33 60.13 0.848 1.001 AFHX-036 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.33 60.14 0.848 1.001 AFHX-037 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.39 60.15 0.847 1.001 AFHX-038 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.35 60.18 0.848 1.001 AFHX-039 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.44 60.22 0.846 1.001 AFHX-040 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.45 60.24 0.846 1.000 AFHX-041 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.44 60.25 0.846 1.000 202 Design Tag Design Problem Fluid Application Vair uair ṁfluid Tair,in Tfluid,in Pfluid,in xfluid,in h ΔPair ΔPfluid Q - - - m³/s m/s g/s K K kPa - W/m².K Pa kPa kW AFHX-042 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.40 60.27 0.847 1.000 AFHX-043 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.41 60.29 0.847 1.000 AFHX-044 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.42 60.30 0.847 1.000 AFHX-045 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.41 60.30 0.847 1.000 AFHX-046 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.42 60.30 0.847 1.000 AFHX-047 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.42 60.30 0.847 1.000 AFHX-048 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.42 60.31 0.846 1.000 AFHX-049 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.41 60.33 0.847 1.000 AFHX-050 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.44 60.33 0.846 1.000 AFHX-051 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.44 60.35 0.846 1.000 AFHX-052 DP I Water Radiator 0.03 2.93 25.00 300.00 350.00 200.00 Liquid 139.44 60.35 0.846 1.000 AFHX-053 DP I Water Radiator 0.03 2.94 25.00 300.00 350.00 200.00 Liquid 139.58 60.77 0.840 1.000 AFHX-054 DP I Water Radiator 0.03 2.94 25.00 300.00 350.00 200.00 Liquid 139.60 60.80 0.840 1.000 AFHX-055 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.69 60.93 0.837 1.001 AFHX-056 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.69 60.94 0.837 1.000 AFHX-057 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.70 60.95 0.837 1.000 AFHX-058 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.69 60.96 0.837 1.000 AFHX-059 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.71 60.96 0.837 1.000 AFHX-060 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.71 60.96 0.837 1.000 AFHX-061 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.70 60.97 0.837 1.000 AFHX-062 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.71 60.98 0.837 1.000 AFHX-063 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.71 60.99 0.837 1.000 AFHX-064 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.67 61.01 0.837 1.000 AFHX-065 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.68 61.01 0.837 1.000 AFHX-066 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.72 61.01 0.836 1.000 AFHX-067 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.72 61.02 0.836 1.000 AFHX-068 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.71 61.03 0.837 1.000 AFHX-069 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.70 61.04 0.837 1.000 AFHX-070 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.70 61.04 0.837 1.000 AFHX-071 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.70 61.04 0.837 1.000 AFHX-072 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.69 61.05 0.837 1.000 AFHX-073 DP I Water Radiator 0.03 2.95 25.00 300.00 350.00 200.00 Liquid 139.70 61.05 0.837 1.000 203 Appendix D – Experimental Materials, Methods and Data Table 40 – Specifications of test facility. Item Capacity Coil Test Dimensions  Max. 24” X 24” (Width X Height) Heat Transfer Capacity  Max. 10 kW Max. Air Velocity  Max. 5 m/s for the largest section (24” by 24”) Inlet Air Conditions  -10°C to 45°C  Humidity control Working Fluids  Refrigerant without oil – pumped system  Refrigerant with oil – standard vapor compression system  Water - water flow rate – up to 2.5 kg/s  Brine Figure 134 - Schematic diagram of air-side test facility. E-1CMH CMH TCTC DP TC DP P P Rota- meter Cold water tank Air Handing Unit Water heater Rota- meter Rota- meterExpansion tank Flow Meter CMH Chilled Mirror Hygrometer TC ThermocoupleDP Differential Pressure P Pressure Transducer Flow Rate Measurement Module Heat Exchanger Testing Module Cooling Cold water loop Dehumidification Glycol water loop Humidifier Fan Test Heat Exchanger Setting means Blower Blower RTD Mixer Mixer Sampling Tree RTD Sampling Tree Settling means Blower Nozzles Sampling tree InletOutlet Heating Hot water loop Diverging Valve Diverging Valve Diverging Valve 204 Figure 135 - Schematic of cold water loop (top), glycol water loop (middle), hot water loop (bottom) (courtesy from Zhiwei Huang). Figure 136 - Schematic diagram of water/brines system loop. TC TC Rotameter Cold Water Tank Cold Water Coil TC TC Rotameter Glycol Water Coil Connected to the Chiller outside Connected to glycol water line TC TC Rotameter Hot Water Coil Gas water heater (tankless) Air relief valve Expansion tank Connected to water loop for test HX Water Tank VFD T P DP T P Pump Mass flow meter P Pressure Measurement T Temperature MeasurementFlow Meter DP Differential Pressure Transducer Water/Brines Loop T T Mixing valve 205 Figure 137 - Schematic diagram of refrigerant system with oil loop. Figure 138 - Schematic diagram of refrigerant system without oil loop (courtesy from Zhiwei Huang). VFD Working as evaporator Working as condenser P T P T Mass flow meter P T DP P T T T Mass flow meter Compressor DP Refrigerant with Oil Loop – Standard Vapor Compression System VFDWorking as condenser Working as evaporator P T P T I-5I-8 V-2 Mass flow meter P T DP P T T T I-6 Mass flow meter Pump DP Refrigerant without Oil Loop – Pumped system P Pressure Measurement T Temperature Measurement I-9 Flow Meter DP Differential Pressure Transducer TIC Temperature Indicator Controller P Pressure Measurement T Temperature Measurement I-10 Flow Meter DP Differential Pressure Transducer TIC Temperature Indicator Controller Testing HX Testing HX VFD Working as evaporator Working as condenser P T P T Mass flow meter P T DP P T T T Mass flow meter Compressor DP Refrigerant with Oil Loop – Standard Vapor Compression System VFDWorking as condenser Working as evaporator P T P T I-5I-8 V-2 Mass flow meter P T DP P T T T I-6 Mass flow meter Pump DP Refrigerant without Oil Loop – Pumped system P Pressure Measurement T Temperature Measurement I-9 Flow Meter DP Differential Pressure Transducer TIC Temperature Indicator Controller P Pressure Measurement T Temperature Measurement I-10 Flow Meter DP Differential Pressure Transducer TIC Temperature Indicator Controller Testing HX Testing HX 206 Table 41 - Accuracy of every sensor of airside. Temperature Sensor Type Company Product Accuracy RTD Omega PR-25AP series Class 1/10 -10 °C 0.03 °C 0 °C 0.03 °C 10 °C 0.04 °C 20 °C 0.04 °C 30 °C 0.05 °C 40 °C 0.06 °C 50 °C 0.07 °C Dew Point Hygrometer Type Company Product Dew Point Accuracy Chilled mirror hygrometer EdgeTech DewTrak II Chilled Mirror Transmitter ± 0.2°C dew/frost point Pressure Sensor Type Company Product Accuracy Differential Setra 2641005WD11T1F ± 3.11Pa Barometric Setra 2781600MA1B2BT1 0-40℃ ±100Pa ‘-20 to 50 ℃ ±150Pa ’-40 to 60 ℃ ±200Pa Measurement of Nozzle Diameter Type Accuracy ASHRAE standard nozzle 0.001D Table 42 - Uncertainty calculation of airside (courtesy from Zhiwei Huang). Flow Rate 5,000 cfm ∆𝑻 2.5°C (35 - 37.5°C) 10°C (35 - 45°C) Value Uncertainty Relative Uncertainty Value Uncertainty Relative Uncertainty T1[°C] 35.00 ± 0.06 0.17% 35.00 ± 0.06 0.17% T2 [°C] 37.50 ± 0.06 0.16% 45.00 ± 0.07 0.16% P1[kPa] 100.98 ± 0.10 0.10% 101.00 ± 0.15 0.15% delta_P[kPa] 0.59 ± 0.00 0.52% 0.58 ± 0.00 0.54% P2[kPa] 100.38 ± 0.10 0.10% 100.43 ± 0.15 0.15% delta_h[kJ/kg] 6.83 ± 0.55 8.05% 30.38 ± 0.70 2.31% mdot[kg/s] 2.62 ± 0.00 0.12% 2.54 ± 0.00 0.13% Q[kW] 17.88 ± 1.44 8.06% 77.17 ± 1.78 2.31% Flow Rate 70 cfm ∆𝑻 2.5°C (35 - 37.5°C) 10°C (35 - 45°C) Value Uncertainty Relative Uncertainty Value Uncertainty Relative Uncertainty T1[°C] 35.00 ± 0.06 0.17% 35.00 ± 0.06 0.17% T2 [°C] 37.50 ± 0.06 0.16% 45.00 ± 0.07 0.16% P1[kPa] 100.98 ± 0.10 0.10% 101.00 ± 0.15 0.15% delta_P[kPa] 0.16 ± 0.00 1.98% 0.15 ± 0.00 2.05% P2[kPa] 100.82 ± 0.10 0.10% 100.20 ± 0.15 0.15% delta_h[kJ/kg] 6.86 ± 0.55 8.00% 30.44 ± 0.70 2.30% mdot[kg/s] 0.04 ± 0.00 0.21% 0.04 ± 0.00 0.22% Q[kW] 0.27 ± 0.02 8.02% 1.22 ± 0.03 2.31% 207 Table 43. RTHX-001 Test data. Twater,i n Twater,o ut ṁwater Tair,in Tair,out Vair uair ΔPair Qwater Qair Qave Energ y Bal. °C °C g/s °C °C m³/s m/s Pa W W W % 60.01 ± 0.06 55.18 ± 0.06 29.95 ± 0.08 35.15 ± 0.15 49.83 ± 0.08 0.0317 ± 0.0005 1.39 ± 0.02 27.1 ± 1.1 605.4 ± 11.4 601.6 ± 11.3 603.5 ± 16.1 0.6 59.99 ± 0.05 54.3 ± 0.05 29.94 ± 0.09 34.93 ± 0.14 48.7 ± 0.09 0.0407 ± 0.0005 1.79 ± 0.02 39.9 ± 1.3 712.4 ± 8.8 717.2 ± 11.4 714.8 ± 14.4 -0.7 59.96 ± 0.07 53.71 ± 0.07 30.44 ± 0.07 35.04 ± 0.09 47.76 ± 0.09 0.0497 ± 0.0005 2.18 ± 0.02 54.7 ± 1.5 795.2 ± 12.4 805.8 ± 10.4 800.5 ± 16.2 -1.3 59.98 ± 0.07 53.09 ± 0.07 30.32 ± 0.07 34.93 ± 0.12 46.85 ± 0.1 0.0589 ± 0.0005 2.58 ± 0.02 71.8 ± 1.8 873.2 ± 12.6 893.6 ± 12.7 883.4 ± 17.9 -2.3 60.08 ± 0.08 52.53 ± 0.07 30.17 ± 0.08 34.94 ± 0.11 45.87 ± 0.13 0.0694 ± 0.0005 3.04 ± 0.02 95.3 ± 2 952.6 ± 13.2 971.9 ± 15.3 962.25 ± 20.2 -2 59.97 ± 0.05 56.98 ± 0.05 50.18 ± 0.09 35.18 ± 0.16 50.37 ± 0.1 0.0317 ± 0.0005 1.39 ± 0.02 27.1 ± 1.1 626.8 ± 15.5 621.6 ± 11.9 624.2 ± 19.5 0.8 59.95 ± 0.05 56.46 ± 0.05 50.26 ± 0.09 35.03 ± 0.16 49.37 ± 0.1 0.0398 ± 0.0005 1.75 ± 0.02 38.7 ± 1.3 733.6 ± 14.1 733.3 ± 12.4 733.45 ± 18.8 0.04 60.01 ± 0.08 56 ± 0.08 50.3 ± 0.09 35.1 ± 0.14 48.44 ± 0.11 0.0502 ± 0.0005 2.2 ± 0.02 55.9 ± 1.4 845 ± 22.4 852.6 ± 12.9 848.8 ± 25.8 -0.9 59.99 ± 0.05 55.52 ± 0.05 50.28 ± 0.09 34.93 ± 0.12 47.52 ± 0.09 0.0605 ± 0.0005 2.65 ± 0.02 74.8 ± 1.8 940.6 ± 15.5 956.3 ± 13.1 948.45 ± 20.3 -1.7 59.94 ± 0.05 55.13 ± 0.05 50.13 ± 0.09 35.11 ± 0.14 46.72 ± 0.13 0.07 ± 0.0005 3.07 ± 0.02 95.7 ± 2 - - - - 60.01 ± 0.06 57.81 ± 0.06 70.05 ± 0.13 34.95 ± 0.12 50.62 ± 0.09 0.0317 ± 0.0005 1.39 ± 0.02 27.1 ± 1.1 646.5 ± 24 639.2 ± 11.4 642.85 ± 26.6 1.1 59.91 ± 0.05 57.33 ± 0.05 69.85 ± 0.11 34.9 ± 0.1 49.59 ± 0.09 0.0398 ± 0.0005 1.75 ± 0.02 38.7 ± 1.3 752.7 ± 21.5 750.4 ± 11 751.55 ± 24.2 0.3 59.95 ± 0.06 56.97 ± 0.06 69.82 ± 0.12 34.92 ± 0.11 48.59 ± 0.1 0.0504 ± 0.0005 2.21 ± 0.02 56.1 ± 1.5 871.2 ± 23.9 876.4 ± 11.7 873.8 ± 26.6 -0.6 60 ± 0.06 56.71 ± 0.06 69.86 ± 0.13 35.15 ± 0.13 47.78 ± 0.08 0.0603 ± 0.0005 2.64 ± 0.02 75.3 ± 1.8 961.2 ± 23.9 970 ± 13.3 965.6 ± 27.4 -0.9 60.01 ± 0.08 56.46 ± 0.08 69.96 ± 0.15 35 ± 0.18 47.28 ± 0.13 0.0695 ± 0.0005 3.05 ± 0.02 93.5 ± 2 - - - - Table 44. NTHX-001 Test data. Twater,i n Twater,o ut ṁwater Tair,in Tair,out Vair uair ΔPair Qwater Qair Qave Energ y Bal. °C °C g/s °C °C m³/s m/s Pa W W W % 60.04 ± 0.08 55.79 ± 0.09 30.2 ± 0.08 34.97 ± 0.11 47.98 ± 0.09 0.0316 ± 0.0005 1.39 ± 0.02 62.3 ± 1.5 536.8 ± 15.3 556 ± 9.8 546.4 ± 18.2 -3.5 60.02 ± 0.08 55.19 ± 0.08 30.15 ± 0.08 35 ± 0.11 46.62 ± 0.1 0.0408 ± 0.0005 1.79 ± 0.02 93.7 ± 2 609 ± 14.4 625.7 ± 9.9 617.35 ± 17.5 -2.7 208 Twater,i n Twater,o ut ṁwater Tair,in Tair,out Vair uair ΔPair Qwater Qair Qave Energ y Bal. °C °C g/s °C °C m³/s m/s Pa W W W % 59.96 ± 0.09 54.65 ± 0.09 30.11 ± 0.09 35.01 ± 0.12 45.61 ± 0.09 0.0504 ± 0.0006 2.21 ± 0.03 129.2 ± 2.4 668.6 ± 16.2 686.1 ± 11.2 677.35 ± 19.7 -2.6 59.96 ± 0.08 54.2 ± 0.09 30.11 ± 0.09 35.02 ± 0.12 44.78 ± 0.09 0.06 ± 0.0005 2.63 ± 0.02 168.9 ± 3.2 725.3 ± 15.3 765.9 ± 12 745.6 ± 19.4 -5.4 60.08 ± 0.1 53.87 ± 0.1 29.97 ± 0.08 35.07 ± 0.07 44.08 ± 0.08 0.0701 ± 0.0005 3.07 ± 0.02 217.4 ± 3.7 778.3 ± 17.9 843.7 ± 10.1 811 ± 20.6 -8.1 59.92 ± 0.12 57.14 ± 0.11 49.9 ± 0.11 35.02 ± 0.08 48.49 ± 0.1 0.0316 ± 0.0005 1.39 ± 0.02 62.2 ± 1.5 580.2 ± 34 574.7 ± 9.8 577.45 ± 35.4 1 59.97 ± 0.08 56.79 ± 0.08 49.89 ± 0.11 34.93 ± 0.11 47.14 ± 0.09 0.0408 ± 0.0005 1.79 ± 0.02 93.6 ± 2 663.5 ± 23.7 656.4 ± 10 659.95 ± 25.7 1.1 59.99 ± 0.13 56.5 ± 0.12 50.05 ± 0.1 35 ± 0.1 46.21 ± 0.1 0.0504 ± 0.0006 2.21 ± 0.03 129.3 ± 2.5 730.5 ± 37.1 724.3 ± 11 727.4 ± 38.7 0.8 60 ± 0.09 56.21 ± 0.1 50.08 ± 0.1 35 ± 0.12 45.38 ± 0.11 0.0602 ± 0.0006 2.64 ± 0.03 169.7 ± 3 793.8 ± 28.2 814.9 ± 13.4 804.35 ± 31.2 -2.6 60.04 ± 0.11 55.96 ± 0.11 49.93 ± 0.11 35 ± 0.13 44.71 ± 0.11 0.0704 ± 0.0006 3.09 ± 0.03 217.8 ± 3.5 852 ± 32.5 909.7 ± 15.2 880.85 ± 35.9 -6.5 59.97 ± 0.08 57.85 ± 0.08 70.05 ± 0.12 35.02 ± 0.08 48.81 ± 0.08 0.0316 ± 0.0005 1.39 ± 0.02 62.4 ± 1.5 621.1 ± 33.2 587.6 ± 9.8 604.35 ± 34.6 5.5 59.93 ± 0.09 57.52 ± 0.09 69.97 ± 0.14 34.98 ± 0.08 47.36 ± 0.09 0.0409 ± 0.0006 1.79 ± 0.03 94.3 ± 1.9 705.3 ± 37.3 668.7 ± 10.4 687 ± 38.7 5.3 60.07 ± 0.12 57.41 ± 0.11 70.14 ± 0.13 35 ± 0.12 46.57 ± 0.1 0.0504 ± 0.0006 2.21 ± 0.03 129.7 ± 2.4 780.3 ± 47.8 746.8 ± 11.8 763.55 ± 49.2 4.4 59.97 ± 0.14 57.08 ± 0.13 70.07 ± 0.13 34.97 ± 0.09 45.65 ± 0.1 0.0606 ± 0.0005 2.66 ± 0.02 172 ± 3 846.9 ± 56 843.4 ± 11.5 845.15 ± 57.2 0.4 59.99 ± 0.14 56.9 ± 0.13 70.2 ± 0.12 34.99 ± 0.18 44.99 ± 0.13 0.0704 ± 0.0005 3.09 ± 0.02 218.2 ± 3.7 907.2 ± 56.1 931.1 ± 18.9 919.15 ± 59.2 -2.6 Table 45. RTHX-468 Test data. Twater ,in Twater ,out ṁwate r Tair,i n Tair, out Vair uair ΔPai r Qwate r Qair Qave Ener gy Bal. °C °C g/s °C °C m³/s m/s Pa W W W % 55.08 ± 0.08 39.99 ± 0.07 70.93 ± 0.12 30 ± 0.1 37.4 ± 0.1 0.4786 ± 0.0045 20.99 ± 0.2 47.1 ± 0.9 4478 ± 33.4 4314. 2 ± 87.4 4396.1 ± 93.6 3.7 54.77 ± 0.06 42.49 ± 0.06 94.68 ± 0.16 30 ± 0.1 38.2 ± 0.1 0.4814 ± 0.0057 21.11 ± 0.25 47.1 ± 1 4859 ± 36 4731 ± 94.1 4795 ± 100.8 2.7 54.95 ± 0.06 44.38 ± 0.06 117.9 ± 0.23 30.1 ± 0.1 38.8 ± 0.1 0.4795 ± 0.0046 21.03 ± 0.2 47 ± 0.9 5210 ± 40.9 5057. 2 ± 90.5 5133.6 ± 99.3 3 209 Twater ,in Twater ,out ṁwate r Tair,i n Tair, out Vair uair ΔPai r Qwate r Qair Qave Ener gy Bal. °C °C g/s °C °C m³/s m/s Pa W W W % 54.72 ± 0.08 45.6 ± 0.07 141 ± 0.23 30 ± 0.1 39.1 ± 0.1 0.4819 ± 0.0057 21.14 ± 0.25 47.2 ± 1 5377 ± 65.2 5245. 6 ± 97.5 5311.3 ± 117.3 2.5 54.82 ± 0.06 46.76 ± 0.06 166.3 ± 0.24 30 ± 0.1 39.5 ± 0.1 0.48 ± 0.0057 21.05 ± 0.25 47 ± 0.9 5608 ± 62.1 5509. 3 ± 99.5 5558.6 5 ± 117.3 1.8 55.08 ± 0.08 39.99 ± 0.07 70.93 ± 0.12 30 ± 0.1 37.4 ± 0.1 0.4786 ± 0.0045 20.99 ± 0.2 47.1 ± 0.9 4478 ± 33.4 4314. 2 ± 87.4 4396.1 ± 93.6 3.7 54.77 ± 0.06 42.49 ± 0.06 94.68 ± 0.16 30 ± 0.1 38.2 ± 0.1 0.4814 ± 0.0057 21.11 ± 0.25 47.1 ± 1 4859 ± 36 4731 ± 94.1 4795 ± 100.8 2.7 54.95 ± 0.06 44.38 ± 0.06 117.9 ± 0.23 30.1 ± 0.1 38.8 ± 0.1 0.4795 ± 0.0046 21.03 ± 0.2 47 ± 0.9 5210 ± 40.9 5057. 2 ± 90.5 5133.6 ± 99.3 3 54.72 ± 0.08 45.6 ± 0.07 141 ± 0.23 30 ± 0.1 39.1 ± 0.1 0.4819 ± 0.0057 21.14 ± 0.25 47.2 ± 1 5377 ± 65.2 5245. 6 ± 97.5 5311.3 ± 117.3 2.5 54.82 ± 0.06 46.76 ± 0.06 166.3 ± 0.24 30 ± 0.1 39.5 ± 0.1 0.48 ± 0.0057 21.05 ± 0.25 47 ± 0.9 5608 ± 62.1 5509. 3 ± 99.5 5558.6 5 ± 117.3 1.8 55.08 ± 0.08 39.99 ± 0.07 70.93 ± 0.12 30 ± 0.1 37.4 ± 0.1 0.4786 ± 0.0045 20.99 ± 0.2 47.1 ± 0.9 4478 ± 33.4 4314. 2 ± 87.4 4396.1 ± 93.6 3.7 54.77 ± 0.06 42.49 ± 0.06 94.68 ± 0.16 30 ± 0.1 38.2 ± 0.1 0.4814 ± 0.0057 21.11 ± 0.25 47.1 ± 1 4859 ± 36 4731 ± 94.1 4795 ± 100.8 2.7 54.95 ± 0.06 44.38 ± 0.06 117.9 ± 0.23 30.1 ± 0.1 38.8 ± 0.1 0.4795 ± 0.0046 21.03 ± 0.2 47 ± 0.9 5210 ± 40.9 5057. 2 ± 90.5 5133.6 ± 99.3 3 54.72 ± 0.08 45.6 ± 0.07 141 ± 0.23 30 ± 0.1 39.1 ± 0.1 0.4819 ± 0.0057 21.14 ± 0.25 47.2 ± 1 5377 ± 65.2 5245. 6 ± 97.5 5311.3 ± 117.3 2.5 54.82 ± 0.06 46.76 ± 0.06 166.3 ± 0.24 30 ± 0.1 39.5 ± 0.1 0.48 ± 0.0057 21.05 ± 0.25 47 ± 0.9 5608 ± 62.1 5509. 3 ± 99.5 5558.6 5 ± 117.3 1.8 210 Appendix E – Correlation Data Wavy Fin Correlation Coefficients Matrices Table 46. Herringbone correlation: parameters power matrices. MNuDh,Herr,N=2-10 = MNuDh,Herr,N=11-20 = MCf,Herr,N=2-10 = MCf,Herr,N=11-20 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 1 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 3 0 0 0 0 0 0 1 2 0 0 0 0 0 3 0 0 0 0 0 0 2 1 0 0 0 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 2 1 0 0 0 0 0 1 2 0 0 0 0 0 0 2 1 0 0 0 0 2 0 1 0 0 0 0 2 0 1 0 0 0 0 2 0 1 0 0 0 0 1 0 2 0 0 0 0 1 1 1 0 0 0 0 0 2 1 0 0 0 0 1 1 1 0 0 0 0 0 1 2 0 0 0 0 0 2 1 0 0 0 0 1 0 2 0 0 0 0 0 2 1 0 0 0 0 0 0 3 0 0 0 0 1 0 2 0 0 0 0 2 0 0 1 0 0 0 1 0 2 0 0 0 0 2 0 0 1 0 0 0 0 1 2 0 0 0 0 1 1 0 1 0 0 0 2 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 3 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 2 0 1 0 0 0 1 0 0 2 0 0 0 0 2 0 1 0 0 0 0 0 2 1 0 0 0 1 0 1 1 0 0 0 0 0 1 2 0 0 0 1 0 1 1 0 0 0 1 0 0 2 0 0 0 1 0 0 2 0 0 0 0 0 0 3 0 0 0 0 1 1 1 0 0 0 0 1 0 2 0 0 0 0 1 0 2 0 0 0 1 0 1 0 1 0 0 0 0 2 1 0 0 0 0 0 1 2 0 0 0 2 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 2 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 2 0 0 0 0 2 0 0 1 0 0 0 0 2 0 1 0 0 0 0 1 0 2 0 0 0 0 1 2 0 0 0 1 0 1 0 1 0 0 0 0 1 0 2 0 0 0 0 0 1 2 0 0 0 0 0 3 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 2 0 0 0 0 1 0 2 0 0 0 1 0 0 0 0 2 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 2 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 2 0 0 0 1 0 0 1 0 0 2 0 0 1 0 0 0 2 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 2 0 0 0 0 1 0 2 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 2 0 0 0 0 1 0 0 0 0 1 2 0 0 0 0 0 1 1 1 0 0 0 2 0 0 1 0 1 1 0 0 0 1 0 0 2 0 0 0 1 0 0 1 0 0 0 2 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 3 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 2 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 2 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 2 1 0 0 1 0 0 1 1 0 1 0 0 0 0 2 0 0 0 0 2 0 0 1 1 0 0 0 0 2 0 0 0 0 0 2 1 0 0 1 0 0 0 2 0 0 0 1 0 1 0 1 0 1 0 0 0 2 0 0 0 0 0 0 3 0 0 0 1 0 0 2 0 0 0 0 0 2 0 1 0 0 1 0 0 2 0 1 1 0 0 0 0 1 2 0 0 0 0 0 1 1 0 0 0 0 0 2 0 0 0 1 0 2 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 2 2 0 0 0 0 0 1 0 1 1 0 0 0 1 0 2 0 0 0 0 1 0 0 1 0 0 0 2 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 2 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 2 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 2 0 0 0 1 0 0 0 0 0 0 3 0 0 2 0 0 0 1 0 0 0 2 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 2 0 0 1 1 0 0 0 0 1 1 0 0 0 2 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 2 0 1 1 0 0 0 0 0 2 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 2 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 2 1 0 0 0 0 0 2 0 0 0 1 0 1 1 0 0 0 1 0 0 2 0 0 1 0 0 0 2 1 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 1 0 0 0 0 2 0 0 1 0 0 0 2 0 0 0 0 1 0 2 0 0 0 0 0 0 3 211 Table 47. Herringbone correlation: coefficients arrays. cNuDh,Herr,N=2-10 = cNuDh,Herr,N=11-20 = cCf,Herr,N=2-10 = cCf,Herr,N=11-20 = -4.3884 29.6938 17.8784 31.2430 3.8241 0.4421 0.0984 -3.6596 -5.5505 -0.8698 -4.1406 12.9874 6.8328 4.4086 -7.9936 -3.5077 -2.6098 1.6331 0.9576 -3.2856 0.0329 4.4418 2.4552 0.6230 -1.1233 -28.0007 -0.1146 -24.6064 1.7374 -1.1637 -5.0085 -6.4867 -0.6462 -0.4560 0.4685 1.0003 1.3482 1.9658 -0.4852 1.5960 0.0349 -0.6269 1.0845 -0.0451 -2.1053 -0.1432 -3.3757 -2.4313 2.7768 0.6684 2.1409 -0.5294 -6.2859 -6.4044 0.7065 1.2628 -0.0234 0.3081 0.0071 -0.6681 0.2687 -0.8489 -0.3017 0.4837 0.5023 -0.4941 0.4226 -0.1296 -0.6451 -0.3928 0.2527 0.3392 0.2754 1.0420 0.1028 0.6159 -0.5167 0.2411 -0.5853 0.5188 -0.8092 -0.5215 -2.7741 -1.1939 -0.3741 1.0004 0.0621 -0.6716 -0.1482 -0.2538 0.1284 0.3266 0.8253 0.5044 0.3281 0.6305 -1.3296 0.7808 -0.3773 -6.5030 0.3194 -0.3608 0.6310 -1.2588 0.1442 -1.1358 -0.1369 0.8830 -0.4880 9.0281 0.0885 0.8434 -0.1178 0.5064 -0.0921 10.5513 -0.9219 -0.0110 0.5127 1.2430 1.2285 0.2786 0.2217 -0.8330 -0.7660 -0.2996 0.4828 0.8205 0.2283 0.0725 0.0237 0.5328 -0.0099 0.2702 -0.0466 -0.1318 0.1554 0.2514 0.1258 0.6846 -0.2247 0.2106 0.6353 0.8623 0.0849 -0.3065 -0.1302 0.1633 -0.2555 0.2558 0.1589 -0.1833 -0.3418 -0.0661 -0.1541 -0.1804 0.2761 0.1316 -0.2403 -0.0977 -0.4108 -0.3520 0.6301 -0.2400 1.7931 -0.3499 -0.1232 0.5677 -0.0554 0.1945 0.1398 -0.2066 0.0616 1.7012 0.0434 0.3265 0.0608 -0.1004 0.1435 -0.1740 0.0762 0.0816 -0.2158 0.1582 0.1009 0.1131 0.1848 0.1835 -0.0712 -0.0637 -0.1618 -0.1225 -0.2624 0.1141 0.1107 0.0856 0.0965 0.0383 -0.1550 -0.3672 0.0831 -0.0478 0.1265 0.4759 -0.1091 -0.0449 -0.3860 -0.1495 -0.0279 -0.0742 0.1174 -0.2621 -0.0984 0.1513 0.6264 0.3994 0.1016 0.1741 -0.0665 0.2041 0.1421 -0.0782 -0.0796 -0.2314 -0.3254 -0.0746 -0.1753 -0.2792 0.2591 0.2177 -0.0224 0.2427 -0.3288 -0.5673 0.1808 0.9620 0.1320 0.8286 -0.1769 -1.4322 -0.1418 -0.5867 0.1315 -0.1285 0.0912 -0.1361 -0.1098 0.0561 -0.0458 0.2567 0.0918 -0.0546 -0.1132 -0.1054 0.0656 0.0814 -0.0965 -0.2954 -0.0820 0.0313 0.1953 -0.2674 0.1100 -0.0376 -0.1630 -1.1494 -0.1341 -0.0260 0.0889 0.0957 -0.1245 -0.0930 -0.1304 -0.2368 0.1035 0.0486 0.0992 0.2510 -0.1045 -0.0695 -0.1002 0.0344 0.0881 -0.0289 0.1873 -0.0405 -0.0973 -0.0468 -0.1797 0.1007 0.1147 -0.0389 0.1826 0.0180 -0.0356 -0.0255 0.0466 0.0379 0.0476 0.0824 0.0335 0.0682 -0.1992 -0.0237 0.0255 0.0993 0.0362 0.0356 -0.0351 -0.0376 -0.1093 0.0358 0.0439 0.1012 -0.0684 -0.0501 0.0357 0.0258 -0.0386 0.0727 -0.0109 -0.0291 -0.0722 0.0415 0.0173 0.0153 212 Table 48. Smooth correlation: parameters power matrices. MNuDh,Smooth,N=2-10 = MNuDh,Smooth,N=11-20 = MCf,Smooth,N=2-10 = MCf,Smooth,N=11-20 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 1 0 0 0 0 1 0 0 0 0 0 2 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 1 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 2 0 1 0 0 0 0 2 1 0 0 0 0 0 1 1 1 0 0 0 0 2 1 0 0 0 0 0 1 1 1 0 0 0 0 1 2 0 0 0 0 0 0 2 1 0 0 0 0 1 2 0 0 0 0 0 1 0 2 0 0 0 0 1 1 1 0 0 0 0 0 1 2 0 0 0 0 0 3 0 0 0 0 0 2 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 3 0 0 0 0 2 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 2 0 0 0 0 2 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 2 0 0 1 0 0 0 1 1 0 1 0 0 0 0 2 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 2 0 0 0 0 0 0 2 1 0 0 0 0 2 0 1 0 0 0 1 0 0 2 0 0 0 0 1 2 0 0 0 0 1 0 0 2 0 0 0 1 0 1 1 0 0 0 0 0 1 2 0 0 0 0 0 3 0 0 0 0 0 1 0 2 0 0 0 0 1 1 1 0 0 0 0 0 0 3 0 0 0 1 1 0 1 0 0 0 0 0 0 3 0 0 0 1 0 0 2 0 0 0 1 0 1 0 1 0 0 0 2 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 2 0 0 0 0 0 2 0 1 0 0 1 0 1 1 0 0 0 0 2 0 0 1 0 0 0 0 1 2 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 3 0 0 0 0 0 1 0 2 0 0 0 1 0 2 0 0 0 0 0 2 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 2 0 0 0 0 0 3 0 0 0 0 0 1 1 1 0 0 0 0 2 0 1 0 0 0 2 0 0 0 1 0 2 0 0 0 1 0 0 0 0 1 0 2 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 2 0 0 0 0 1 0 2 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 2 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 2 0 0 1 0 1 0 0 1 1 0 0 0 2 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 2 0 0 0 0 2 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 2 1 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 2 0 0 0 0 2 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 2 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 2 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 2 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 2 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 2 0 0 0 1 0 0 0 1 0 2 0 0 0 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 2 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 3 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 2 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 2 0 0 0 1 0 1 1 0 0 2 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 2 1 0 0 0 0 0 2 0 1 0 1 0 0 1 0 0 2 0 0 0 1 0 0 0 0 1 0 2 0 0 0 0 0 0 3 0 0 0 2 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 3 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 2 0 1 0 0 0 2 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 2 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 2 0 0 1 0 0 1 1 0 1 0 0 0 0 2 0 0 0 1 0 1 1 0 0 0 1 0 0 2 1 0 0 0 0 0 2 0 1 0 0 0 0 2 0 0 0 1 0 0 2 213 Table 49: Smooth correlation: coefficients arrays. cNuDh,Smooth,N=2-10 = cNuDh,Smooth,N=11-20 = cCf,Smooth,N=2-10 = cCf,Smooth,N=11-20 = -5.7057 32.2699 14.9492 11.7049 0.7473 2.0889 -0.9612 1.0108 -4.5714 -3.1603 -0.4285 7.8943 6.3303 4.1082 -5.0439 -0.3384 -3.2949 0.9142 -0.4762 -2.4832 -2.4175 3.2453 3.1646 4.6503 0.9464 -35.5205 -0.1368 1.2865 0.3337 0.7006 -4.6918 -4.6596 -0.6172 -1.0000 0.5159 -0.2212 1.9777 1.6918 -0.0760 1.8546 0.0537 -0.3625 0.1598 -0.3146 -0.9572 0.0047 -2.1545 -1.5804 2.7932 1.0831 0.7870 1.4594 -6.8360 -7.6816 0.3519 -0.0988 -0.0045 -0.2817 -0.8495 -1.2066 0.3399 -0.4810 0.4980 2.1100 0.5966 0.5453 0.6811 0.1105 -0.7793 -0.4627 0.7015 0.5710 0.0933 0.0978 0.6195 0.9489 0.0596 -0.1604 -0.5583 0.0665 -0.3317 -0.9331 -1.9039 -0.9244 -0.3773 -0.0080 -0.2504 -0.1326 -0.2579 0.3454 0.1632 0.7059 1.3956 -2.1642 0.0526 -1.7413 -1.4858 1.6837 -0.5721 -4.7211 0.4491 3.1080 -0.1079 -0.8095 0.0695 -1.1988 -0.3252 0.7196 0.4728 -1.8974 0.7386 -1.1130 -0.2903 9.8103 -0.1823 -0.6272 -0.3905 0.1866 0.6262 0.4534 1.3207 -0.0075 0.2840 -0.1177 -0.1277 -0.2406 -0.3062 0.0192 0.3739 -0.1284 0.0800 0.3436 0.2949 0.2087 0.6087 0.1479 0.0615 0.6082 -0.1902 0.6544 0.0571 -0.0295 0.1648 -0.2253 0.0945 -0.1252 -0.2062 0.4438 -0.3789 0.2862 -0.2885 -0.3248 -0.4326 -0.2511 0.4604 -0.2162 -0.3846 0.1345 -0.0767 -0.2127 1.9147 -0.0775 0.1900 0.4146 -0.0462 0.1997 0.1951 -0.2267 0.0663 -0.2700 0.0818 0.5053 0.0945 -0.3423 -0.2735 -0.2157 0.0895 0.2240 0.1020 0.3168 0.1016 1.8685 -0.1274 -0.1215 -0.1016 -0.1436 0.0458 0.1229 -0.1997 0.0875 -0.1859 -0.0968 -0.1353 0.2195 0.1968 0.0773 0.0979 -0.2477 -0.3822 0.0307 -0.0975 -0.0412 0.3896 -0.1800 -0.0315 -0.0428 0.0842 0.4379 0.1976 -0.1031 -0.1322 0.1251 -0.1907 0.1234 -0.0227 -0.0899 0.1413 0.2216 -0.0641 -0.1935 -0.3685 -0.1005 0.2633 -0.2338 0.1526 -0.0485 0.1523 -0.2705 -0.1252 -0.3657 0.1703 -0.2061 0.0773 0.6953 -0.0937 0.8248 -0.0741 -0.5997 0.1492 -0.1370 0.1074 -0.1672 -0.1325 0.0679 -0.1246 0.2013 0.0748 0.0801 0.1560 -0.3093 -0.0862 -0.1531 0.1376 0.2249 0.0726 0.1493 -0.1009 -0.1340 -0.1042 0.0842 0.0863 -0.2201 0.0351 -0.1070 -0.1619 -1.2405 0.0697 0.1313 0.1194 0.0950 -0.0492 0.1652 -0.2065 -0.1990 -0.0418 -0.0729 0.1284 0.2272 -0.0137 -0.0646 -0.0394 0.1003 0.0211 -0.0324 0.0525 0.0702 -0.0259 0.0220 -0.0540 0.0302 0.0248 -0.1072 0.0569 0.0476 0.0245 0.0245 0.1427 -0.0458 -0.2270 0.0407 -0.1487 -0.0945 0.0595 -0.0088 -0.0197 0.0382 0.0141 214 Appendix F – Optimum Heat Transfer Surfaces Surface Optimization Study Results Figure 139. Surface optimization results (Dh=0.5mm). 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm 1.0 /u m s 4 0.5ch o A D d mm A   3.0 /u m s 4 0.5ch o A D d mm A   5.0 /u m s 4 0.5ch o A D d mm A   2.0 /u m s 4 0.5ch o A D d mm A   Legend: 215 Figure 140. Surface optimization results (Dh=1.0mm). 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm 1.0 /u m s 4 1.0ch o A D d mm A   3.0 /u m s 4 1.0ch o A D d mm A   5.0 /u m s 4 1.0ch o A D d mm A   2.0 /u m s 4 1.0ch o A D d mm A   Legend: 216 Figure 141. Surface optimization results (Dh=1.5mm). 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm 1.0 /u m s 4 1.5ch o A D d mm A   3.0 /u m s 4 1.5ch o A D d mm A   5.0 /u m s 4 1.5ch o A D d mm A   2.0 /u m s 4 1.5ch o A D d mm A   Legend: 217 Figure 142. Surface optimization results (Dh=2.5mm). 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm 1.0 /u m s 4 2.5ch o A D d mm A   3.0 /u m s 4 2.5ch o A D d mm A   5.0 /u m s 4 2.5ch o A D d mm A   2.0 /u m s 4 2.5ch o A D d mm A   Legend: 218 Figure 143. Surface optimization results (Dh=3.0mm). 0.5oD mm 1.0oD mm 1.5oD mm 2.0oD mm 3.0oD mm 4.0oD mm 5.0oD mm 1.0 /u m s 4 3.0ch o A D d mm A   3.0 /u m s 4 3.0ch o A D d mm A   5.0 /u m s 4 3.0ch o A D d mm A   2.0 /u m s 4 3.0ch o A D d mm A   Legend: 219 8.3.1.2Optimum Wavy Fin Surfaces (WFTS) Figure 144. Wavy fin surface segment. Table 50. WFTS Optimum designs dimensions. TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-001 2.00 1.25 1.73 1.38 2 0.574 44.286 0.072 0.264 0.165 0.625 0.368 0.50 5.00 2.0E-06 7.3E-07 2.9E-05 0.010 29.311 WFTS-002 2.00 1.25 1.87 1.49 8 2.534 10.024 0.051 0.324 0.202 0.625 0.455 1.51 20.00 9.5E-06 4.3E-06 2.3E-04 0.189 12.097 WFTS-003 2.00 1.25 1.87 1.49 8 2.534 10.024 0.058 0.330 0.206 0.625 0.454 1.50 20.00 9.5E-06 4.3E-06 2.3E-04 0.189 12.087 WFTS-004 2.00 1.25 1.87 1.49 8 2.534 10.024 0.068 0.330 0.206 0.625 0.452 1.50 20.00 9.5E-06 4.3E-06 2.3E-04 0.189 12.061 WFTS-005 2.00 1.25 1.87 1.49 9 2.534 10.024 0.073 0.329 0.205 0.625 0.451 1.50 22.50 9.5E-06 4.3E-06 2.6E-04 0.213 12.047 WFTS-006 2.00 1.25 1.87 1.49 9 2.534 10.024 0.083 0.330 0.206 0.625 0.450 1.50 22.50 9.5E-06 4.3E-06 2.6E-04 0.213 12.021 WFTS-007 2.00 1.25 1.87 1.49 9 2.534 10.024 0.097 0.330 0.206 0.625 0.447 1.49 22.50 9.5E-06 4.2E-06 2.6E-04 0.213 11.984 WFTS-008 2.00 1.25 1.96 1.57 2 0.528 48.119 0.094 0.341 0.213 0.626 0.403 0.50 5.01 2.1E-06 8.4E-07 3.4E-05 0.010 32.493 WFTS-009 2.00 1.26 2.35 1.86 2 0.967 26.271 0.050 0.476 0.300 0.630 0.544 1.00 5.04 4.5E-06 2.5E-06 5.0E-05 0.023 21.862 WFTS-010 2.00 1.26 2.35 1.86 3 0.999 25.435 0.067 0.511 0.323 0.632 0.536 1.00 7.58 4.7E-06 2.5E-06 7.7E-05 0.036 21.478 oD lP 2tP pF 2 2f lX P dP f Uniform airflow u d 220 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-011 2.00 1.31 1.51 1.15 2 0.723 35.155 0.056 0.386 0.253 0.655 0.313 0.50 5.24 2.2E-06 6.8E-07 2.9E-05 0.012 25.226 WFTS-012 2.00 1.31 1.52 1.15 2 0.723 35.155 0.051 0.374 0.246 0.656 0.316 0.50 5.25 2.2E-06 6.9E-07 2.9E-05 0.012 25.224 WFTS-013 2.00 1.31 1.52 1.15 2 0.723 35.155 0.051 0.374 0.246 0.656 0.316 0.50 5.25 2.2E-06 6.9E-07 2.9E-05 0.012 25.224 WFTS-014 2.00 1.32 2.26 1.71 2 1.654 15.356 0.074 0.312 0.206 0.660 0.533 1.49 5.28 7.5E-06 4.0E-06 5.7E-05 0.040 14.359 WFTS-015 2.00 1.36 1.99 1.46 2 0.514 49.420 0.073 0.301 0.204 0.679 0.426 0.50 5.43 2.0E-06 8.7E-07 3.8E-05 0.011 33.803 WFTS-016 2.00 1.38 3.99 2.90 2 1.164 21.831 0.065 0.303 0.209 0.688 0.674 1.49 5.51 9.3E-06 6.3E-06 9.3E-05 0.051 18.094 WFTS-017 2.00 1.38 1.97 1.43 2 0.528 48.119 0.087 0.336 0.232 0.691 0.412 0.50 5.53 2.1E-06 8.6E-07 3.8E-05 0.012 33.270 WFTS-018 2.00 1.41 2.71 1.93 2 0.899 28.244 0.075 0.465 0.327 0.704 0.579 1.00 5.63 4.9E-06 2.8E-06 6.4E-05 0.028 23.252 WFTS-019 2.00 1.41 1.99 1.41 2 0.510 49.805 0.069 0.288 0.203 0.707 0.430 0.50 5.66 2.0E-06 8.7E-07 3.9E-05 0.012 34.241 WFTS-020 2.00 1.43 1.62 1.13 2 0.659 38.546 0.074 0.273 0.195 0.715 0.338 0.50 5.72 2.1E-06 7.2E-07 3.3E-05 0.012 26.801 WFTS-021 2.00 1.43 2.07 1.45 3 1.152 22.056 0.098 0.478 0.342 0.715 0.472 0.99 8.58 4.8E-06 2.3E-06 7.8E-05 0.041 18.998 WFTS-022 2.00 1.44 2.35 1.63 2 0.965 26.325 0.050 0.464 0.333 0.718 0.544 0.99 5.74 4.5E-06 2.5E-06 5.7E-05 0.026 21.944 WFTS-023 2.00 1.46 2.51 1.72 2 0.875 29.013 0.075 0.157 0.115 0.730 0.550 1.00 5.84 4.4E-06 2.4E-06 5.7E-05 0.026 22.089 WFTS-024 2.00 1.46 4.00 2.74 2 1.102 23.051 0.053 0.255 0.186 0.730 0.702 1.50 5.84 8.8E-06 6.2E-06 9.7E-05 0.052 18.772 WFTS-025 2.00 1.47 1.78 1.22 2 1.334 19.036 0.075 0.280 0.205 0.733 0.415 1.00 5.86 4.8E-06 2.0E-06 4.6E-05 0.028 16.562 WFTS-026 2.00 1.47 2.69 1.84 2 0.834 30.464 0.062 0.232 0.170 0.734 0.582 0.99 5.87 4.5E-06 2.6E-06 6.2E-05 0.026 23.409 WFTS-027 2.00 1.47 1.70 1.15 2 0.609 41.687 0.075 0.305 0.224 0.735 0.360 0.50 5.88 2.1E-06 7.5E-07 3.5E-05 0.012 29.035 WFTS-028 2.00 1.47 1.78 1.21 2 1.334 19.036 0.062 0.280 0.206 0.735 0.419 1.01 5.88 4.8E-06 2.0E-06 4.7E-05 0.028 16.615 WFTS-029 2.00 1.49 1.72 1.15 2 0.605 41.961 0.072 0.317 0.236 0.744 0.369 0.50 5.95 2.1E-06 7.7E-07 3.7E-05 0.012 29.433 WFTS-030 2.00 1.49 1.72 1.15 2 0.605 41.961 0.072 0.317 0.236 0.744 0.369 0.50 5.95 2.1E-06 7.7E-07 3.7E-05 0.012 29.433 WFTS-031 2.00 1.49 1.72 1.15 2 0.605 41.961 0.072 0.317 0.236 0.744 0.369 0.50 5.95 2.1E-06 7.7E-07 3.7E-05 0.012 29.433 WFTS-032 2.00 1.49 1.72 1.15 2 0.605 41.961 0.072 0.317 0.236 0.744 0.369 0.50 5.95 2.1E-06 7.7E-07 3.7E-05 0.012 29.433 WFTS-033 2.00 1.49 1.72 1.15 2 1.459 17.404 0.092 0.355 0.264 0.744 0.392 0.99 5.95 5.0E-06 2.0E-06 4.7E-05 0.030 15.829 WFTS-034 2.00 1.49 1.72 1.15 2 0.587 43.238 0.054 0.344 0.257 0.745 0.380 0.50 5.96 2.0E-06 7.7E-07 3.7E-05 0.012 30.541 WFTS-035 2.00 1.49 1.72 1.15 2 0.587 43.238 0.054 0.344 0.257 0.745 0.380 0.50 5.96 2.0E-06 7.7E-07 3.7E-05 0.012 30.541 WFTS-036 2.00 1.53 1.77 1.15 2 1.446 17.572 0.087 0.466 0.357 0.766 0.408 1.00 6.13 5.1E-06 2.1E-06 5.1E-05 0.031 16.286 WFTS-037 2.00 1.53 1.77 1.15 2 1.301 19.531 0.050 0.195 0.149 0.767 0.419 1.00 6.14 4.6E-06 1.9E-06 4.7E-05 0.028 16.698 WFTS-038 2.00 1.53 1.77 1.15 2 1.316 19.295 0.055 0.266 0.204 0.767 0.417 1.00 6.14 4.7E-06 2.0E-06 4.8E-05 0.029 16.715 WFTS-039 2.00 1.54 2.23 1.45 2 1.606 15.812 0.069 0.210 0.162 0.769 0.528 1.49 6.15 7.2E-06 3.8E-06 6.3E-05 0.044 14.192 WFTS-040 2.00 1.54 1.78 1.15 2 1.301 19.531 0.050 0.198 0.152 0.770 0.421 1.01 6.16 4.6E-06 2.0E-06 4.8E-05 0.029 16.695 WFTS-041 2.00 1.55 1.98 1.27 2 0.528 48.119 0.076 0.342 0.266 0.777 0.423 0.50 6.22 2.1E-06 8.8E-07 4.4E-05 0.013 34.187 WFTS-042 2.00 1.56 1.80 1.15 2 0.564 45.066 0.064 0.285 0.223 0.780 0.395 0.50 6.24 2.0E-06 8.0E-07 4.0E-05 0.013 31.543 WFTS-043 2.00 1.56 1.80 1.15 2 0.564 45.066 0.064 0.285 0.223 0.780 0.395 0.50 6.24 2.0E-06 8.0E-07 4.0E-05 0.013 31.543 WFTS-044 2.00 1.56 1.80 1.15 10 2.486 10.216 0.055 0.278 0.217 0.780 0.435 1.52 31.19 9.0E-06 3.9E-06 3.2E-04 0.279 11.483 WFTS-045 2.00 1.56 1.80 1.15 10 2.490 10.200 0.058 0.290 0.226 0.780 0.434 1.51 31.19 9.0E-06 3.9E-06 3.2E-04 0.280 11.485 WFTS-046 2.00 1.56 1.80 1.15 10 2.486 10.216 0.068 0.293 0.228 0.780 0.433 1.51 31.19 9.0E-06 3.9E-06 3.2E-04 0.279 11.476 WFTS-047 2.00 1.56 1.80 1.15 10 2.522 10.071 0.081 0.295 0.230 0.780 0.431 1.51 31.19 9.1E-06 3.9E-06 3.2E-04 0.283 11.369 WFTS-048 2.00 1.56 1.80 1.15 10 2.522 10.071 0.083 0.343 0.267 0.780 0.430 1.50 31.19 9.1E-06 3.9E-06 3.2E-04 0.283 11.447 WFTS-049 2.00 1.56 1.80 1.15 10 2.522 10.071 0.093 0.363 0.283 0.780 0.428 1.49 31.19 9.1E-06 3.9E-06 3.3E-04 0.283 11.465 WFTS-050 2.00 1.57 2.30 1.46 3 0.951 26.710 0.070 0.241 0.189 0.785 0.523 1.00 9.42 4.4E-06 2.3E-06 8.6E-05 0.041 20.953 WFTS-051 2.00 1.57 2.30 1.46 3 0.951 26.710 0.070 0.241 0.189 0.785 0.523 1.00 9.42 4.4E-06 2.3E-06 8.6E-05 0.041 20.953 WFTS-052 2.00 1.58 1.99 1.26 2 0.510 49.805 0.057 0.289 0.228 0.788 0.441 0.50 6.30 2.0E-06 8.9E-07 4.5E-05 0.013 35.036 WFTS-053 2.00 1.58 1.82 1.15 10 2.538 10.008 0.099 0.419 0.331 0.788 0.433 1.51 31.54 9.2E-06 4.0E-06 3.3E-04 0.291 11.464 WFTS-054 2.00 1.58 1.82 1.15 10 2.395 10.605 0.097 0.305 0.240 0.790 0.433 1.50 31.58 8.7E-06 3.8E-06 3.2E-04 0.276 11.584 WFTS-055 2.00 1.58 1.82 1.15 10 2.522 10.071 0.099 0.421 0.332 0.790 0.434 1.51 31.58 9.2E-06 4.0E-06 3.3E-04 0.290 11.498 WFTS-056 2.00 1.59 1.83 1.15 10 2.335 10.876 0.092 0.309 0.245 0.793 0.436 1.49 31.71 8.6E-06 3.7E-06 3.2E-04 0.271 11.737 WFTS-057 2.00 1.59 1.83 1.15 10 2.341 10.848 0.093 0.262 0.208 0.794 0.436 1.50 31.75 8.6E-06 3.8E-06 3.2E-04 0.273 11.629 WFTS-058 2.00 1.59 1.83 1.15 10 2.467 10.298 0.093 0.397 0.315 0.794 0.437 1.51 31.75 9.0E-06 4.0E-06 3.3E-04 0.287 11.563 WFTS-059 2.00 1.59 2.51 1.58 2 0.879 28.882 0.075 0.151 0.120 0.794 0.550 1.00 6.35 4.4E-06 2.4E-06 6.2E-05 0.028 22.072 WFTS-060 2.00 1.59 3.34 2.09 2 0.766 33.150 0.063 0.271 0.216 0.797 0.642 1.00 6.38 5.1E-06 3.3E-06 8.4E-05 0.033 25.757 221 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-061 2.00 1.60 1.84 1.15 10 2.286 11.112 0.056 0.283 0.226 0.798 0.446 1.50 31.92 8.4E-06 3.8E-06 3.2E-04 0.269 11.874 WFTS-062 2.00 1.60 1.84 1.15 10 2.286 11.112 0.067 0.276 0.220 0.798 0.444 1.50 31.92 8.4E-06 3.7E-06 3.2E-04 0.269 11.835 WFTS-063 2.00 1.60 1.85 1.15 2 0.530 47.938 0.050 0.210 0.168 0.799 0.415 0.50 6.39 2.0E-06 8.1E-07 4.1E-05 0.013 33.125 WFTS-064 2.00 1.60 1.85 1.15 2 0.530 47.938 0.050 0.216 0.173 0.799 0.415 0.50 6.39 2.0E-06 8.1E-07 4.2E-05 0.013 33.159 WFTS-065 2.00 1.60 1.85 1.15 2 0.550 46.206 0.059 0.277 0.222 0.799 0.409 0.50 6.39 2.0E-06 8.3E-07 4.2E-05 0.013 32.460 WFTS-066 2.00 1.60 1.85 1.15 2 0.568 44.751 0.077 0.277 0.222 0.799 0.396 0.50 6.39 2.1E-06 8.3E-07 4.2E-05 0.013 31.430 WFTS-067 2.00 1.60 1.85 1.15 2 0.570 44.594 0.087 0.277 0.222 0.799 0.388 0.50 6.39 2.1E-06 8.2E-07 4.2E-05 0.013 31.251 WFTS-068 2.00 1.60 1.62 1.01 2 0.635 39.992 0.053 0.226 0.181 0.800 0.351 0.50 6.40 2.1E-06 7.2E-07 3.7E-05 0.013 28.057 WFTS-069 2.00 1.60 1.63 1.02 2 0.651 39.016 0.065 0.263 0.211 0.800 0.346 0.50 6.40 2.1E-06 7.3E-07 3.7E-05 0.014 27.609 WFTS-070 2.00 1.60 1.85 1.15 10 2.278 11.151 0.052 0.276 0.221 0.800 0.448 1.51 32.01 8.4E-06 3.8E-06 3.2E-04 0.269 11.878 WFTS-071 2.00 1.60 1.85 1.15 10 2.282 11.132 0.076 0.276 0.221 0.800 0.444 1.50 32.01 8.4E-06 3.7E-06 3.2E-04 0.270 11.810 WFTS-072 2.00 1.61 1.86 1.15 2 0.530 47.938 0.056 0.146 0.117 0.804 0.412 0.50 6.43 2.0E-06 8.1E-07 4.2E-05 0.013 32.808 WFTS-073 2.00 1.62 1.88 1.15 2 0.512 49.612 0.052 0.090 0.073 0.812 0.420 0.50 6.50 1.9E-06 8.1E-07 4.2E-05 0.013 33.747 WFTS-074 2.00 1.63 1.89 1.15 2 0.514 49.420 0.050 0.134 0.109 0.816 0.424 0.50 6.53 1.9E-06 8.2E-07 4.3E-05 0.013 33.850 WFTS-075 2.00 1.66 1.92 1.15 2 0.512 49.612 0.052 0.095 0.079 0.829 0.429 0.50 6.63 2.0E-06 8.4E-07 4.4E-05 0.013 33.978 WFTS-076 2.00 1.66 1.92 1.15 2 0.512 49.612 0.050 0.183 0.152 0.829 0.431 0.50 6.63 2.0E-06 8.5E-07 4.5E-05 0.013 34.357 WFTS-077 2.00 1.67 1.93 1.15 2 0.556 45.711 0.086 0.299 0.249 0.834 0.406 0.50 6.67 2.1E-06 8.7E-07 4.6E-05 0.014 32.511 WFTS-078 2.00 1.72 1.98 1.15 2 0.524 48.483 0.064 0.293 0.251 0.858 0.435 0.50 6.87 2.1E-06 9.0E-07 4.9E-05 0.014 34.652 WFTS-079 2.00 1.72 1.98 1.15 2 0.524 48.483 0.064 0.293 0.251 0.858 0.435 0.50 6.87 2.1E-06 9.0E-07 4.9E-05 0.014 34.652 WFTS-080 2.00 1.74 2.00 1.15 2 0.508 50.000 0.061 0.194 0.169 0.868 0.441 0.50 6.94 2.0E-06 9.0E-07 5.0E-05 0.014 35.029 WFTS-081 2.00 1.77 2.01 1.14 2 0.510 49.805 0.057 0.289 0.256 0.884 0.446 0.50 7.08 2.1E-06 9.1E-07 5.2E-05 0.015 35.728 WFTS-082 2.00 1.77 2.07 1.17 3 1.152 22.056 0.082 0.476 0.421 0.884 0.479 1.00 10.61 4.8E-06 2.3E-06 9.7E-05 0.051 19.091 WFTS-083 2.00 1.78 2.05 1.15 2 1.811 14.025 0.058 0.279 0.248 0.888 0.496 1.51 7.11 7.4E-06 3.7E-06 7.0E-05 0.053 13.166 WFTS-084 2.00 1.78 2.05 1.15 2 1.096 23.177 0.090 0.313 0.279 0.890 0.471 0.99 7.12 4.5E-06 2.1E-06 6.1E-05 0.032 18.961 WFTS-085 2.00 1.78 2.36 1.32 2 0.901 28.182 0.050 0.193 0.172 0.890 0.544 0.99 7.12 4.3E-06 2.3E-06 6.6E-05 0.030 21.905 WFTS-086 2.00 1.79 2.07 1.15 2 1.811 14.025 0.096 0.279 0.250 0.896 0.489 1.50 7.17 7.5E-06 3.7E-06 7.0E-05 0.054 13.050 WFTS-087 2.00 1.79 2.07 1.15 2 1.811 14.025 0.099 0.328 0.294 0.897 0.489 1.49 7.18 7.5E-06 3.7E-06 7.1E-05 0.054 13.162 WFTS-088 2.00 1.80 2.08 1.15 2 0.514 49.420 0.071 0.276 0.248 0.900 0.447 0.50 7.20 2.1E-06 9.6E-07 5.5E-05 0.015 35.515 WFTS-089 2.00 1.80 2.08 1.15 2 0.514 49.420 0.075 0.309 0.278 0.900 0.443 0.50 7.20 2.1E-06 9.5E-07 5.5E-05 0.015 35.768 WFTS-090 2.00 1.80 2.08 1.15 2 0.514 49.420 0.075 0.309 0.278 0.900 0.443 0.50 7.20 2.1E-06 9.5E-07 5.5E-05 0.015 35.768 WFTS-091 2.00 1.80 2.08 1.15 2 0.514 49.420 0.075 0.309 0.278 0.900 0.443 0.50 7.20 2.1E-06 9.5E-07 5.5E-05 0.015 35.768 WFTS-092 2.00 1.80 2.08 1.15 2 0.514 49.420 0.075 0.309 0.278 0.900 0.443 0.50 7.20 2.1E-06 9.5E-07 5.5E-05 0.015 35.768 WFTS-093 2.00 1.80 2.08 1.15 2 0.524 48.483 0.080 0.308 0.278 0.902 0.440 0.50 7.22 2.2E-06 9.6E-07 5.5E-05 0.016 35.141 WFTS-094 2.00 1.80 2.08 1.15 2 0.540 47.056 0.100 0.321 0.290 0.902 0.424 0.50 7.22 2.3E-06 9.5E-07 5.6E-05 0.016 34.196 WFTS-095 2.00 1.81 3.21 1.78 2 1.175 21.610 0.054 0.213 0.193 0.903 0.657 1.49 7.23 7.6E-06 5.0E-06 9.6E-05 0.055 17.625 WFTS-096 2.00 1.81 2.09 1.15 3 1.128 22.524 0.075 0.483 0.437 0.904 0.486 1.00 10.84 4.7E-06 2.3E-06 9.9E-05 0.051 19.483 WFTS-097 2.00 1.81 2.09 1.15 3 1.128 22.524 0.075 0.483 0.437 0.904 0.486 1.00 10.84 4.7E-06 2.3E-06 9.9E-05 0.051 19.483 WFTS-098 2.00 1.82 2.11 1.15 3 1.112 22.846 0.059 0.477 0.435 0.912 0.497 1.01 10.95 4.7E-06 2.3E-06 1.0E-04 0.051 19.729 WFTS-099 2.00 1.83 2.50 1.37 2 1.438 17.668 0.073 0.260 0.238 0.913 0.569 1.50 7.30 7.2E-06 4.1E-06 8.0E-05 0.052 15.171 WFTS-100 2.00 1.83 2.53 1.38 2 1.398 18.170 0.054 0.190 0.173 0.914 0.581 1.51 7.31 7.1E-06 4.1E-06 7.9E-05 0.052 15.356 WFTS-101 2.00 1.85 3.32 1.79 2 0.762 33.322 0.061 0.185 0.171 0.927 0.642 1.00 7.42 5.1E-06 3.3E-06 9.6E-05 0.038 25.623 WFTS-102 2.00 1.88 3.99 2.12 2 1.175 21.610 0.084 0.440 0.414 0.942 0.696 1.50 7.54 9.4E-06 6.5E-06 1.3E-04 0.071 18.587 WFTS-103 2.00 1.90 2.80 1.48 2 0.826 30.758 0.061 0.232 0.220 0.949 0.595 1.00 7.59 4.6E-06 2.8E-06 8.4E-05 0.035 23.923 WFTS-104 2.00 1.90 3.07 1.62 2 1.253 20.273 0.083 0.291 0.276 0.949 0.629 1.49 7.59 7.7E-06 4.8E-06 9.9E-05 0.058 16.903 WFTS-105 2.00 1.91 3.10 1.62 2 1.251 20.305 0.081 0.319 0.305 0.954 0.633 1.49 7.63 7.8E-06 4.9E-06 1.0E-04 0.059 17.037 WFTS-106 2.00 1.93 2.53 1.31 2 0.883 28.752 0.075 0.152 0.146 0.966 0.553 1.00 7.73 4.5E-06 2.5E-06 7.7E-05 0.035 22.159 WFTS-107 2.00 1.94 1.99 1.02 2 0.510 49.805 0.057 0.111 0.108 0.970 0.442 0.50 7.76 2.0E-06 9.0E-07 5.5E-05 0.016 35.042 WFTS-108 2.00 1.94 1.99 1.02 2 0.510 49.805 0.057 0.205 0.199 0.970 0.442 0.50 7.76 2.0E-06 9.0E-07 5.6E-05 0.016 35.501 WFTS-109 2.00 1.94 2.33 1.20 9 1.507 16.854 0.059 0.250 0.243 0.970 0.549 1.50 34.94 7.0E-06 3.9E-06 3.6E-04 0.245 14.641 WFTS-110 2.00 1.94 2.33 1.20 9 1.507 16.854 0.059 0.250 0.243 0.970 0.549 1.50 34.94 7.0E-06 3.9E-06 3.6E-04 0.245 14.641 222 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-111 2.00 1.94 2.24 1.15 2 0.508 50.000 0.087 0.285 0.276 0.971 0.459 0.50 7.77 2.3E-06 1.1E-06 6.5E-05 0.018 36.539 WFTS-112 2.00 1.94 2.25 1.15 2 0.508 50.000 0.086 0.282 0.274 0.972 0.461 0.50 7.78 2.3E-06 1.1E-06 6.5E-05 0.018 36.535 WFTS-113 2.00 1.94 2.25 1.15 2 0.508 50.000 0.086 0.282 0.274 0.972 0.461 0.50 7.78 2.3E-06 1.1E-06 6.5E-05 0.018 36.535 WFTS-114 2.00 1.97 2.28 1.15 2 0.925 27.456 0.050 0.145 0.143 0.985 0.530 0.99 7.88 4.2E-06 2.2E-06 7.1E-05 0.033 21.331 WFTS-115 2.00 1.97 2.28 1.15 2 1.015 25.037 0.092 0.380 0.375 0.985 0.509 0.99 7.88 4.6E-06 2.4E-06 7.5E-05 0.036 20.581 WFTS-116 2.00 2.01 2.73 1.36 11 2.536 10.016 0.050 0.360 0.361 1.003 0.621 2.49 44.12 1.4E-05 8.6E-06 6.1E-04 0.611 9.992 WFTS-117 2.00 2.01 2.95 1.47 11 2.536 10.016 0.050 0.558 0.559 1.003 0.648 2.48 44.12 1.5E-05 9.7E-06 6.9E-04 0.659 10.435 WFTS-118 2.00 2.04 2.35 1.15 2 0.943 26.935 0.059 0.327 0.334 1.020 0.539 0.99 8.16 4.4E-06 2.4E-06 7.9E-05 0.036 21.733 WFTS-119 2.00 2.06 4.00 1.95 2 1.080 23.516 0.053 0.253 0.260 1.028 0.713 1.49 8.23 8.6E-06 6.2E-06 1.4E-04 0.071 19.091 WFTS-120 2.00 2.09 2.41 1.15 2 0.919 27.634 0.054 0.242 0.252 1.043 0.551 1.01 8.35 4.4E-06 2.4E-06 8.1E-05 0.037 21.831 WFTS-121 2.00 2.09 2.41 1.15 2 0.919 27.634 0.054 0.242 0.252 1.043 0.551 1.01 8.35 4.4E-06 2.4E-06 8.1E-05 0.037 21.831 WFTS-122 2.00 2.09 2.41 1.15 2 0.911 27.875 0.055 0.243 0.253 1.043 0.550 1.00 8.35 4.4E-06 2.4E-06 8.1E-05 0.037 21.993 WFTS-123 2.00 2.09 2.23 1.07 2 1.559 16.295 0.074 0.221 0.231 1.047 0.526 1.49 8.38 7.0E-06 3.7E-06 8.2E-05 0.058 14.132 WFTS-124 2.00 2.11 2.44 1.15 10 1.469 17.286 0.077 0.290 0.306 1.055 0.559 1.50 42.20 7.2E-06 4.0E-06 4.5E-04 0.302 14.902 WFTS-125 2.00 2.11 2.44 1.15 10 1.517 16.744 0.087 0.352 0.371 1.055 0.556 1.51 42.20 7.4E-06 4.1E-06 4.6E-04 0.312 14.720 WFTS-126 2.00 2.11 2.07 0.98 3 1.152 22.056 0.076 0.476 0.503 1.056 0.482 1.01 12.68 4.8E-06 2.3E-06 1.2E-04 0.060 19.134 WFTS-127 2.00 2.18 2.98 1.37 2 2.264 11.220 0.089 0.235 0.257 1.091 0.638 2.48 8.73 1.4E-05 8.6E-06 1.2E-04 0.118 10.299 WFTS-128 2.00 2.23 1.99 0.89 2 0.510 49.805 0.050 0.113 0.126 1.116 0.448 0.50 8.92 2.0E-06 9.1E-07 6.5E-05 0.018 35.671 WFTS-129 2.00 2.23 2.52 1.13 2 0.875 29.013 0.050 0.149 0.167 1.117 0.568 1.01 8.94 4.4E-06 2.5E-06 8.9E-05 0.039 22.505 WFTS-130 2.00 2.24 3.99 1.79 2 1.080 23.516 0.053 0.175 0.196 1.118 0.713 1.52 8.95 8.6E-06 6.2E-06 1.5E-04 0.077 18.818 WFTS-131 2.00 2.26 2.50 1.10 3 1.493 17.010 0.083 0.429 0.485 1.132 0.566 1.49 13.58 7.5E-06 4.2E-06 1.5E-04 0.101 15.173 WFTS-132 2.00 2.26 3.01 1.33 2 2.224 11.420 0.074 0.229 0.260 1.132 0.645 2.48 9.05 1.3E-05 8.6E-06 1.3E-04 0.121 10.393 WFTS-133 2.00 2.26 2.64 1.17 2 2.518 10.087 0.075 0.235 0.266 1.132 0.603 2.50 9.05 1.3E-05 8.0E-06 1.2E-04 0.120 9.638 WFTS-134 2.00 2.27 2.64 1.16 2 2.518 10.087 0.087 0.235 0.267 1.133 0.600 2.49 9.06 1.3E-05 8.0E-06 1.2E-04 0.121 9.623 WFTS-135 2.00 2.27 3.07 1.35 2 2.224 11.420 0.071 0.235 0.267 1.134 0.653 2.52 9.08 1.4E-05 8.9E-06 1.3E-04 0.124 10.379 WFTS-136 2.00 2.27 2.64 1.16 2 2.518 10.087 0.099 0.235 0.267 1.134 0.596 2.48 9.08 1.3E-05 7.9E-06 1.2E-04 0.121 9.610 WFTS-137 2.00 2.28 3.35 1.47 2 0.766 33.150 0.053 0.247 0.282 1.141 0.652 1.00 9.13 5.1E-06 3.4E-06 1.2E-04 0.047 26.037 WFTS-138 2.00 2.29 4.00 1.74 2 1.908 13.310 0.081 0.256 0.293 1.147 0.718 2.49 9.17 1.5E-05 1.1E-05 1.6E-04 0.140 11.532 WFTS-139 2.00 2.29 4.00 1.74 2 2.004 12.677 0.077 0.415 0.476 1.147 0.721 2.50 9.17 1.6E-05 1.2E-05 1.7E-04 0.147 11.528 WFTS-140 2.00 2.34 4.00 1.71 2 2.163 11.745 0.093 0.621 0.725 1.168 0.718 2.48 9.34 1.7E-05 1.2E-05 1.9E-04 0.162 11.579 WFTS-141 2.00 2.34 2.70 1.15 2 1.307 19.441 0.052 0.240 0.280 1.169 0.604 1.50 9.35 7.1E-06 4.3E-06 1.1E-04 0.066 16.173 WFTS-142 2.00 2.34 2.70 1.15 2 1.307 19.441 0.051 0.238 0.278 1.171 0.606 1.50 9.37 7.1E-06 4.3E-06 1.1E-04 0.066 16.167 WFTS-143 2.00 2.35 2.90 1.24 11 2.266 11.210 0.050 0.268 0.315 1.175 0.641 2.48 51.69 1.3E-05 8.4E-06 7.0E-04 0.680 10.337 WFTS-144 2.00 2.35 3.19 1.35 2 1.169 21.721 0.054 0.143 0.168 1.176 0.654 1.50 9.41 7.5E-06 4.9E-06 1.2E-04 0.070 17.464 WFTS-145 2.00 2.35 2.95 1.25 11 2.234 11.369 0.050 0.160 0.189 1.177 0.646 2.52 51.81 1.3E-05 8.5E-06 7.0E-04 0.682 10.254 WFTS-146 2.00 2.35 2.90 1.23 11 2.266 11.210 0.050 0.181 0.213 1.177 0.641 2.52 51.81 1.3E-05 8.4E-06 6.9E-04 0.681 10.188 WFTS-147 2.00 2.39 2.76 1.15 11 2.413 10.527 0.050 0.341 0.407 1.195 0.624 2.49 52.58 1.3E-05 8.3E-06 7.0E-04 0.700 10.046 WFTS-148 2.00 2.39 2.76 1.15 2 2.520 10.079 0.082 0.452 0.541 1.196 0.617 2.48 9.57 1.4E-05 8.6E-06 1.3E-04 0.133 9.975 WFTS-149 2.00 2.39 2.76 1.15 3 2.520 10.079 0.082 0.452 0.541 1.196 0.617 2.48 14.35 1.4E-05 8.6E-06 2.0E-04 0.200 9.976 WFTS-150 2.00 2.41 2.78 1.15 11 2.397 10.597 0.050 0.276 0.332 1.204 0.627 2.52 52.95 1.3E-05 8.4E-06 7.0E-04 0.706 9.939 WFTS-151 2.00 2.42 2.80 1.15 11 2.345 10.830 0.050 0.208 0.252 1.211 0.629 2.52 53.28 1.3E-05 8.3E-06 7.0E-04 0.699 9.970 WFTS-152 2.00 2.42 2.80 1.15 11 2.349 10.812 0.050 0.274 0.331 1.211 0.629 2.50 53.28 1.3E-05 8.3E-06 7.1E-04 0.700 10.072 WFTS-153 2.00 2.43 2.80 1.15 11 2.322 10.941 0.050 0.161 0.196 1.214 0.630 2.52 53.43 1.3E-05 8.2E-06 6.9E-04 0.696 9.977 WFTS-154 2.00 2.49 2.51 1.01 2 0.875 29.013 0.050 0.139 0.173 1.247 0.567 1.01 9.98 4.4E-06 2.5E-06 9.9E-05 0.044 22.537 WFTS-155 2.00 2.52 3.31 1.32 2 0.762 33.322 0.058 0.090 0.114 1.259 0.645 1.01 10.08 5.1E-06 3.3E-06 1.3E-04 0.051 25.605 WFTS-156 2.00 2.53 4.00 1.58 2 2.224 11.420 0.050 0.088 0.111 1.267 0.733 2.98 10.14 1.8E-05 1.3E-05 1.8E-04 0.180 9.841 WFTS-157 2.00 2.56 2.95 1.15 2 2.471 10.281 0.098 0.537 0.687 1.279 0.635 2.48 10.23 1.5E-05 9.3E-06 1.5E-04 0.149 10.230 WFTS-158 2.00 2.56 2.01 0.78 2 0.510 49.805 0.050 0.089 0.114 1.282 0.453 0.50 10.26 2.1E-06 9.3E-07 7.6E-05 0.021 36.120 WFTS-159 2.00 2.57 2.96 1.15 2 2.248 11.299 0.091 0.265 0.340 1.283 0.636 2.48 10.26 1.3E-05 8.5E-06 1.4E-04 0.137 10.235 WFTS-160 2.00 2.57 2.97 1.15 11 2.163 11.745 0.050 0.130 0.167 1.284 0.647 2.50 56.50 1.3E-05 8.3E-06 7.5E-04 0.725 10.379 223 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-161 2.00 2.57 2.97 1.15 2 0.810 31.361 0.059 0.233 0.300 1.285 0.615 1.00 10.28 4.8E-06 3.0E-06 1.2E-04 0.049 24.655 WFTS-162 2.00 2.58 3.03 1.18 4 2.532 10.031 0.096 0.644 0.831 1.289 0.644 2.48 20.62 1.5E-05 9.9E-06 3.3E-04 0.316 10.386 WFTS-163 2.00 2.60 3.01 1.15 2 2.173 11.692 0.054 0.213 0.277 1.302 0.651 2.50 10.42 1.3E-05 8.5E-06 1.4E-04 0.136 10.423 WFTS-164 2.00 2.63 3.03 1.15 2 0.792 32.069 0.050 0.230 0.302 1.313 0.628 1.00 10.51 4.8E-06 3.0E-06 1.3E-04 0.051 25.204 WFTS-165 2.00 2.63 3.98 1.51 2 2.403 10.571 0.063 0.371 0.487 1.313 0.729 3.01 10.51 1.9E-05 1.4E-05 1.9E-04 0.201 9.674 WFTS-166 2.00 2.63 2.17 0.83 2 0.528 48.119 0.091 0.171 0.225 1.315 0.447 0.50 10.52 2.3E-06 1.0E-06 8.5E-05 0.024 35.432 WFTS-167 2.00 2.63 3.04 1.15 11 2.151 11.810 0.051 0.246 0.324 1.315 0.655 2.48 57.87 1.3E-05 8.6E-06 8.0E-04 0.756 10.555 WFTS-168 2.00 2.63 3.04 1.15 11 2.151 11.810 0.051 0.246 0.324 1.315 0.655 2.48 57.87 1.3E-05 8.6E-06 8.0E-04 0.756 10.555 WFTS-169 2.00 2.63 3.04 1.15 2 0.792 32.069 0.054 0.127 0.168 1.317 0.626 1.01 10.54 4.8E-06 3.0E-06 1.3E-04 0.051 24.788 WFTS-170 2.00 2.64 3.05 1.15 2 0.792 32.069 0.050 0.266 0.350 1.319 0.629 0.99 10.55 4.8E-06 3.0E-06 1.3E-04 0.051 25.405 WFTS-171 2.00 2.64 4.00 1.52 2 2.258 11.249 0.055 0.202 0.266 1.319 0.732 2.98 10.55 1.8E-05 1.3E-05 1.9E-04 0.191 9.816 WFTS-172 2.00 2.64 3.41 1.29 11 2.532 10.031 0.050 0.305 0.403 1.321 0.693 3.00 58.14 1.7E-05 1.2E-05 9.3E-04 1.010 9.246 WFTS-173 2.00 2.69 3.11 1.15 11 2.103 12.078 0.050 0.143 0.193 1.345 0.662 2.51 59.20 1.3E-05 8.7E-06 8.2E-04 0.774 10.539 WFTS-174 2.00 2.71 3.13 1.15 2 0.782 32.476 0.058 0.207 0.281 1.354 0.629 0.99 10.83 4.9E-06 3.1E-06 1.4E-04 0.053 25.412 WFTS-175 2.00 2.73 3.15 1.15 2 1.265 20.082 0.073 0.372 0.508 1.364 0.643 1.51 10.91 8.0E-06 5.1E-06 1.5E-04 0.087 17.052 WFTS-176 2.00 2.73 3.16 1.15 2 0.814 31.208 0.052 0.395 0.540 1.367 0.640 0.99 10.94 5.1E-06 3.3E-06 1.5E-04 0.056 25.719 WFTS-177 2.00 2.76 3.41 1.24 11 2.476 10.257 0.050 0.188 0.259 1.379 0.693 3.02 60.68 1.7E-05 1.2E-05 9.4E-04 1.030 9.167 WFTS-178 2.00 2.78 4.00 1.44 2 1.086 23.389 0.053 0.218 0.302 1.388 0.713 1.51 11.11 8.7E-06 6.2E-06 1.8E-04 0.097 18.859 WFTS-179 2.00 2.80 1.70 0.61 2 0.635 39.992 0.052 0.227 0.318 1.402 0.378 0.50 11.22 2.2E-06 8.2E-07 7.3E-05 0.024 29.996 WFTS-180 2.00 2.84 1.98 0.70 2 0.528 48.119 0.052 0.107 0.152 1.422 0.445 0.50 11.38 2.1E-06 9.3E-07 8.4E-05 0.024 35.301 WFTS-181 2.00 2.91 3.36 1.15 2 2.498 10.167 0.089 0.227 0.330 1.456 0.678 2.98 11.65 1.7E-05 1.1E-05 1.8E-04 0.196 9.097 WFTS-182 2.00 2.92 3.27 1.12 2 1.183 21.465 0.078 0.233 0.340 1.460 0.649 1.49 11.68 7.7E-06 5.0E-06 1.6E-04 0.090 17.464 WFTS-183 2.00 3.02 3.21 1.06 2 1.152 22.056 0.054 0.119 0.180 1.512 0.656 1.49 12.10 7.4E-06 4.8E-06 1.6E-04 0.089 17.617 WFTS-184 2.00 3.04 2.97 0.98 11 2.131 11.920 0.050 0.135 0.206 1.522 0.647 2.50 66.95 1.3E-05 8.2E-06 8.8E-04 0.847 10.347 WFTS-185 2.00 3.05 4.00 1.31 2 1.813 14.010 0.053 0.111 0.169 1.524 0.728 2.50 12.19 1.5E-05 1.1E-05 2.1E-04 0.177 11.635 WFTS-186 2.00 3.08 3.56 1.15 2 1.906 13.324 0.057 0.101 0.155 1.542 0.698 2.50 12.34 1.4E-05 9.5E-06 1.9E-04 0.168 11.177 WFTS-187 2.00 3.14 3.62 1.15 2 0.748 33.942 0.059 0.204 0.321 1.569 0.667 1.00 12.55 5.4E-06 3.6E-06 1.8E-04 0.068 26.666 WFTS-188 2.00 3.14 3.33 1.06 2 0.762 33.322 0.062 0.088 0.137 1.571 0.643 1.00 12.57 5.1E-06 3.3E-06 1.6E-04 0.064 25.741 WFTS-189 2.00 3.15 1.70 0.54 2 0.635 39.992 0.052 0.210 0.331 1.574 0.379 0.50 12.59 2.2E-06 8.2E-07 8.2E-05 0.027 30.156 WFTS-190 2.00 3.17 3.66 1.15 2 1.910 13.296 0.051 0.165 0.262 1.585 0.708 2.52 12.68 1.4E-05 9.9E-06 2.0E-04 0.177 11.211 WFTS-191 2.00 3.18 3.67 1.15 11 2.413 10.527 0.050 0.378 0.601 1.590 0.712 2.97 69.94 1.8E-05 1.3E-05 1.2E-03 1.240 9.583 WFTS-192 2.00 3.23 3.73 1.15 2 2.264 11.220 0.059 0.113 0.182 1.616 0.713 2.98 12.93 1.7E-05 1.2E-05 2.1E-04 0.219 9.580 WFTS-193 2.00 3.25 3.75 1.15 2 1.855 13.695 0.059 0.132 0.214 1.623 0.710 2.48 12.98 1.4E-05 9.9E-06 2.1E-04 0.180 11.424 WFTS-194 2.00 3.25 3.75 1.15 2 1.855 13.695 0.059 0.132 0.214 1.623 0.710 2.48 12.98 1.4E-05 9.9E-06 2.1E-04 0.180 11.424 WFTS-195 2.00 3.25 3.75 1.15 2 1.855 13.695 0.059 0.132 0.214 1.623 0.710 2.48 12.98 1.4E-05 9.9E-06 2.1E-04 0.180 11.424 WFTS-196 2.00 3.25 3.75 1.15 3 2.375 10.694 0.084 0.800 1.299 1.625 0.708 2.50 19.50 1.8E-05 1.3E-05 3.9E-04 0.348 11.329 WFTS-197 2.00 3.26 3.76 1.15 11 1.885 13.478 0.050 0.224 0.364 1.628 0.715 2.50 71.64 1.4E-05 1.0E-05 1.2E-03 1.020 11.426 WFTS-198 2.00 3.26 3.76 1.15 3 2.375 10.694 0.084 0.802 1.306 1.629 0.708 2.50 19.55 1.8E-05 1.3E-05 4.0E-04 0.349 11.337 WFTS-199 2.00 3.26 3.27 1.00 2 1.183 21.465 0.078 0.234 0.382 1.632 0.649 1.49 13.05 7.7E-06 5.0E-06 1.8E-04 0.101 17.455 WFTS-200 2.00 3.28 3.79 1.15 2 2.417 10.510 0.088 0.366 0.599 1.639 0.709 2.99 13.11 1.8E-05 1.3E-05 2.3E-04 0.240 9.473 WFTS-201 2.00 3.28 3.79 1.15 2 2.480 10.240 0.094 0.460 0.754 1.641 0.708 2.97 13.13 1.9E-05 1.3E-05 2.4E-04 0.247 9.529 WFTS-202 2.00 3.30 3.81 1.15 11 2.294 11.074 0.052 0.197 0.325 1.651 0.721 3.02 72.64 1.8E-05 1.3E-05 1.2E-03 1.270 9.553 WFTS-203 2.00 3.32 3.33 1.00 11 2.536 10.016 0.050 0.310 0.514 1.660 0.686 3.03 73.04 1.7E-05 1.2E-05 1.1E-03 1.230 9.063 WFTS-204 2.00 3.33 3.85 1.15 2 2.417 10.510 0.090 0.416 0.693 1.667 0.713 2.97 13.34 1.9E-05 1.3E-05 2.4E-04 0.248 9.591 WFTS-205 2.00 3.34 3.85 1.15 11 1.845 13.768 0.051 0.092 0.153 1.668 0.720 2.52 73.39 1.4E-05 1.0E-05 1.2E-03 1.040 11.410 WFTS-206 2.00 3.34 2.98 0.89 2 2.137 11.887 0.064 0.235 0.393 1.669 0.645 2.48 13.36 1.3E-05 8.2E-06 1.8E-04 0.170 10.387 WFTS-207 2.00 3.34 2.98 0.89 2 2.137 11.887 0.070 0.188 0.315 1.672 0.643 2.50 13.38 1.3E-05 8.2E-06 1.8E-04 0.171 10.297 WFTS-208 2.00 3.35 4.00 1.20 2 1.082 23.475 0.053 0.207 0.347 1.673 0.713 1.51 13.39 8.7E-06 6.2E-06 2.2E-04 0.116 18.886 WFTS-209 2.00 3.37 3.89 1.15 11 2.250 11.289 0.050 0.183 0.308 1.683 0.726 3.00 74.05 1.8E-05 1.3E-05 1.3E-03 1.300 9.668 WFTS-210 2.00 3.39 3.92 1.15 11 1.837 13.828 0.050 0.157 0.266 1.697 0.725 2.52 74.67 1.4E-05 1.0E-05 1.2E-03 1.080 11.519 224 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-211 2.00 3.84 1.72 0.45 2 0.635 39.992 0.052 0.208 0.399 1.918 0.383 0.50 15.34 2.2E-06 8.3E-07 1.0E-04 0.033 30.516 WFTS-212 2.00 3.40 3.93 1.15 11 1.849 13.739 0.050 0.190 0.324 1.700 0.725 2.52 74.81 1.5E-05 1.1E-05 1.3E-03 1.090 11.509 WFTS-213 2.00 3.40 3.93 1.15 11 1.831 13.873 0.050 0.114 0.194 1.700 0.725 2.52 74.81 1.4E-05 1.0E-05 1.2E-03 1.080 11.492 WFTS-214 2.00 3.41 3.93 1.15 2 1.906 13.324 0.057 0.326 0.555 1.704 0.724 2.51 13.63 1.5E-05 1.1E-05 2.4E-04 0.204 11.524 WFTS-215 2.00 3.42 3.94 1.15 2 2.288 11.103 0.082 0.226 0.386 1.708 0.720 3.01 13.66 1.8E-05 1.3E-05 2.4E-04 0.247 9.565 WFTS-216 2.00 3.42 3.94 1.15 2 2.288 11.103 0.082 0.226 0.386 1.708 0.720 3.01 13.66 1.8E-05 1.3E-05 2.4E-04 0.247 9.565 WFTS-217 2.00 3.42 3.94 1.15 2 2.288 11.103 0.082 0.226 0.386 1.708 0.720 3.01 13.66 1.8E-05 1.3E-05 2.4E-04 0.247 9.565 WFTS-218 2.00 3.42 3.95 1.15 2 1.924 13.200 0.082 0.366 0.625 1.710 0.715 2.48 13.68 1.5E-05 1.1E-05 2.4E-04 0.208 11.537 WFTS-219 2.00 3.43 4.00 1.17 2 1.082 23.475 0.066 0.112 0.192 1.714 0.704 1.51 13.71 8.7E-06 6.1E-06 2.2E-04 0.119 18.610 WFTS-220 2.00 3.44 3.97 1.15 11 2.228 11.400 0.055 0.137 0.235 1.719 0.730 3.02 75.62 1.8E-05 1.3E-05 1.3E-03 1.340 9.662 WFTS-221 2.00 3.44 3.97 1.15 11 2.228 11.400 0.055 0.137 0.235 1.719 0.730 3.02 75.62 1.8E-05 1.3E-05 1.3E-03 1.340 9.662 WFTS-222 2.00 3.44 3.97 1.15 11 2.232 11.379 0.053 0.143 0.245 1.719 0.730 3.03 75.62 1.8E-05 1.3E-05 1.3E-03 1.340 9.654 WFTS-223 2.00 3.44 3.97 1.15 2 2.234 11.369 0.057 0.160 0.275 1.721 0.729 3.02 13.77 1.8E-05 1.3E-05 2.4E-04 0.244 9.664 WFTS-224 2.00 3.44 3.97 1.15 2 2.234 11.369 0.057 0.160 0.275 1.721 0.729 3.02 13.77 1.8E-05 1.3E-05 2.4E-04 0.244 9.664 WFTS-225 2.00 3.44 3.98 1.15 11 2.234 11.369 0.050 0.231 0.398 1.722 0.732 2.99 75.76 1.8E-05 1.3E-05 1.3E-03 1.350 9.782 WFTS-226 2.00 3.45 3.98 1.15 10 1.815 13.994 0.053 0.097 0.167 1.723 0.727 2.52 68.91 1.4E-05 1.1E-05 1.2E-03 0.995 11.549 WFTS-227 2.00 3.45 3.98 1.15 10 1.811 14.025 0.050 0.091 0.157 1.723 0.728 2.52 68.91 1.4E-05 1.1E-05 1.2E-03 0.993 11.569 WFTS-228 2.00 3.45 3.98 1.15 12 1.817 13.979 0.050 0.097 0.167 1.723 0.728 2.52 82.70 1.5E-05 1.1E-05 1.4E-03 1.200 11.540 WFTS-229 2.00 3.45 3.98 1.15 2 1.906 13.324 0.082 0.330 0.570 1.725 0.717 2.49 13.80 1.5E-05 1.1E-05 2.4E-04 0.210 11.511 WFTS-230 2.00 3.45 3.98 1.15 2 1.970 12.894 0.082 0.424 0.732 1.725 0.718 2.50 13.80 1.6E-05 1.1E-05 2.5E-04 0.217 11.494 WFTS-231 2.00 3.45 3.98 1.15 2 1.986 12.791 0.082 0.463 0.798 1.725 0.718 2.48 13.80 1.6E-05 1.1E-05 2.5E-04 0.218 11.558 WFTS-232 2.00 3.45 3.98 1.15 11 2.226 11.410 0.052 0.149 0.258 1.725 0.732 3.02 75.90 1.8E-05 1.3E-05 1.3E-03 1.350 9.681 WFTS-233 2.00 3.45 3.98 1.15 11 2.226 11.410 0.052 0.149 0.258 1.725 0.732 3.02 75.90 1.8E-05 1.3E-05 1.3E-03 1.350 9.681 WFTS-234 2.00 3.45 3.98 1.15 11 2.226 11.410 0.052 0.149 0.258 1.725 0.732 3.02 75.90 1.8E-05 1.3E-05 1.3E-03 1.350 9.681 WFTS-235 2.00 3.45 3.98 1.15 11 2.226 11.410 0.052 0.149 0.258 1.725 0.732 3.02 75.90 1.8E-05 1.3E-05 1.3E-03 1.350 9.681 WFTS-236 2.00 3.52 2.51 0.71 2 0.879 28.882 0.050 0.103 0.181 1.762 0.568 1.01 14.10 4.4E-06 2.5E-06 1.4E-04 0.062 22.507 WFTS-237 2.00 3.66 3.38 0.92 2 0.776 32.726 0.081 0.088 0.160 1.829 0.631 0.99 14.63 5.3E-06 3.3E-06 2.0E-04 0.077 25.363 WFTS-238 2.00 3.66 4.00 1.09 2 2.230 11.390 0.052 0.202 0.369 1.829 0.733 3.02 14.63 1.8E-05 1.3E-05 2.5E-04 0.261 9.706 WFTS-239 2.00 3.73 4.00 1.07 2 1.789 14.196 0.053 0.120 0.224 1.866 0.728 2.49 14.93 1.4E-05 1.0E-05 2.5E-04 0.214 11.686 WFTS-240 2.00 3.83 4.00 1.04 2 2.226 11.410 0.055 0.182 0.349 1.915 0.732 3.03 15.32 1.8E-05 1.3E-05 2.6E-04 0.273 9.664 WFTS-241 2.00 3.83 4.00 1.04 2 2.226 11.410 0.055 0.182 0.349 1.915 0.732 3.03 15.32 1.8E-05 1.3E-05 2.6E-04 0.273 9.664 WFTS-242 2.00 3.83 4.00 1.04 2 2.226 11.410 0.055 0.182 0.349 1.915 0.732 3.03 15.32 1.8E-05 1.3E-05 2.6E-04 0.273 9.664 WFTS-243 2.00 3.90 3.33 0.85 2 0.770 32.979 0.059 0.090 0.176 1.949 0.645 1.01 15.59 5.1E-06 3.3E-06 2.1E-04 0.080 25.612 WFTS-244 2.00 3.93 3.48 0.89 2 1.908 13.310 0.054 0.112 0.219 1.964 0.693 2.51 15.71 1.3E-05 9.2E-06 2.3E-04 0.209 11.056 WFTS-245 2.00 3.95 2.51 0.64 2 0.879 28.882 0.050 0.092 0.181 1.974 0.567 1.01 15.80 4.4E-06 2.5E-06 1.6E-04 0.070 22.522 WFTS-246 2.00 3.97 3.48 0.88 2 1.908 13.310 0.055 0.118 0.234 1.985 0.692 2.50 15.88 1.3E-05 9.2E-06 2.3E-04 0.211 11.056 WFTS-247 2.00 4.00 4.00 1.00 2 2.161 11.756 0.050 0.089 0.178 2.000 0.733 2.99 16.00 1.7E-05 1.3E-05 2.7E-04 0.277 9.796 WFTS-248 3.00 1.44 2.37 1.64 2 1.392 18.248 0.087 0.337 0.365 1.083 0.541 1.49 8.66 9.9E-06 5.4E-06 1.3E-04 0.086 14.550 WFTS-249 3.00 1.64 1.82 1.11 2 0.508 50.000 0.054 0.155 0.191 1.230 0.403 0.50 9.84 2.8E-06 1.1E-06 8.9E-05 0.027 32.495 WFTS-250 3.00 2.06 2.38 1.15 2 1.446 17.572 0.076 0.398 0.614 1.544 0.549 1.51 12.35 1.0E-05 5.7E-06 1.9E-04 0.127 14.529 WFTS-251 3.00 2.07 2.39 1.15 3 0.889 28.560 0.067 0.291 0.450 1.550 0.537 0.99 18.61 6.4E-06 3.4E-06 2.6E-04 0.118 21.651 WFTS-252 3.00 2.07 2.39 1.15 3 0.953 26.655 0.065 0.467 0.724 1.550 0.542 1.01 18.61 6.8E-06 3.7E-06 2.7E-04 0.127 21.455 WFTS-253 3.00 2.11 1.85 0.88 2 0.532 47.759 0.050 0.238 0.376 1.583 0.415 0.50 12.66 3.0E-06 1.2E-06 1.2E-04 0.037 33.294 WFTS-254 3.00 2.15 2.49 1.15 11 2.427 10.466 0.050 0.330 0.533 1.615 0.585 2.51 71.06 1.8E-05 1.1E-05 1.2E-03 1.290 9.321 WFTS-255 3.00 2.19 2.53 1.15 11 2.300 11.045 0.050 0.145 0.238 1.641 0.591 2.52 72.19 1.7E-05 1.0E-05 1.2E-03 1.260 9.392 WFTS-256 3.00 2.19 2.53 1.15 11 2.300 11.045 0.050 0.145 0.238 1.641 0.591 2.52 72.19 1.7E-05 1.0E-05 1.2E-03 1.260 9.392 WFTS-257 3.00 2.23 2.58 1.15 2 2.429 10.458 0.100 0.381 0.638 1.675 0.587 2.51 13.40 1.9E-05 1.1E-05 2.4E-04 0.252 9.354 WFTS-258 3.00 2.33 2.69 1.15 3 0.844 30.106 0.069 0.291 0.510 1.750 0.578 1.00 21.01 6.8E-06 3.9E-06 3.3E-04 0.143 23.137 WFTS-259 3.00 2.41 4.00 1.66 2 2.161 11.756 0.071 0.187 0.337 1.804 0.725 2.99 14.44 2.6E-05 1.9E-05 3.6E-04 0.374 9.701 WFTS-260 3.00 2.46 4.00 1.63 2 1.779 14.276 0.070 0.208 0.384 1.843 0.720 2.49 14.74 2.1E-05 1.5E-05 3.7E-04 0.315 11.588 225 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-261 3.00 2.48 4.00 1.61 2 2.161 11.756 0.056 0.183 0.340 1.859 0.730 3.01 14.87 2.6E-05 1.9E-05 3.7E-04 0.386 9.694 WFTS-262 3.00 2.49 2.88 1.15 11 2.540 10.000 0.050 0.165 0.308 1.870 0.640 3.00 82.27 2.2E-05 1.4E-05 1.5E-03 1.800 8.537 WFTS-263 3.00 2.51 2.90 1.15 11 2.540 10.000 0.050 0.191 0.360 1.883 0.642 3.00 82.84 2.2E-05 1.4E-05 1.6E-03 1.830 8.562 WFTS-264 3.00 2.51 2.90 1.15 11 2.540 10.000 0.050 0.227 0.426 1.883 0.642 2.98 82.84 2.2E-05 1.4E-05 1.6E-03 1.830 8.613 WFTS-265 3.00 2.51 2.90 1.15 11 2.540 10.000 0.050 0.144 0.272 1.884 0.642 3.02 82.91 2.2E-05 1.4E-05 1.6E-03 1.830 8.507 WFTS-266 3.00 2.51 2.90 1.15 11 2.540 10.000 0.050 0.250 0.471 1.884 0.642 2.97 82.91 2.2E-05 1.4E-05 1.6E-03 1.830 8.650 WFTS-267 3.00 2.53 2.92 1.15 11 2.032 12.503 0.050 0.088 0.166 1.894 0.641 2.51 83.34 1.8E-05 1.1E-05 1.5E-03 1.480 10.216 WFTS-268 3.00 2.57 3.75 1.46 2 1.785 14.228 0.051 0.092 0.177 1.927 0.712 2.50 15.42 2.0E-05 1.4E-05 3.5E-04 0.310 11.390 WFTS-269 3.00 2.58 2.98 1.15 11 2.492 10.191 0.050 0.143 0.277 1.934 0.651 3.02 85.11 2.2E-05 1.5E-05 1.6E-03 1.890 8.614 WFTS-270 3.00 2.63 1.82 0.69 2 0.572 44.440 0.068 0.149 0.294 1.970 0.397 0.50 15.76 3.1E-06 1.2E-06 1.6E-04 0.049 31.497 WFTS-271 3.00 2.63 3.04 1.15 11 2.413 10.527 0.050 0.118 0.232 1.975 0.657 2.98 86.88 2.2E-05 1.5E-05 1.7E-03 1.910 8.808 WFTS-272 3.00 2.66 3.07 1.15 11 2.413 10.527 0.050 0.188 0.374 1.994 0.660 2.97 87.73 2.2E-05 1.5E-05 1.7E-03 1.950 8.878 WFTS-273 3.00 2.68 3.09 1.15 2 2.014 12.614 0.091 0.231 0.463 2.007 0.646 2.48 16.06 1.9E-05 1.2E-05 3.1E-04 0.300 10.435 WFTS-274 3.00 2.69 3.11 1.15 11 2.411 10.535 0.050 0.105 0.212 2.020 0.664 3.03 88.87 2.3E-05 1.5E-05 1.8E-03 2.000 8.783 WFTS-275 3.00 2.82 3.26 1.15 11 2.341 10.848 0.050 0.094 0.199 2.117 0.678 3.03 93.13 2.3E-05 1.6E-05 1.9E-03 2.130 8.962 WFTS-276 3.00 2.84 3.91 1.38 2 2.169 11.713 0.057 0.140 0.297 2.129 0.725 3.03 17.03 2.5E-05 1.8E-05 4.2E-04 0.433 9.572 WFTS-277 3.00 2.86 3.30 1.15 2 0.746 34.032 0.052 0.101 0.217 2.142 0.648 1.01 17.14 7.4E-06 4.8E-06 3.3E-04 0.127 25.723 WFTS-278 3.00 2.96 3.42 1.15 2 0.752 33.762 0.071 0.103 0.228 2.218 0.640 1.00 17.75 7.7E-06 4.9E-06 3.5E-04 0.137 25.586 WFTS-279 3.00 2.96 3.42 1.15 2 0.752 33.762 0.071 0.103 0.228 2.218 0.640 1.00 17.75 7.7E-06 4.9E-06 3.5E-04 0.137 25.586 WFTS-280 3.00 2.97 1.78 0.60 2 0.572 44.440 0.054 0.092 0.205 2.228 0.398 0.50 17.82 3.1E-06 1.2E-06 1.7E-04 0.055 31.719 WFTS-281 3.00 2.97 3.43 1.15 11 2.274 11.171 0.050 0.100 0.223 2.231 0.693 3.03 98.17 2.3E-05 1.6E-05 2.1E-03 2.300 9.163 WFTS-282 3.00 2.97 3.43 1.15 11 2.278 11.151 0.050 0.132 0.295 2.231 0.693 3.02 98.17 2.4E-05 1.6E-05 2.1E-03 2.300 9.179 WFTS-283 3.00 2.99 3.45 1.15 2 1.118 22.723 0.078 0.115 0.257 2.241 0.660 1.50 17.93 1.2E-05 7.6E-06 3.7E-04 0.207 17.581 WFTS-284 3.00 3.00 3.47 1.15 2 1.144 22.211 0.065 0.280 0.632 2.254 0.671 1.51 18.03 1.2E-05 8.0E-06 3.8E-04 0.215 17.741 WFTS-285 3.00 3.17 3.66 1.15 2 2.224 11.420 0.087 0.193 0.458 2.379 0.699 2.97 19.04 2.4E-05 1.7E-05 4.4E-04 0.465 9.404 WFTS-286 3.00 3.17 3.66 1.15 2 2.224 11.420 0.087 0.193 0.458 2.379 0.699 2.97 19.04 2.4E-05 1.7E-05 4.4E-04 0.465 9.404 WFTS-287 3.00 3.17 3.66 1.15 2 2.224 11.420 0.087 0.193 0.458 2.379 0.699 2.97 19.04 2.4E-05 1.7E-05 4.4E-04 0.465 9.404 WFTS-288 3.00 3.17 2.70 0.85 2 0.818 31.056 0.061 0.088 0.208 2.381 0.583 1.00 19.05 6.6E-06 3.9E-06 3.0E-04 0.126 23.430 WFTS-289 3.00 3.18 3.67 1.15 4 1.108 22.926 0.066 0.276 0.658 2.386 0.685 1.50 38.17 1.2E-05 8.4E-06 8.5E-04 0.466 18.311 WFTS-290 3.00 3.19 3.69 1.15 4 1.096 23.177 0.082 0.106 0.254 2.396 0.674 1.50 38.33 1.2E-05 8.2E-06 8.3E-04 0.465 17.951 WFTS-291 3.00 3.22 3.72 1.15 2 1.813 14.010 0.068 0.189 0.457 2.417 0.704 2.48 19.33 2.0E-05 1.4E-05 4.4E-04 0.391 11.332 WFTS-292 3.00 3.23 3.73 1.15 2 1.823 13.934 0.077 0.206 0.498 2.420 0.701 2.48 19.36 2.0E-05 1.4E-05 4.5E-04 0.394 11.304 WFTS-293 3.00 3.27 3.78 1.15 11 2.159 11.767 0.050 0.153 0.375 2.452 0.718 2.99 107.89 2.4E-05 1.8E-05 2.5E-03 2.640 9.605 WFTS-294 3.00 3.31 3.54 1.07 2 1.120 22.683 0.076 0.162 0.402 2.486 0.669 1.51 19.89 1.2E-05 8.0E-06 4.2E-04 0.237 17.715 WFTS-295 3.00 3.33 3.84 1.15 11 2.159 11.767 0.050 0.118 0.294 2.497 0.723 3.03 109.88 2.5E-05 1.8E-05 2.6E-03 2.740 9.556 WFTS-296 3.00 3.38 3.90 1.15 2 1.783 14.244 0.067 0.110 0.280 2.536 0.716 2.52 20.29 2.1E-05 1.5E-05 4.8E-04 0.424 11.376 WFTS-297 3.00 3.39 3.91 1.15 11 2.159 11.767 0.050 0.176 0.447 2.542 0.727 3.02 111.86 2.5E-05 1.8E-05 2.7E-03 2.840 9.621 WFTS-298 3.00 3.41 3.94 1.15 2 2.099 12.101 0.050 0.093 0.239 2.558 0.728 2.98 20.47 2.5E-05 1.8E-05 5.0E-04 0.508 9.771 WFTS-299 3.00 3.44 3.97 1.15 11 2.095 12.124 0.050 0.106 0.273 2.581 0.730 2.98 113.57 2.5E-05 1.8E-05 2.8E-03 2.840 9.795 WFTS-300 3.00 3.44 3.97 1.15 11 2.159 11.767 0.050 0.235 0.607 2.581 0.731 3.01 113.57 2.6E-05 1.9E-05 2.8E-03 2.920 9.719 WFTS-301 3.00 3.49 3.98 1.14 2 1.779 14.276 0.070 0.112 0.292 2.617 0.719 2.52 20.94 2.1E-05 1.5E-05 5.1E-04 0.445 11.396 WFTS-302 3.00 3.78 1.90 0.50 2 0.574 44.286 0.078 0.177 0.501 2.839 0.410 0.50 22.71 3.3E-06 1.3E-06 2.4E-04 0.074 32.806 WFTS-303 3.00 3.83 1.83 0.48 2 0.572 44.440 0.050 0.139 0.399 2.873 0.412 0.50 22.98 3.1E-06 1.3E-06 2.4E-04 0.072 32.725 WFTS-304 3.00 3.95 3.80 0.96 2 1.054 24.094 0.054 0.089 0.264 2.964 0.699 1.49 23.71 1.2E-05 8.4E-06 5.3E-04 0.285 18.712 WFTS-305 4.00 1.73 2.00 1.15 2 0.528 48.119 0.100 0.303 0.525 1.734 0.406 0.50 13.87 4.2E-06 1.7E-06 1.9E-04 0.059 32.469 WFTS-306 4.00 1.75 2.39 1.37 2 1.303 19.501 0.098 0.177 0.310 1.750 0.538 1.49 14.00 1.3E-05 6.7E-06 2.5E-04 0.175 14.404 WFTS-307 4.00 1.75 2.39 1.37 2 1.303 19.501 0.098 0.177 0.310 1.750 0.538 1.49 14.00 1.3E-05 6.7E-06 2.5E-04 0.175 14.404 WFTS-308 4.00 1.98 2.28 1.15 11 2.528 10.047 0.051 0.430 0.851 1.977 0.551 2.50 86.98 2.3E-05 1.3E-05 1.8E-03 2.010 8.818 WFTS-309 4.00 2.25 2.60 1.15 2 0.842 30.177 0.095 0.118 0.267 2.254 0.546 1.00 18.03 8.8E-06 4.8E-06 3.5E-04 0.158 21.913 WFTS-310 4.00 2.35 2.71 1.15 11 2.540 10.000 0.050 0.259 0.609 2.351 0.619 2.97 103.45 2.8E-05 1.7E-05 2.4E-03 2.850 8.339 226 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-311 4.00 2.35 2.72 1.15 3 1.271 19.989 0.100 0.285 0.670 2.353 0.582 1.50 28.24 1.4E-05 8.0E-06 6.0E-04 0.390 15.487 WFTS-312 4.00 2.36 2.72 1.15 2 1.271 19.989 0.100 0.285 0.671 2.358 0.583 1.51 18.86 1.4E-05 8.1E-06 4.0E-04 0.261 15.490 WFTS-313 4.00 2.43 2.80 1.15 4 1.271 19.989 0.100 0.380 0.923 2.426 0.593 1.49 38.82 1.4E-05 8.4E-06 8.8E-04 0.553 15.958 WFTS-314 4.00 2.56 2.95 1.15 2 0.780 32.559 0.067 0.095 0.243 2.558 0.605 1.01 20.46 9.2E-06 5.6E-06 4.5E-04 0.189 24.025 WFTS-315 4.00 2.59 2.99 1.15 2 0.762 33.322 0.054 0.088 0.229 2.592 0.619 1.01 20.74 9.1E-06 5.7E-06 4.7E-04 0.189 24.614 WFTS-316 4.00 2.61 1.87 0.72 2 0.538 47.230 0.059 0.093 0.244 2.608 0.413 0.50 20.86 4.0E-06 1.7E-06 2.7E-04 0.084 32.759 WFTS-317 4.00 2.76 3.19 1.15 2 0.764 33.236 0.067 0.119 0.329 2.762 0.626 1.01 22.09 9.8E-06 6.1E-06 5.4E-04 0.215 24.819 WFTS-318 4.00 2.94 3.39 1.15 2 2.224 11.420 0.064 0.088 0.257 2.938 0.685 3.02 23.51 3.0E-05 2.1E-05 6.4E-04 0.710 9.080 WFTS-319 4.00 2.97 3.43 1.15 2 1.813 14.010 0.050 0.088 0.260 2.973 0.689 2.51 23.78 2.5E-05 1.7E-05 6.5E-04 0.592 10.970 WFTS-320 4.00 3.06 2.97 0.97 2 0.792 32.069 0.075 0.091 0.279 3.057 0.601 1.00 24.45 9.4E-06 5.7E-06 5.5E-04 0.230 23.946 WFTS-321 4.00 3.14 4.00 1.27 11 2.057 12.346 0.050 0.088 0.274 3.137 0.732 3.00 138.03 3.3E-05 2.4E-05 4.4E-03 4.540 9.759 WFTS-322 4.00 3.18 3.67 1.15 11 1.779 14.276 0.051 0.106 0.336 3.177 0.707 2.52 139.78 2.6E-05 1.8E-05 4.1E-03 3.650 11.197 WFTS-323 4.00 3.18 3.67 1.15 2 2.121 11.976 0.068 0.088 0.278 3.177 0.704 2.97 25.42 3.1E-05 2.2E-05 7.5E-04 0.791 9.481 WFTS-324 4.00 3.18 4.00 1.26 2 2.065 12.298 0.050 0.088 0.278 3.177 0.732 3.01 25.42 3.3E-05 2.4E-05 8.2E-04 0.840 9.723 WFTS-325 4.00 3.19 2.46 0.77 2 0.862 29.481 0.065 0.111 0.354 3.186 0.549 1.00 25.48 8.5E-06 4.7E-06 4.7E-04 0.216 21.942 WFTS-326 4.00 3.21 3.70 1.15 11 1.781 14.260 0.050 0.181 0.580 3.207 0.709 2.51 141.11 2.6E-05 1.9E-05 4.2E-03 3.720 11.299 WFTS-327 4.00 3.21 3.71 1.15 2 2.113 12.021 0.069 0.088 0.281 3.213 0.707 2.97 25.71 3.1E-05 2.2E-05 7.7E-04 0.806 9.513 WFTS-328 4.00 3.21 3.71 1.15 2 2.113 12.021 0.069 0.088 0.281 3.213 0.707 2.97 25.71 3.1E-05 2.2E-05 7.7E-04 0.806 9.513 WFTS-329 4.00 3.21 3.71 1.15 2 2.113 12.021 0.069 0.088 0.281 3.213 0.707 2.97 25.71 3.1E-05 2.2E-05 7.7E-04 0.806 9.513 WFTS-330 4.00 3.21 3.71 1.15 2 2.113 12.021 0.069 0.088 0.281 3.213 0.707 2.97 25.71 3.1E-05 2.2E-05 7.7E-04 0.806 9.513 WFTS-331 4.00 3.23 3.73 1.15 2 1.779 14.276 0.071 0.088 0.285 3.229 0.702 2.51 25.83 2.7E-05 1.9E-05 7.7E-04 0.685 11.175 WFTS-332 4.00 3.24 3.74 1.15 3 0.750 33.852 0.094 0.120 0.388 3.239 0.641 1.00 38.87 1.1E-05 7.2E-06 1.1E-03 0.436 25.672 WFTS-333 4.00 3.24 3.74 1.15 3 0.750 33.852 0.094 0.120 0.388 3.239 0.641 1.00 38.87 1.1E-05 7.2E-06 1.1E-03 0.436 25.672 WFTS-334 4.00 3.25 3.75 1.15 11 1.761 14.420 0.050 0.088 0.284 3.248 0.713 2.52 142.90 2.6E-05 1.9E-05 4.3E-03 3.780 11.290 WFTS-335 4.00 3.25 3.75 1.15 11 1.761 14.420 0.050 0.088 0.284 3.248 0.713 2.52 142.90 2.6E-05 1.9E-05 4.3E-03 3.780 11.290 WFTS-336 4.00 3.25 3.75 1.15 2 1.070 23.736 0.083 0.094 0.306 3.250 0.677 1.49 26.00 1.6E-05 1.1E-05 7.6E-04 0.418 18.158 WFTS-337 4.00 3.25 1.77 0.54 2 0.585 43.384 0.063 0.088 0.287 3.253 0.388 0.50 26.02 4.1E-06 1.6E-06 3.3E-04 0.108 30.830 WFTS-338 4.00 3.30 3.81 1.15 2 2.097 12.112 0.052 0.088 0.289 3.297 0.719 3.00 26.38 3.2E-05 2.3E-05 8.1E-04 0.842 9.585 WFTS-339 4.00 3.30 3.81 1.15 2 0.510 49.805 0.095 0.804 2.653 3.300 0.600 0.50 26.40 7.8E-06 4.7E-06 9.8E-04 0.205 47.684 WFTS-340 4.00 3.31 4.00 1.21 2 2.065 12.298 0.050 0.088 0.289 3.307 0.732 3.01 26.45 3.3E-05 2.4E-05 8.5E-04 0.874 9.723 WFTS-341 4.00 3.36 3.87 1.15 11 2.097 12.112 0.050 0.107 0.358 3.355 0.724 3.02 147.64 3.3E-05 2.4E-05 4.6E-03 4.800 9.601 WFTS-342 4.00 3.37 3.89 1.15 3 1.070 23.736 0.057 0.241 0.812 3.366 0.704 1.51 40.39 1.7E-05 1.2E-05 1.3E-03 0.672 18.641 WFTS-343 4.00 3.37 3.89 1.15 11 2.099 12.101 0.050 0.099 0.332 3.370 0.725 3.03 148.30 3.3E-05 2.4E-05 4.6E-03 4.850 9.585 WFTS-344 4.00 3.37 3.89 1.15 13 0.508 50.000 0.095 0.814 2.746 3.373 0.605 0.50 175.38 7.9E-06 4.8E-06 6.7E-03 1.390 48.220 WFTS-345 4.00 3.42 3.95 1.15 11 2.097 12.112 0.050 0.130 0.446 3.424 0.729 3.03 150.66 3.3E-05 2.4E-05 4.8E-03 5.000 9.626 WFTS-346 4.00 3.42 3.95 1.15 11 2.097 12.112 0.050 0.133 0.456 3.424 0.729 3.03 150.66 3.3E-05 2.4E-05 4.8E-03 5.000 9.629 WFTS-347 4.00 3.42 3.95 1.15 11 2.105 12.067 0.050 0.168 0.577 3.424 0.729 3.03 150.66 3.3E-05 2.4E-05 4.8E-03 5.020 9.643 WFTS-348 4.00 3.43 3.96 1.15 11 2.097 12.112 0.050 0.148 0.507 3.433 0.730 3.03 151.04 3.3E-05 2.4E-05 4.9E-03 5.020 9.648 WFTS-349 4.00 3.43 3.96 1.15 11 2.109 12.044 0.050 0.177 0.608 3.433 0.730 3.03 151.04 3.3E-05 2.4E-05 4.9E-03 5.050 9.639 WFTS-350 4.00 3.44 3.97 1.15 11 2.127 11.943 0.050 0.251 0.862 3.437 0.730 3.01 151.23 3.4E-05 2.5E-05 5.0E-03 5.110 9.699 WFTS-351 4.00 3.44 3.97 1.15 11 2.121 11.976 0.050 0.224 0.772 3.441 0.731 3.02 151.42 3.4E-05 2.5E-05 4.9E-03 5.100 9.670 WFTS-352 4.00 3.45 3.98 1.15 11 2.113 12.021 0.050 0.202 0.695 3.450 0.731 3.03 151.80 3.4E-05 2.5E-05 4.9E-03 5.110 9.662 WFTS-353 4.00 3.68 2.51 0.68 11 0.554 45.874 0.065 0.760 2.796 3.680 0.531 0.50 161.92 5.6E-06 3.0E-06 3.8E-03 0.901 42.264 WFTS-354 4.00 3.70 2.47 0.67 2 0.877 28.948 0.070 0.088 0.324 3.702 0.548 1.01 29.61 8.7E-06 4.8E-06 5.6E-04 0.257 21.705 WFTS-355 4.00 3.74 4.00 1.07 2 2.065 12.298 0.050 0.088 0.327 3.737 0.732 3.01 29.89 3.3E-05 2.4E-05 9.6E-04 0.988 9.723 WFTS-356 4.00 3.90 3.38 0.87 3 1.084 23.432 0.050 0.091 0.355 3.898 0.672 1.49 46.77 1.5E-05 9.9E-06 1.2E-03 0.686 17.991 WFTS-357 4.00 3.93 3.06 0.78 2 0.774 32.809 0.059 0.097 0.381 3.927 0.622 1.00 31.42 9.5E-06 5.9E-06 7.4E-04 0.298 24.863 WFTS-358 4.00 3.94 1.77 0.45 2 0.597 42.519 0.064 0.088 0.345 3.941 0.388 0.50 31.53 4.2E-06 1.6E-06 4.1E-04 0.133 30.827 WFTS-359 4.00 3.95 3.87 0.98 2 1.787 14.212 0.087 0.119 0.471 3.952 0.705 2.52 31.61 2.8E-05 2.0E-05 9.8E-04 0.874 11.180 WFTS-360 4.00 3.99 2.52 0.63 12 0.550 46.206 0.052 0.782 3.117 3.987 0.546 0.50 191.36 5.5E-06 3.0E-06 4.6E-03 1.060 43.276 227 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-361 4.00 3.99 2.17 0.54 2 0.514 49.420 0.065 0.311 1.240 3.987 0.471 0.50 31.89 4.5E-06 2.1E-06 5.4E-04 0.142 37.848 WFTS-362 4.00 3.99 2.17 0.54 2 0.514 49.420 0.065 0.311 1.240 3.987 0.471 0.50 31.89 4.5E-06 2.1E-06 5.4E-04 0.142 37.848 WFTS-363 4.00 3.99 4.00 1.00 2 2.065 12.298 0.050 0.088 0.350 3.995 0.732 3.01 31.96 3.3E-05 2.4E-05 1.0E-03 1.060 9.722 WFTS-364 4.00 4.00 2.15 0.54 2 0.613 41.417 0.069 0.747 2.984 3.997 0.474 0.50 31.98 5.3E-06 2.5E-06 6.4E-04 0.168 37.787 WFTS-365 4.00 4.00 2.15 0.54 2 0.613 41.417 0.069 0.747 2.984 3.997 0.474 0.50 31.98 5.3E-06 2.5E-06 6.4E-04 0.168 37.787 WFTS-366 4.00 4.00 4.00 1.00 11 2.077 12.228 0.050 0.091 0.364 3.997 0.732 3.03 175.88 3.3E-05 2.4E-05 5.7E-03 5.850 9.673 WFTS-367 5.00 1.98 2.29 1.15 4 1.342 18.923 0.094 0.230 0.569 2.474 0.523 1.50 39.58 1.5E-05 8.0E-06 8.5E-04 0.607 13.927 WFTS-368 5.00 2.45 2.83 1.15 3 1.158 21.944 0.062 0.103 0.315 3.060 0.612 1.50 36.72 1.6E-05 1.0E-05 9.8E-04 0.601 16.258 WFTS-369 5.00 2.48 2.87 1.15 3 0.802 31.672 0.085 0.104 0.324 3.103 0.582 1.01 37.23 1.2E-05 6.7E-06 9.9E-04 0.428 23.097 WFTS-370 5.00 2.52 4.00 1.59 11 2.036 12.479 0.050 0.089 0.280 3.145 0.731 3.02 138.39 4.1E-05 3.0E-05 5.5E-03 5.630 9.703 WFTS-371 5.00 2.54 2.94 1.15 2 1.938 13.106 0.096 0.089 0.283 3.181 0.627 2.49 25.45 2.9E-05 1.8E-05 7.3E-04 0.725 10.071 WFTS-372 5.00 2.59 2.99 1.15 2 1.906 13.324 0.075 0.089 0.288 3.235 0.639 2.50 25.88 2.9E-05 1.8E-05 7.6E-04 0.737 10.243 WFTS-373 5.00 2.61 2.85 1.09 2 0.774 32.809 0.059 0.088 0.288 3.259 0.599 1.00 26.08 1.1E-05 6.6E-06 6.9E-04 0.287 23.971 WFTS-374 5.00 2.61 3.01 1.15 2 0.520 48.854 0.094 0.736 2.399 3.261 0.548 0.50 26.09 7.8E-06 4.3E-06 8.9E-04 0.204 43.637 WFTS-375 5.00 2.63 3.03 1.15 2 1.162 21.868 0.098 0.088 0.290 3.283 0.613 1.50 26.26 1.8E-05 1.1E-05 7.5E-04 0.462 16.303 WFTS-376 5.00 2.72 3.03 1.12 2 1.146 22.172 0.073 0.088 0.299 3.394 0.627 1.51 27.15 1.7E-05 1.1E-05 7.8E-04 0.471 16.567 WFTS-377 5.00 2.72 4.00 1.47 2 1.028 24.699 0.068 0.088 0.298 3.401 0.701 1.50 27.20 2.1E-05 1.4E-05 1.0E-03 0.560 18.653 WFTS-378 5.00 2.91 3.37 1.15 2 0.762 33.322 0.082 0.105 0.383 3.643 0.627 1.01 29.15 1.3E-05 8.0E-06 9.3E-04 0.374 24.842 WFTS-379 5.00 2.92 3.37 1.15 2 1.084 23.432 0.069 0.101 0.368 3.649 0.659 1.49 29.19 1.8E-05 1.2E-05 9.4E-04 0.533 17.661 WFTS-380 5.00 2.92 3.38 1.15 4 1.108 22.926 0.093 0.136 0.497 3.654 0.645 1.49 58.46 1.9E-05 1.2E-05 1.9E-03 1.090 17.352 WFTS-381 5.00 2.94 1.56 0.53 2 0.671 37.861 0.050 0.182 0.667 3.673 0.332 0.50 29.38 5.2E-06 1.7E-06 4.1E-04 0.154 26.374 WFTS-382 5.00 3.02 3.49 1.15 2 1.783 14.244 0.079 0.092 0.347 3.778 0.682 2.48 30.22 3.1E-05 2.1E-05 1.0E-03 0.940 10.994 WFTS-383 5.00 3.06 3.53 1.15 11 1.761 14.420 0.050 0.089 0.340 3.823 0.697 2.50 168.22 3.1E-05 2.2E-05 5.8E-03 5.230 11.136 WFTS-384 5.00 3.09 3.57 1.15 2 1.811 14.025 0.090 0.092 0.355 3.864 0.684 2.52 30.91 3.2E-05 2.2E-05 1.1E-03 0.999 10.842 WFTS-385 5.00 3.16 3.64 1.15 2 2.135 11.898 0.075 0.088 0.345 3.944 0.700 3.01 31.55 3.9E-05 2.7E-05 1.1E-03 1.230 9.289 WFTS-386 5.00 3.17 3.66 1.15 11 0.522 48.668 0.099 0.831 3.294 3.963 0.588 0.50 174.37 9.6E-06 5.6E-06 7.8E-03 1.670 46.897 WFTS-387 5.00 3.17 3.67 1.15 16 0.508 50.000 0.090 0.838 3.325 3.968 0.599 0.50 253.98 9.3E-06 5.6E-06 1.1E-02 2.360 48.340 WFTS-388 5.00 3.17 3.67 1.15 2 0.508 50.000 0.089 0.832 3.301 3.968 0.600 0.50 31.75 9.3E-06 5.6E-06 1.4E-03 0.296 48.202 WFTS-389 5.00 3.23 2.46 0.76 11 0.516 49.230 0.056 0.648 2.613 4.032 0.529 0.50 177.42 6.4E-06 3.4E-06 4.8E-03 1.130 42.324 WFTS-390 5.00 3.23 2.44 0.75 2 0.852 29.825 0.052 0.089 0.360 4.042 0.553 1.01 32.34 1.0E-05 5.7E-06 7.4E-04 0.335 21.974 WFTS-391 5.00 3.32 3.84 1.15 2 1.738 14.619 0.070 0.088 0.363 4.154 0.709 2.51 33.23 3.3E-05 2.4E-05 1.3E-03 1.110 11.315 WFTS-392 5.00 3.33 3.84 1.15 2 1.722 14.754 0.061 0.088 0.364 4.162 0.714 2.50 33.30 3.3E-05 2.4E-05 1.3E-03 1.100 11.420 WFTS-393 5.00 3.34 2.35 0.70 4 0.530 47.938 0.061 0.594 2.480 4.173 0.508 0.50 66.77 6.2E-06 3.2E-06 1.7E-03 0.415 40.216 WFTS-394 5.00 3.35 3.87 1.15 2 2.065 12.298 0.068 0.088 0.367 4.192 0.717 2.99 33.53 4.0E-05 2.9E-05 1.3E-03 1.340 9.601 WFTS-395 5.00 3.36 3.88 1.15 2 2.065 12.298 0.074 0.088 0.368 4.202 0.716 2.98 33.62 4.0E-05 2.9E-05 1.3E-03 1.350 9.600 WFTS-396 5.00 3.37 3.89 1.15 2 1.783 14.244 0.098 0.162 0.681 4.208 0.702 2.52 33.66 3.5E-05 2.4E-05 1.3E-03 1.170 11.134 WFTS-397 5.00 3.37 3.89 1.15 3 1.783 14.244 0.098 0.161 0.678 4.208 0.702 2.52 50.49 3.5E-05 2.4E-05 2.0E-03 1.750 11.132 WFTS-398 5.00 3.39 1.56 0.46 2 0.673 37.749 0.050 0.088 0.371 4.241 0.332 0.50 33.93 5.3E-06 1.7E-06 4.7E-04 0.178 26.506 WFTS-399 5.00 3.39 1.56 0.46 2 0.673 37.749 0.050 0.088 0.371 4.241 0.332 0.50 33.93 5.3E-06 1.7E-06 4.7E-04 0.178 26.506 WFTS-400 5.00 3.39 1.56 0.46 2 0.673 37.749 0.050 0.088 0.371 4.241 0.332 0.50 33.93 5.3E-06 1.7E-06 4.7E-04 0.178 26.506 WFTS-401 5.00 3.40 3.03 0.89 2 1.146 22.172 0.073 0.088 0.375 4.251 0.627 1.50 34.01 1.7E-05 1.1E-05 9.9E-04 0.590 16.760 WFTS-402 5.00 3.42 3.95 1.15 11 1.696 14.978 0.050 0.143 0.613 4.272 0.724 2.48 187.97 3.4E-05 2.4E-05 7.3E-03 6.290 11.673 WFTS-403 5.00 3.42 3.43 1.00 2 1.104 23.009 0.076 0.088 0.375 4.281 0.660 1.51 34.25 1.9E-05 1.3E-05 1.1E-03 0.648 17.469 WFTS-404 5.00 3.43 3.96 1.15 2 2.065 12.298 0.055 0.088 0.375 4.288 0.728 3.03 34.31 4.1E-05 3.0E-05 1.4E-03 1.400 9.609 WFTS-405 5.00 3.44 3.98 1.15 11 2.059 12.334 0.050 0.091 0.392 4.304 0.730 3.03 189.39 4.1E-05 3.0E-05 7.5E-03 7.750 9.641 WFTS-406 5.00 3.44 3.98 1.15 11 2.063 12.310 0.050 0.124 0.532 4.304 0.730 3.03 189.39 4.1E-05 3.0E-05 7.5E-03 7.770 9.655 WFTS-407 5.00 3.44 3.98 1.15 11 2.063 12.310 0.050 0.150 0.646 4.304 0.730 3.02 189.39 4.1E-05 3.0E-05 7.5E-03 7.770 9.687 WFTS-408 5.00 3.50 1.94 0.56 12 0.649 39.135 0.057 0.777 3.396 4.372 0.443 0.50 209.84 6.3E-06 2.8E-06 4.7E-03 1.320 35.354 WFTS-409 5.00 3.50 1.94 0.56 12 0.649 39.135 0.057 0.777 3.396 4.372 0.443 0.50 209.84 6.3E-06 2.8E-06 4.7E-03 1.320 35.354 WFTS-410 5.00 3.61 2.37 0.66 4 0.580 43.830 0.057 0.825 3.727 4.516 0.521 0.50 72.26 6.9E-06 3.6E-06 2.1E-03 0.497 41.309 228 TAG Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nr (-) Fp (mm) FPI (in-1) δf (mm) Tanθ (-) Pd (mm) Xf(mm) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) V (cm³) Ao/V(cm²/cm³) WFTS-411 5.00 3.65 3.96 1.08 11 1.716 14.804 0.050 0.108 0.493 4.563 0.725 2.52 200.78 3.4E-05 2.5E-05 7.8E-03 6.820 11.510 WFTS-412 5.00 3.76 3.81 1.01 2 1.044 24.323 0.068 0.088 0.412 4.704 0.690 1.49 37.63 2.0E-05 1.4E-05 1.4E-03 0.749 18.583 WFTS-413 5.00 3.84 2.44 0.63 2 0.856 29.686 0.051 0.088 0.420 4.795 0.555 1.00 38.36 1.0E-05 5.8E-06 8.8E-04 0.400 22.125 WFTS-414 5.00 3.85 3.97 1.03 2 2.097 12.112 0.093 0.088 0.421 4.815 0.715 3.02 38.52 4.2E-05 3.0E-05 1.5E-03 1.600 9.474 WFTS-415 5.00 3.90 2.09 0.54 3 0.546 46.542 0.094 0.213 1.038 4.869 0.431 0.50 58.43 5.7E-06 2.5E-06 1.2E-03 0.333 34.495 WFTS-416 5.00 3.90 2.60 0.67 11 0.530 47.938 0.081 0.630 3.068 4.872 0.521 0.50 214.38 6.9E-06 3.6E-06 6.2E-03 1.480 41.672 WFTS-417 5.00 3.93 4.00 1.02 2 2.049 12.394 0.050 0.088 0.430 4.909 0.732 3.02 39.27 4.1E-05 3.0E-05 1.6E-03 1.610 9.696 WFTS-418 5.00 3.94 2.04 0.52 2 0.985 25.794 0.054 0.089 0.438 4.926 0.482 1.01 39.41 1.0E-05 4.8E-06 7.6E-04 0.396 19.136 WFTS-419 5.00 3.99 3.96 0.99 2 1.716 14.804 0.050 0.088 0.436 4.987 0.725 2.52 39.89 3.4E-05 2.5E-05 1.6E-03 1.350 11.506 WFTS-420 5.00 3.99 1.98 0.49 12 0.647 39.256 0.050 0.819 4.085 4.990 0.455 0.50 239.51 6.4E-06 2.9E-06 5.6E-03 1.530 36.705 Table 51. WFTS optimum designs performance. TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-001 2.000 63.743 0.005 10.624 77.852 0.113 296.680 5.805 0.037 0.993 0.994 1.828 WFTS-002 3.000 286.340 0.034 12.484 100.680 0.074 205.430 12.037 0.021 0.991 0.996 1.395 WFTS-003 3.000 285.751 0.034 13.866 111.740 0.082 220.910 12.917 0.023 0.992 0.996 1.499 WFTS-004 3.000 285.199 0.034 15.611 125.520 0.091 238.620 13.927 0.024 0.992 0.997 1.616 WFTS-005 3.000 284.990 0.034 17.336 156.630 0.100 255.150 14.880 0.026 0.992 0.997 1.942 WFTS-006 3.000 284.419 0.034 19.213 173.220 0.110 270.450 15.741 0.028 0.993 0.997 2.055 WFTS-007 3.000 283.659 0.034 21.763 195.600 0.122 287.940 16.715 0.029 0.994 0.997 2.181 WFTS-008 5.000 157.348 0.012 117.030 381.080 0.104 463.150 8.948 0.025 0.988 0.990 1.262 WFTS-009 3.000 189.322 0.016 15.809 58.100 0.160 245.060 9.494 0.030 0.981 0.985 0.750 WFTS-010 3.000 189.870 0.017 21.934 119.040 0.213 261.480 10.160 0.032 0.985 0.988 1.186 WFTS-011 3.000 94.293 0.008 48.619 214.250 0.094 366.050 7.018 0.026 0.991 0.994 1.355 WFTS-012 3.000 95.291 0.008 44.778 197.640 0.089 360.350 6.978 0.026 0.990 0.993 1.335 WFTS-013 3.000 95.291 0.008 44.778 197.640 0.089 360.350 6.978 0.026 0.990 0.993 1.335 WFTS-014 1.000 94.147 0.009 0.594 4.500 0.153 131.970 7.628 0.048 0.993 0.995 0.842 WFTS-015 2.000 63.974 0.005 7.457 68.441 0.123 270.110 5.304 0.039 0.989 0.990 2.075 WFTS-016 1.000 94.452 0.011 0.301 3.002 0.157 113.610 6.588 0.052 0.971 0.975 0.933 WFTS-017 5.000 156.946 0.012 96.447 354.670 0.092 435.950 8.401 0.024 0.984 0.986 1.337 WFTS-018 2.000 126.207 0.012 4.353 28.518 0.179 195.890 7.589 0.038 0.982 0.985 1.068 WFTS-019 2.000 63.670 0.005 6.786 65.711 0.115 260.960 5.100 0.038 0.987 0.989 2.113 WFTS-020 1.000 31.993 0.003 1.913 29.331 0.126 194.230 3.815 0.045 0.994 0.996 2.506 WFTS-021 5.000 315.204 0.028 113.530 370.130 0.163 356.090 13.781 0.023 0.986 0.990 0.971 WFTS-022 3.000 188.523 0.016 14.194 59.616 0.144 240.260 9.269 0.030 0.976 0.981 0.837 WFTS-023 1.000 63.145 0.005 0.528 6.816 0.150 137.990 5.349 0.052 0.989 0.991 1.490 WFTS-024 1.000 94.838 0.010 0.253 2.776 0.149 107.340 6.249 0.051 0.965 0.969 0.964 WFTS-025 2.000 127.093 0.011 6.996 33.954 0.106 215.510 8.408 0.030 0.992 0.994 0.879 WFTS-026 2.000 126.064 0.011 2.702 18.566 0.113 180.900 7.000 0.036 0.979 0.982 1.032 WFTS-027 2.000 62.908 0.005 10.050 85.756 0.100 277.730 5.321 0.034 0.990 0.992 1.988 WFTS-028 2.000 127.955 0.011 6.500 31.758 0.102 210.140 8.254 0.030 0.990 0.993 0.862 229 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-029 2.000 63.506 0.005 9.441 82.737 0.100 273.750 5.291 0.034 0.989 0.991 2.011 WFTS-030 2.000 63.506 0.005 9.441 82.737 0.100 273.750 5.291 0.034 0.989 0.991 2.011 WFTS-031 2.000 63.506 0.005 9.441 82.737 0.100 273.750 5.291 0.034 0.989 0.991 2.011 WFTS-032 2.000 63.506 0.005 9.441 82.737 0.100 273.750 5.291 0.034 0.989 0.991 2.011 WFTS-033 3.000 188.246 0.018 28.216 88.655 0.107 265.090 10.160 0.023 0.992 0.995 0.701 WFTS-034 3.000 94.715 0.007 24.386 148.050 0.084 329.080 6.292 0.028 0.983 0.986 1.666 WFTS-035 3.000 94.715 0.007 24.386 148.050 0.084 329.080 6.292 0.028 0.983 0.986 1.666 WFTS-036 2.000 127.157 0.012 9.586 47.827 0.139 225.410 8.750 0.031 0.992 0.995 0.946 WFTS-037 1.000 63.566 0.005 0.811 8.314 0.101 149.170 5.784 0.042 0.990 0.994 1.284 WFTS-038 1.000 63.282 0.006 0.897 9.195 0.111 156.490 6.042 0.044 0.991 0.994 1.349 WFTS-039 1.000 94.344 0.008 0.501 4.373 0.125 124.970 7.238 0.045 0.990 0.993 0.916 WFTS-040 1.000 63.914 0.005 0.801 8.239 0.101 148.890 5.804 0.042 0.990 0.993 1.286 WFTS-041 5.000 156.933 0.012 78.011 331.500 0.080 403.680 7.778 0.023 0.978 0.981 1.422 WFTS-042 3.000 95.120 0.007 20.257 132.880 0.078 315.320 6.050 0.028 0.983 0.986 1.724 WFTS-043 3.000 95.120 0.007 20.257 132.880 0.078 315.320 6.050 0.028 0.983 0.986 1.724 WFTS-044 5.000 480.117 0.053 51.686 370.270 0.058 282.130 16.478 0.017 0.982 0.991 1.693 WFTS-045 5.000 479.420 0.053 54.956 393.780 0.061 293.390 17.113 0.017 0.983 0.991 1.761 WFTS-046 5.000 477.772 0.053 61.851 442.840 0.068 316.050 18.384 0.018 0.984 0.992 1.897 WFTS-047 5.000 480.022 0.054 68.799 487.990 0.075 338.090 19.776 0.020 0.986 0.992 2.012 WFTS-048 5.000 476.283 0.054 79.010 564.230 0.085 360.700 20.928 0.021 0.985 0.992 2.160 WFTS-049 5.000 473.716 0.054 90.011 643.820 0.096 382.960 22.105 0.022 0.986 0.992 2.298 WFTS-050 5.000 316.155 0.026 45.412 179.250 0.088 271.500 10.539 0.019 0.977 0.982 0.889 WFTS-051 5.000 316.155 0.026 45.412 179.250 0.088 271.500 10.539 0.019 0.977 0.982 0.889 WFTS-052 2.000 63.850 0.005 5.535 61.098 0.101 239.590 4.696 0.036 0.982 0.984 2.200 WFTS-053 5.000 478.945 0.055 104.310 754.270 0.115 405.220 23.638 0.024 0.985 0.992 2.457 WFTS-054 2.000 189.676 0.021 5.914 108.170 0.102 202.840 11.760 0.030 0.992 0.996 3.123 WFTS-055 2.000 191.299 0.022 7.484 135.880 0.130 221.960 12.975 0.033 0.992 0.996 3.391 WFTS-056 2.000 188.345 0.020 5.793 107.790 0.102 198.620 11.431 0.029 0.992 0.995 3.110 WFTS-057 2.000 190.272 0.020 5.293 97.711 0.093 190.680 11.089 0.028 0.992 0.996 2.963 WFTS-058 2.000 191.755 0.021 6.711 123.200 0.119 212.580 12.453 0.031 0.991 0.995 3.283 WFTS-059 1.000 63.219 0.005 0.493 6.913 0.140 132.410 5.139 0.049 0.987 0.989 1.553 WFTS-060 3.000 189.666 0.018 6.181 33.839 0.103 190.520 7.395 0.028 0.960 0.965 0.851 WFTS-061 3.000 285.827 0.030 12.475 157.630 0.070 203.790 11.826 0.020 0.986 0.992 2.160 WFTS-062 3.000 285.332 0.030 13.727 172.890 0.076 217.750 12.625 0.022 0.987 0.993 2.302 WFTS-063 1.000 31.754 0.002 0.998 21.145 0.121 156.430 3.018 0.044 0.988 0.990 2.772 WFTS-064 1.000 31.721 0.002 1.008 21.374 0.122 156.960 3.025 0.044 0.988 0.990 2.784 WFTS-065 1.000 31.963 0.002 1.176 24.398 0.137 163.820 3.185 0.045 0.989 0.991 2.848 WFTS-066 1.000 31.922 0.002 1.356 27.245 0.143 169.300 3.294 0.045 0.991 0.993 2.855 WFTS-067 1.000 31.502 0.002 1.471 29.392 0.146 172.090 3.306 0.045 0.992 0.993 2.888 WFTS-068 1.000 31.736 0.002 1.300 23.342 0.096 166.480 3.244 0.040 0.991 0.993 2.508 WFTS-069 1.000 31.814 0.003 1.521 26.866 0.107 173.170 3.382 0.041 0.992 0.994 2.570 WFTS-070 3.000 287.101 0.030 11.705 148.350 0.066 195.240 11.376 0.020 0.985 0.992 2.075 WFTS-071 3.000 285.617 0.030 14.810 186.640 0.081 227.600 13.215 0.023 0.988 0.993 2.409 WFTS-072 1.000 31.866 0.002 0.934 19.688 0.111 149.170 2.892 0.041 0.989 0.991 2.635 WFTS-073 1.000 31.538 0.002 0.836 18.323 0.105 135.490 2.599 0.038 0.989 0.991 2.488 WFTS-074 1.000 31.742 0.002 0.849 18.759 0.110 142.490 2.748 0.041 0.988 0.990 2.635 WFTS-075 1.000 32.005 0.002 0.795 17.928 0.107 134.000 2.606 0.039 0.988 0.990 2.528 WFTS-076 1.000 31.813 0.002 0.879 20.037 0.120 146.710 2.832 0.042 0.987 0.988 2.794 WFTS-077 5.000 158.467 0.013 76.585 332.080 0.070 402.940 7.692 0.022 0.978 0.981 1.449 WFTS-078 3.000 95.539 0.007 15.227 120.770 0.079 291.790 5.585 0.028 0.976 0.979 1.915 230 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-079 3.000 95.539 0.007 15.227 120.770 0.079 291.790 5.585 0.028 0.976 0.979 1.915 WFTS-080 3.000 95.841 0.007 12.140 98.434 0.066 272.490 5.228 0.027 0.975 0.978 1.827 WFTS-081 2.000 63.348 0.005 4.870 61.555 0.092 221.470 4.306 0.034 0.977 0.980 2.318 WFTS-082 5.000 318.335 0.028 85.174 345.150 0.128 325.270 12.713 0.021 0.976 0.981 1.093 WFTS-083 2.000 191.045 0.018 3.384 15.832 0.088 162.140 9.398 0.027 0.983 0.988 0.634 WFTS-084 5.000 315.004 0.027 57.676 155.640 0.082 297.360 11.316 0.019 0.980 0.984 0.667 WFTS-085 3.000 188.746 0.015 7.468 38.818 0.076 206.880 7.991 0.025 0.967 0.972 0.884 WFTS-086 2.000 190.120 0.018 3.945 18.450 0.098 170.780 9.888 0.028 0.989 0.992 0.670 WFTS-087 2.000 188.383 0.018 4.278 20.205 0.106 174.780 10.026 0.029 0.989 0.992 0.692 WFTS-088 2.000 63.865 0.005 4.947 63.266 0.094 224.320 4.317 0.033 0.980 0.982 2.381 WFTS-089 2.000 62.852 0.005 5.402 69.575 0.100 227.850 4.319 0.034 0.980 0.982 2.437 WFTS-090 2.000 62.852 0.005 5.402 69.575 0.100 227.850 4.319 0.034 0.980 0.982 2.437 WFTS-091 2.000 62.852 0.005 5.402 69.575 0.100 227.850 4.319 0.034 0.980 0.982 2.437 WFTS-092 2.000 62.852 0.005 5.402 69.575 0.100 227.850 4.319 0.034 0.980 0.982 2.437 WFTS-093 5.000 158.822 0.013 58.082 294.700 0.067 375.390 7.125 0.022 0.970 0.973 1.567 WFTS-094 5.000 157.168 0.013 69.205 341.690 0.072 394.370 7.436 0.022 0.975 0.977 1.609 WFTS-095 2.000 188.966 0.018 1.672 10.644 0.101 135.470 7.858 0.030 0.963 0.968 0.706 WFTS-096 2.000 126.509 0.011 6.486 68.500 0.158 202.590 7.755 0.033 0.982 0.986 1.783 WFTS-097 2.000 126.509 0.011 6.486 68.500 0.158 202.590 7.755 0.033 0.982 0.986 1.783 WFTS-098 2.000 127.803 0.011 5.788 62.494 0.151 197.250 7.598 0.033 0.977 0.982 1.768 WFTS-099 2.000 190.259 0.017 2.553 14.138 0.100 154.010 8.994 0.030 0.980 0.984 0.710 WFTS-100 2.000 191.819 0.017 2.175 12.212 0.091 144.710 8.521 0.029 0.974 0.979 0.673 WFTS-101 2.000 127.131 0.012 1.742 16.556 0.098 151.500 5.912 0.033 0.959 0.963 1.172 WFTS-102 3.000 284.686 0.033 6.299 29.415 0.133 171.850 10.012 0.027 0.951 0.956 0.648 WFTS-103 2.000 126.186 0.011 2.184 19.828 0.098 165.720 6.419 0.034 0.966 0.970 1.234 WFTS-104 5.000 471.973 0.045 25.692 65.932 0.087 197.750 11.460 0.017 0.964 0.970 0.416 WFTS-105 5.000 471.180 0.046 26.442 68.787 0.091 200.060 11.574 0.017 0.962 0.968 0.426 WFTS-106 1.000 63.322 0.005 0.422 7.237 0.122 120.240 4.674 0.045 0.982 0.985 1.715 WFTS-107 2.000 63.893 0.005 3.452 46.957 0.063 186.630 3.660 0.028 0.977 0.979 2.101 WFTS-108 2.000 63.067 0.005 3.983 54.892 0.073 201.510 3.901 0.030 0.975 0.977 2.295 WFTS-109 5.000 475.015 0.042 36.385 372.220 0.082 217.730 12.698 0.016 0.965 0.973 1.833 WFTS-110 5.000 475.015 0.042 36.385 372.220 0.082 217.730 12.698 0.016 0.965 0.973 1.833 WFTS-111 5.000 159.142 0.013 48.511 275.460 0.064 353.960 6.698 0.021 0.966 0.968 1.646 WFTS-112 5.000 159.903 0.013 47.496 269.950 0.063 351.580 6.682 0.021 0.965 0.968 1.635 WFTS-113 5.000 159.903 0.013 47.496 269.950 0.063 351.580 6.682 0.021 0.965 0.968 1.635 WFTS-114 3.000 189.008 0.015 6.940 38.892 0.065 203.520 7.630 0.024 0.964 0.969 0.935 WFTS-115 3.000 188.255 0.016 12.418 67.144 0.103 235.430 8.890 0.027 0.977 0.980 1.055 WFTS-116 3.000 472.968 0.049 7.807 114.720 0.118 188.310 18.226 0.026 0.950 0.964 2.256 WFTS-117 3.000 471.960 0.053 11.221 172.200 0.192 192.360 18.578 0.028 0.943 0.957 2.388 WFTS-118 3.000 188.786 0.016 8.853 52.315 0.087 222.500 8.311 0.026 0.961 0.967 1.075 WFTS-119 1.000 94.680 0.010 0.226 3.552 0.139 101.220 5.884 0.049 0.948 0.953 1.280 WFTS-120 1.000 63.965 0.005 0.426 7.771 0.121 125.780 4.825 0.046 0.973 0.977 1.893 WFTS-121 1.000 63.965 0.005 0.426 7.771 0.121 125.780 4.825 0.046 0.973 0.977 1.893 WFTS-122 1.000 63.349 0.005 0.431 7.906 0.121 126.070 4.792 0.046 0.974 0.977 1.912 WFTS-123 1.000 94.401 0.008 0.435 5.149 0.108 117.680 6.820 0.042 0.983 0.987 1.163 WFTS-124 5.000 475.363 0.042 37.141 467.170 0.088 226.650 12.859 0.017 0.965 0.972 2.343 WFTS-125 5.000 478.659 0.044 45.144 560.920 0.105 242.440 13.871 0.018 0.967 0.974 2.479 WFTS-126 5.000 319.476 0.028 70.312 341.110 0.107 304.140 11.930 0.020 0.964 0.970 1.210 WFTS-127 1.000 157.149 0.016 0.251 2.260 0.111 87.058 8.399 0.038 0.982 0.986 0.652 WFTS-128 2.000 63.718 0.005 2.897 46.112 0.055 168.800 3.302 0.026 0.968 0.971 2.205 231 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-129 1.000 63.978 0.005 0.353 7.100 0.110 109.380 4.296 0.042 0.969 0.972 1.808 WFTS-130 1.000 96.023 0.010 0.201 3.387 0.124 95.085 5.605 0.046 0.945 0.950 1.285 WFTS-131 3.000 283.830 0.026 10.862 74.606 0.124 189.090 10.983 0.024 0.967 0.973 1.068 WFTS-132 1.000 157.358 0.016 0.240 2.261 0.110 85.226 8.233 0.037 0.977 0.982 0.666 WFTS-133 1.000 158.556 0.016 0.276 2.409 0.103 89.463 8.708 0.037 0.981 0.986 0.650 WFTS-134 1.000 158.011 0.016 0.286 2.493 0.105 91.190 8.846 0.037 0.983 0.987 0.664 WFTS-135 1.000 159.424 0.016 0.233 2.194 0.110 83.982 8.219 0.037 0.975 0.981 0.656 WFTS-136 1.000 157.314 0.016 0.296 2.578 0.106 92.606 8.943 0.038 0.985 0.989 0.675 WFTS-137 3.000 190.602 0.018 4.681 37.087 0.082 172.760 6.738 0.026 0.925 0.931 1.077 WFTS-138 2.000 315.819 0.036 1.199 6.342 0.094 109.700 10.635 0.027 0.956 0.962 0.472 WFTS-139 2.000 317.226 0.038 1.541 8.149 0.123 116.400 11.334 0.029 0.951 0.958 0.498 WFTS-140 2.000 314.260 0.041 2.406 13.017 0.189 124.520 12.012 0.030 0.955 0.961 0.547 WFTS-141 2.000 189.524 0.017 1.853 14.015 0.087 145.750 8.142 0.029 0.953 0.960 0.895 WFTS-142 2.000 190.019 0.017 1.834 13.890 0.087 145.240 8.125 0.029 0.952 0.959 0.892 WFTS-143 3.000 471.694 0.047 5.737 102.180 0.095 159.530 15.399 0.023 0.938 0.952 2.286 WFTS-144 2.000 189.993 0.018 1.386 11.385 0.082 126.000 7.348 0.028 0.947 0.953 0.834 WFTS-145 3.000 479.033 0.047 4.594 81.336 0.078 144.980 14.212 0.021 0.942 0.954 2.071 WFTS-146 3.000 478.387 0.047 4.817 84.736 0.080 150.020 14.686 0.022 0.941 0.954 2.129 WFTS-147 3.000 472.720 0.047 7.434 130.880 0.114 183.790 16.904 0.025 0.936 0.951 2.601 WFTS-148 2.000 313.753 0.033 2.566 12.243 0.128 126.040 11.867 0.026 0.971 0.978 0.497 WFTS-149 2.000 313.753 0.033 2.706 19.367 0.135 126.590 11.918 0.026 0.971 0.978 0.749 WFTS-150 3.000 479.737 0.047 6.315 110.780 0.098 176.590 16.493 0.024 0.937 0.951 2.491 WFTS-151 5.000 799.403 0.078 21.367 227.020 0.072 250.000 22.887 0.020 0.913 0.933 2.095 WFTS-152 5.000 791.322 0.078 24.861 266.850 0.084 263.770 23.819 0.021 0.909 0.929 2.225 WFTS-153 5.000 799.878 0.077 19.677 209.770 0.067 237.810 21.834 0.019 0.916 0.935 2.004 WFTS-154 1.000 63.825 0.005 0.325 7.300 0.101 102.180 4.004 0.039 0.964 0.968 1.880 WFTS-155 2.000 127.752 0.012 1.342 17.305 0.077 132.130 5.181 0.029 0.938 0.942 1.357 WFTS-156 2.000 377.717 0.042 1.251 6.242 0.105 107.130 12.421 0.027 0.921 0.934 0.422 WFTS-157 1.000 157.377 0.017 0.394 4.119 0.171 95.137 9.020 0.040 0.977 0.981 0.826 WFTS-158 2.000 63.601 0.005 2.449 45.365 0.048 150.740 2.943 0.023 0.961 0.964 2.276 WFTS-159 1.000 157.453 0.016 0.254 2.672 0.111 89.259 8.463 0.038 0.976 0.981 0.778 WFTS-160 5.000 790.751 0.076 17.206 201.810 0.063 218.350 19.631 0.018 0.908 0.926 2.005 WFTS-161 3.000 189.691 0.017 4.924 41.610 0.072 183.550 6.673 0.024 0.931 0.937 1.228 WFTS-162 2.000 314.615 0.036 3.857 41.307 0.219 129.750 12.530 0.028 0.966 0.972 1.142 WFTS-163 1.000 158.315 0.015 0.220 2.392 0.103 83.857 7.896 0.036 0.962 0.969 0.746 WFTS-164 1.000 63.164 0.006 0.304 8.052 0.128 102.170 3.777 0.042 0.950 0.953 2.180 WFTS-165 1.000 191.020 0.023 0.188 1.907 0.123 77.786 9.122 0.039 0.951 0.958 0.640 WFTS-166 5.000 159.874 0.014 33.527 249.840 0.041 283.690 5.569 0.017 0.952 0.955 1.707 WFTS-167 3.000 471.922 0.046 5.239 106.680 0.093 154.120 14.003 0.021 0.928 0.941 2.496 WFTS-168 3.000 471.922 0.046 5.239 106.680 0.093 154.120 14.003 0.021 0.928 0.941 2.496 WFTS-169 1.000 64.016 0.006 0.261 6.810 0.109 95.434 3.594 0.039 0.955 0.958 2.020 WFTS-170 1.000 62.787 0.006 0.322 8.630 0.136 103.400 3.795 0.042 0.948 0.952 2.230 WFTS-171 1.000 188.986 0.021 0.151 1.560 0.100 73.691 8.550 0.037 0.946 0.954 0.615 WFTS-172 3.000 570.151 0.061 5.173 92.686 0.108 152.080 17.744 0.024 0.909 0.926 2.132 WFTS-173 3.000 477.778 0.046 4.109 85.447 0.075 140.880 12.950 0.020 0.928 0.940 2.329 WFTS-174 5.000 313.990 0.029 16.117 88.725 0.055 216.220 7.620 0.017 0.908 0.914 0.920 WFTS-175 3.000 286.777 0.028 5.847 36.256 0.098 168.540 9.331 0.023 0.937 0.943 0.834 WFTS-176 5.000 315.198 0.030 22.507 126.610 0.080 237.230 8.223 0.018 0.888 0.896 1.011 WFTS-177 3.000 574.638 0.060 3.847 71.329 0.080 138.370 16.271 0.022 0.911 0.927 2.010 WFTS-178 1.000 95.859 0.010 0.197 4.121 0.121 89.610 5.273 0.043 0.928 0.933 1.481 232 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-179 1.000 31.991 0.003 0.687 23.094 0.063 100.750 1.979 0.026 0.977 0.979 2.805 WFTS-180 5.000 159.972 0.012 24.159 194.040 0.029 245.990 4.832 0.015 0.930 0.935 1.561 WFTS-181 1.000 188.852 0.020 0.196 2.081 0.104 78.659 8.876 0.035 0.968 0.973 0.686 WFTS-182 3.000 282.461 0.027 4.167 28.330 0.072 144.670 8.362 0.021 0.936 0.941 0.783 WFTS-183 2.000 188.776 0.017 1.162 12.386 0.070 116.730 6.764 0.026 0.924 0.931 0.979 WFTS-184 3.000 475.972 0.045 3.965 91.555 0.068 132.830 12.938 0.019 0.917 0.930 2.412 WFTS-185 3.000 475.877 0.051 2.979 14.089 0.072 121.360 11.818 0.020 0.892 0.903 0.438 WFTS-186 2.000 316.516 0.032 1.140 7.863 0.082 111.190 10.071 0.025 0.923 0.932 0.604 WFTS-187 3.000 190.121 0.019 3.470 38.718 0.065 163.190 5.704 0.022 0.893 0.898 1.383 WFTS-188 2.000 126.661 0.012 1.159 18.749 0.065 119.450 4.644 0.026 0.923 0.927 1.515 WFTS-189 1.000 31.844 0.003 0.611 23.193 0.056 89.697 1.754 0.023 0.974 0.976 2.810 WFTS-190 2.000 319.989 0.033 1.019 7.245 0.077 107.930 9.765 0.024 0.911 0.921 0.597 WFTS-191 5.000 942.392 0.105 23.537 315.500 0.116 253.010 24.868 0.021 0.825 0.849 2.435 WFTS-192 2.000 377.489 0.040 1.148 7.107 0.088 105.040 11.308 0.024 0.918 0.929 0.511 WFTS-193 1.000 157.497 0.016 0.163 2.415 0.099 78.316 7.145 0.036 0.937 0.944 0.927 WFTS-194 1.000 157.497 0.016 0.163 2.415 0.099 78.316 7.145 0.036 0.937 0.944 0.927 WFTS-195 1.000 157.497 0.016 0.163 2.415 0.099 78.316 7.145 0.036 0.937 0.944 0.927 WFTS-196 2.000 316.681 0.042 3.716 41.050 0.280 134.800 12.225 0.030 0.925 0.933 1.175 WFTS-197 5.000 792.748 0.084 13.752 225.150 0.068 208.960 17.427 0.017 0.839 0.857 2.478 WFTS-198 2.000 316.757 0.042 3.722 41.251 0.281 134.930 12.232 0.030 0.924 0.932 1.179 WFTS-199 3.000 282.594 0.027 3.921 29.779 0.067 139.280 8.054 0.020 0.926 0.932 0.833 WFTS-200 2.000 379.467 0.043 1.401 8.702 0.106 109.660 12.085 0.025 0.938 0.946 0.545 WFTS-201 2.000 376.817 0.044 1.691 10.580 0.128 114.310 12.522 0.026 0.939 0.947 0.572 WFTS-202 3.000 574.163 0.062 3.268 75.578 0.077 138.820 14.603 0.020 0.880 0.895 2.430 WFTS-203 3.000 575.494 0.060 5.085 112.190 0.103 145.480 17.133 0.023 0.880 0.898 2.438 WFTS-204 1.000 188.352 0.022 0.230 2.942 0.141 82.938 9.174 0.038 0.951 0.957 0.858 WFTS-205 3.000 479.946 0.050 2.662 74.316 0.063 116.030 10.295 0.017 0.892 0.903 2.474 WFTS-206 1.000 157.415 0.015 0.220 3.049 0.100 81.119 7.839 0.036 0.951 0.958 0.911 WFTS-207 1.000 158.309 0.015 0.210 2.897 0.095 79.747 7.750 0.035 0.955 0.962 0.893 WFTS-208 1.000 95.726 0.010 0.182 4.605 0.112 81.041 4.763 0.039 0.913 0.918 1.591 WFTS-209 5.000 952.153 0.103 12.028 172.230 0.063 215.900 21.312 0.018 0.823 0.844 2.207 WFTS-210 5.000 797.311 0.085 10.545 181.400 0.055 195.450 16.246 0.016 0.832 0.849 2.413 WFTS-211 1.000 31.797 0.003 0.521 24.403 0.050 74.139 1.447 0.019 0.968 0.970 2.847 WFTS-212 3.000 479.223 0.052 3.072 88.162 0.074 125.020 10.922 0.018 0.879 0.891 2.702 WFTS-213 5.000 799.625 0.085 9.579 164.710 0.050 186.730 15.644 0.016 0.837 0.853 2.316 WFTS-214 3.000 477.493 0.053 3.746 19.611 0.089 135.590 11.851 0.020 0.883 0.894 0.537 WFTS-215 1.000 190.786 0.021 0.163 2.124 0.103 76.272 8.511 0.036 0.946 0.953 0.803 WFTS-216 1.000 190.786 0.021 0.163 2.124 0.103 76.272 8.511 0.036 0.946 0.953 0.803 WFTS-217 1.000 190.786 0.021 0.163 2.124 0.103 76.272 8.511 0.036 0.946 0.953 0.803 WFTS-218 2.000 314.222 0.036 1.377 10.867 0.107 116.760 10.471 0.026 0.922 0.930 0.724 WFTS-219 1.000 95.973 0.010 0.167 4.256 0.099 76.293 4.495 0.037 0.930 0.934 1.536 WFTS-220 5.000 957.414 0.105 10.638 155.440 0.056 197.420 19.848 0.017 0.836 0.855 2.086 WFTS-221 5.000 957.414 0.105 10.638 155.440 0.056 197.420 19.848 0.017 0.836 0.855 2.086 WFTS-222 5.000 958.998 0.105 10.646 155.430 0.056 201.570 20.166 0.017 0.830 0.850 2.114 WFTS-223 2.000 382.661 0.042 0.919 6.113 0.076 102.950 11.057 0.023 0.903 0.914 0.529 WFTS-224 2.000 382.661 0.042 0.919 6.113 0.076 102.950 11.057 0.023 0.903 0.914 0.529 WFTS-225 5.000 948.065 0.105 13.513 200.280 0.072 225.760 21.852 0.019 0.810 0.831 2.352 WFTS-226 5.000 797.597 0.085 8.985 143.020 0.047 140.980 12.179 0.012 0.870 0.882 1.674 WFTS-227 5.000 797.660 0.085 8.867 141.370 0.046 141.700 12.158 0.012 0.863 0.876 1.673 WFTS-228 5.000 799.688 0.086 9.065 173.020 0.048 176.520 14.813 0.015 0.839 0.855 2.434 233 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-229 2.000 315.730 0.036 1.272 10.103 0.099 114.620 10.321 0.026 0.922 0.929 0.715 WFTS-230 2.000 316.630 0.037 1.532 12.150 0.120 119.850 10.791 0.027 0.919 0.926 0.744 WFTS-231 2.000 314.970 0.037 1.653 13.184 0.130 121.980 10.913 0.028 0.918 0.925 0.761 WFTS-232 3.000 574.829 0.063 2.713 66.439 0.067 130.900 13.664 0.019 0.873 0.887 2.405 WFTS-233 3.000 574.829 0.063 2.713 66.439 0.067 130.900 13.664 0.019 0.873 0.887 2.405 WFTS-234 3.000 574.829 0.063 2.713 66.439 0.067 130.900 13.664 0.019 0.873 0.887 2.405 WFTS-235 3.000 574.829 0.063 2.713 66.439 0.067 130.900 13.664 0.019 0.873 0.887 2.405 WFTS-236 1.000 63.927 0.005 0.244 7.743 0.076 80.087 3.143 0.031 0.947 0.951 2.042 WFTS-237 3.000 189.162 0.019 3.044 37.665 0.048 134.410 5.203 0.019 0.913 0.917 1.289 WFTS-238 1.000 191.375 0.021 0.142 2.020 0.095 68.992 8.106 0.034 0.912 0.921 0.763 WFTS-239 3.000 473.538 0.051 2.571 14.948 0.062 113.280 10.977 0.019 0.864 0.876 0.488 WFTS-240 1.000 191.920 0.021 0.140 2.067 0.093 67.975 8.009 0.034 0.912 0.921 0.783 WFTS-241 1.000 191.920 0.021 0.140 2.067 0.093 67.975 8.009 0.034 0.912 0.921 0.783 WFTS-242 1.000 191.920 0.021 0.140 2.067 0.093 67.975 8.009 0.034 0.912 0.921 0.783 WFTS-243 2.000 127.790 0.012 0.964 19.238 0.055 105.160 4.125 0.023 0.901 0.905 1.606 WFTS-244 2.000 317.771 0.031 0.964 8.370 0.068 96.418 9.405 0.023 0.893 0.904 0.640 WFTS-245 1.000 63.876 0.005 0.221 7.850 0.069 73.471 2.881 0.028 0.940 0.944 2.087 WFTS-246 2.000 317.517 0.031 0.957 8.398 0.067 95.650 9.322 0.022 0.894 0.905 0.642 WFTS-247 2.000 379.213 0.041 0.903 7.079 0.075 97.131 11.306 0.024 0.862 0.875 0.563 WFTS-248 3.000 283.050 0.035 10.246 43.038 0.102 180.440 10.452 0.022 0.976 0.980 0.628 WFTS-249 3.000 94.329 0.010 10.959 116.790 0.045 218.040 4.209 0.020 0.964 0.968 1.901 WFTS-250 3.000 287.348 0.037 8.861 53.002 0.092 175.690 9.856 0.021 0.947 0.954 0.848 WFTS-251 5.000 314.447 0.038 28.407 228.860 0.060 240.450 8.618 0.016 0.921 0.928 1.520 WFTS-252 5.000 319.983 0.040 39.989 319.250 0.086 262.930 9.507 0.018 0.912 0.920 1.633 WFTS-253 3.000 94.810 0.010 9.264 130.170 0.042 195.340 3.790 0.018 0.938 0.943 2.187 WFTS-254 5.000 796.170 0.107 31.493 417.190 0.086 275.360 24.177 0.020 0.872 0.898 2.770 WFTS-255 5.000 797.628 0.103 19.443 263.660 0.055 230.070 20.424 0.017 0.883 0.906 2.391 WFTS-256 5.000 797.628 0.103 19.443 263.660 0.055 230.070 20.424 0.017 0.883 0.906 2.391 WFTS-257 2.000 318.202 0.044 2.365 14.818 0.102 117.040 11.078 0.023 0.962 0.969 0.601 WFTS-258 5.000 316.519 0.040 21.859 212.460 0.057 220.540 7.736 0.016 0.896 0.903 1.636 WFTS-259 1.000 189.562 0.031 0.146 2.046 0.095 68.173 7.934 0.034 0.927 0.935 0.754 WFTS-260 1.000 157.624 0.025 0.161 2.749 0.102 72.914 7.056 0.036 0.919 0.926 0.975 WFTS-261 1.000 191.045 0.031 0.139 2.000 0.092 66.176 7.761 0.033 0.908 0.918 0.740 WFTS-262 5.000 949.966 0.130 15.043 211.310 0.054 228.750 23.024 0.017 0.835 0.863 2.344 WFTS-263 5.000 950.632 0.131 15.832 224.580 0.057 234.080 23.439 0.018 0.830 0.858 2.408 WFTS-264 5.000 945.023 0.131 17.443 248.900 0.063 241.710 23.966 0.018 0.826 0.855 2.492 WFTS-265 5.000 957.287 0.131 14.194 200.210 0.051 223.260 22.630 0.017 0.835 0.862 2.296 WFTS-266 5.000 941.378 0.131 18.638 267.340 0.067 246.310 24.260 0.018 0.823 0.852 2.545 WFTS-267 3.000 477.151 0.063 3.363 95.421 0.056 125.680 11.128 0.017 0.892 0.907 2.734 WFTS-268 2.000 317.150 0.048 0.950 8.338 0.073 93.889 9.140 0.023 0.870 0.882 0.615 WFTS-269 5.000 957.762 0.132 13.439 197.040 0.050 218.170 21.925 0.016 0.828 0.855 2.311 WFTS-270 3.000 95.877 0.011 7.594 125.640 0.030 167.440 3.285 0.015 0.938 0.942 2.205 WFTS-271 3.000 567.451 0.078 3.128 79.796 0.056 136.270 14.085 0.018 0.871 0.890 2.616 WFTS-272 3.000 565.645 0.079 3.532 91.710 0.064 142.420 14.557 0.019 0.864 0.883 2.760 WFTS-273 1.000 156.927 0.022 0.208 3.479 0.095 77.908 7.167 0.033 0.949 0.955 1.054 WFTS-274 3.000 575.266 0.080 2.955 76.899 0.055 133.810 13.932 0.018 0.866 0.884 2.603 WFTS-275 3.000 575.722 0.081 2.663 74.070 0.052 128.250 13.180 0.017 0.854 0.872 2.631 WFTS-276 1.000 191.958 0.030 0.133 2.161 0.086 63.691 7.506 0.031 0.896 0.906 0.795 WFTS-277 1.000 63.908 0.009 0.210 9.269 0.097 75.058 2.674 0.030 0.904 0.908 2.540 WFTS-278 3.000 190.374 0.027 2.815 42.607 0.047 140.640 4.774 0.018 0.866 0.871 1.568 234 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-279 3.000 190.374 0.027 2.815 42.607 0.047 140.640 4.774 0.018 0.866 0.871 1.568 WFTS-280 3.000 95.385 0.011 5.739 108.150 0.023 145.870 2.847 0.013 0.917 0.921 2.141 WFTS-281 5.000 959.125 0.139 9.241 166.230 0.042 193.840 18.414 0.015 0.783 0.807 2.378 WFTS-282 5.000 957.509 0.139 9.782 176.280 0.044 199.700 18.849 0.015 0.779 0.803 2.443 WFTS-283 2.000 190.412 0.027 0.926 14.590 0.057 108.010 5.695 0.022 0.897 0.902 1.298 WFTS-284 3.000 287.823 0.042 3.341 35.619 0.064 139.600 7.074 0.018 0.852 0.860 1.083 WFTS-285 1.000 188.352 0.029 0.149 2.670 0.086 68.679 7.386 0.030 0.923 0.930 0.967 WFTS-286 1.000 188.352 0.029 0.149 2.670 0.086 68.679 7.386 0.030 0.923 0.930 0.967 WFTS-287 1.000 188.352 0.029 0.149 2.670 0.086 68.679 7.386 0.030 0.923 0.930 0.967 WFTS-288 5.000 315.343 0.039 10.650 95.058 0.029 159.790 6.187 0.013 0.843 0.851 1.026 WFTS-289 5.000 474.032 0.072 12.786 178.750 0.056 178.040 8.421 0.013 0.804 0.813 1.710 WFTS-290 5.000 476.251 0.072 9.649 132.780 0.040 150.290 7.518 0.012 0.849 0.855 1.496 WFTS-291 1.000 157.428 0.024 0.146 3.188 0.086 72.223 6.323 0.031 0.898 0.906 1.212 WFTS-292 1.000 157.149 0.024 0.152 3.322 0.089 72.401 6.384 0.031 0.907 0.914 1.224 WFTS-293 3.000 568.592 0.087 2.220 76.674 0.052 122.530 11.710 0.016 0.805 0.821 2.939 WFTS-294 1.000 95.795 0.014 0.167 5.869 0.085 66.336 3.901 0.030 0.908 0.912 1.802 WFTS-295 3.000 575.266 0.088 1.955 68.406 0.046 119.310 11.479 0.016 0.801 0.817 2.885 WFTS-296 1.000 159.532 0.025 0.125 2.891 0.078 70.686 6.186 0.031 0.886 0.894 1.232 WFTS-297 3.000 574.924 0.090 2.228 79.939 0.054 125.480 11.866 0.017 0.787 0.804 3.059 WFTS-298 2.000 377.946 0.059 0.740 7.403 0.061 101.890 9.767 0.021 0.812 0.826 0.712 WFTS-299 3.000 567.185 0.089 1.790 66.387 0.044 116.780 10.928 0.016 0.790 0.806 2.952 WFTS-300 3.000 572.033 0.091 2.620 96.416 0.064 131.040 12.147 0.017 0.775 0.792 3.228 WFTS-301 1.000 159.995 0.025 0.125 2.986 0.079 62.400 6.129 0.030 0.883 0.891 1.121 WFTS-302 5.000 158.410 0.019 22.343 332.900 0.021 181.730 3.535 0.010 0.880 0.884 2.024 WFTS-303 3.000 95.810 0.011 4.567 114.510 0.020 122.880 2.409 0.011 0.879 0.884 2.303 WFTS-304 5.000 473.494 0.071 6.077 53.921 0.028 121.150 7.043 0.012 0.732 0.741 0.674 WFTS-305 5.000 158.521 0.025 46.209 416.230 0.042 289.920 5.332 0.015 0.942 0.945 2.086 WFTS-306 3.000 284.210 0.044 5.763 38.736 0.057 144.140 8.383 0.018 0.954 0.959 0.786 WFTS-307 3.000 284.210 0.044 5.763 38.736 0.057 144.140 8.383 0.018 0.954 0.959 0.786 WFTS-308 5.000 791.449 0.137 45.034 690.900 0.102 285.950 24.278 0.019 0.843 0.874 3.240 WFTS-309 5.000 316.142 0.052 14.480 114.440 0.032 182.900 6.432 0.012 0.901 0.906 1.107 WFTS-310 3.000 564.770 0.098 4.824 138.700 0.072 150.320 15.021 0.018 0.842 0.865 3.160 WFTS-311 5.000 476.599 0.082 19.430 169.940 0.052 186.310 9.795 0.013 0.890 0.898 1.238 WFTS-312 5.000 477.011 0.082 18.755 109.580 0.050 173.290 9.171 0.012 0.896 0.904 0.773 WFTS-313 5.000 470.705 0.084 25.561 316.700 0.072 196.370 10.033 0.014 0.876 0.884 1.818 WFTS-314 2.000 127.689 0.022 1.072 26.335 0.050 109.370 3.775 0.020 0.876 0.881 2.001 WFTS-315 1.000 63.737 0.011 0.210 10.722 0.085 69.460 2.439 0.026 0.894 0.898 2.690 WFTS-316 2.000 63.959 0.009 2.118 72.349 0.032 99.712 1.958 0.014 0.924 0.927 2.670 WFTS-317 3.000 191.876 0.035 2.651 48.463 0.041 129.710 4.262 0.015 0.831 0.837 1.677 WFTS-318 1.000 191.229 0.036 0.135 2.878 0.074 66.638 6.925 0.027 0.875 0.885 1.064 WFTS-319 3.000 477.797 0.088 2.203 19.157 0.045 118.630 9.146 0.015 0.773 0.789 0.688 WFTS-320 2.000 127.233 0.022 0.961 28.132 0.044 88.292 3.448 0.018 0.861 0.866 1.892 WFTS-321 3.000 570.208 0.117 1.489 66.833 0.037 82.941 9.678 0.014 0.739 0.755 2.377 WFTS-322 5.000 800.005 0.154 6.724 210.480 0.032 165.790 11.609 0.011 0.695 0.713 3.128 WFTS-323 2.000 376.602 0.074 0.715 8.609 0.053 92.193 8.852 0.018 0.818 0.831 0.780 WFTS-324 2.000 381.622 0.078 0.627 7.753 0.052 77.080 9.029 0.019 0.749 0.764 0.615 WFTS-325 1.000 63.407 0.010 0.205 11.436 0.057 59.013 2.297 0.022 0.907 0.911 2.542 WFTS-326 5.000 795.949 0.156 8.200 261.460 0.040 178.170 12.106 0.012 0.677 0.695 3.339 WFTS-327 1.000 188.339 0.037 0.119 2.912 0.071 66.216 6.611 0.027 0.854 0.864 1.182 WFTS-328 1.000 188.339 0.037 0.119 2.912 0.071 66.216 6.611 0.027 0.854 0.864 1.182 235 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-329 1.000 188.339 0.037 0.119 2.912 0.071 66.216 6.611 0.027 0.854 0.864 1.182 WFTS-330 1.000 188.339 0.037 0.119 2.912 0.071 66.216 6.611 0.027 0.854 0.864 1.182 WFTS-331 2.000 318.709 0.063 0.696 10.039 0.051 94.718 7.650 0.019 0.815 0.826 0.954 WFTS-332 5.000 316.329 0.066 8.973 179.090 0.032 157.100 4.822 0.011 0.786 0.790 2.095 WFTS-333 5.000 316.329 0.066 8.973 179.090 0.032 157.100 4.822 0.011 0.786 0.790 2.095 WFTS-334 3.000 480.041 0.094 1.642 88.280 0.037 96.003 7.326 0.012 0.764 0.777 3.391 WFTS-335 3.000 480.041 0.094 1.642 88.280 0.037 96.003 7.326 0.012 0.764 0.777 3.391 WFTS-336 2.000 189.017 0.038 0.708 16.706 0.047 98.645 4.761 0.019 0.826 0.832 1.637 WFTS-337 2.000 63.822 0.010 1.852 74.294 0.023 87.146 1.707 0.011 0.911 0.915 2.703 WFTS-338 2.000 380.380 0.076 0.639 8.078 0.050 97.187 8.808 0.018 0.761 0.776 0.806 WFTS-339 5.000 159.576 0.046 20.031 504.240 0.059 163.030 2.481 0.010 0.774 0.777 2.694 WFTS-340 2.000 381.660 0.078 0.602 7.745 0.050 75.884 8.890 0.019 0.739 0.755 0.622 WFTS-341 5.000 956.146 0.192 5.966 169.120 0.031 190.130 14.857 0.012 0.644 0.666 3.033 WFTS-342 3.000 287.043 0.059 2.239 56.205 0.049 125.360 5.421 0.015 0.728 0.736 1.958 WFTS-343 3.000 575.399 0.116 1.535 72.711 0.037 110.090 9.654 0.013 0.728 0.745 3.284 WFTS-344 5.000 158.965 0.047 12.410 2099.000 0.037 27.860 0.510 0.002 0.937 0.937 3.734 WFTS-345 5.000 960.234 0.196 6.132 177.860 0.032 197.310 15.144 0.013 0.629 0.651 3.150 WFTS-346 5.000 960.044 0.196 6.174 179.140 0.033 198.800 15.201 0.013 0.627 0.649 3.163 WFTS-347 5.000 958.650 0.197 6.954 202.050 0.037 206.340 15.647 0.013 0.622 0.644 3.265 WFTS-348 5.000 959.030 0.197 6.442 187.760 0.034 202.610 15.377 0.013 0.622 0.645 3.218 WFTS-349 5.000 960.076 0.198 7.110 207.030 0.038 209.880 15.815 0.013 0.617 0.639 3.302 WFTS-350 5.000 954.688 0.200 9.065 265.930 0.048 224.690 16.545 0.014 0.605 0.628 3.501 WFTS-351 5.000 957.699 0.199 8.306 243.240 0.044 219.360 16.313 0.014 0.610 0.632 3.435 WFTS-352 5.000 959.379 0.199 7.640 224.100 0.041 216.150 16.098 0.014 0.610 0.632 3.389 WFTS-353 3.000 95.594 0.020 4.017 916.410 0.038 15.958 0.312 0.002 0.964 0.964 2.968 WFTS-354 1.000 63.952 0.010 0.174 11.163 0.048 52.500 2.061 0.020 0.900 0.904 2.578 WFTS-355 2.000 381.622 0.078 0.530 7.702 0.044 71.876 8.420 0.018 0.713 0.728 0.643 WFTS-356 5.000 473.145 0.087 5.637 94.878 0.023 110.410 6.414 0.010 0.661 0.671 1.055 WFTS-357 2.000 126.789 0.022 0.732 28.592 0.037 72.819 2.834 0.015 0.789 0.794 1.909 WFTS-358 2.000 63.875 0.010 1.561 75.838 0.019 75.208 1.475 0.010 0.893 0.897 2.770 WFTS-359 3.000 479.908 0.098 1.615 19.022 0.036 78.289 7.688 0.013 0.785 0.794 0.619 WFTS-360 3.000 95.881 0.020 3.322 917.070 0.034 13.592 0.267 0.002 0.956 0.957 3.034 WFTS-361 3.000 94.656 0.016 4.424 177.990 0.029 91.105 1.765 0.010 0.838 0.841 2.607 WFTS-362 3.000 94.656 0.016 4.424 177.990 0.029 91.105 1.765 0.010 0.838 0.841 2.607 WFTS-363 2.000 381.673 0.078 0.492 7.640 0.041 69.463 8.138 0.017 0.697 0.712 0.650 WFTS-364 5.000 159.076 0.031 16.806 406.160 0.024 128.960 2.519 0.008 0.798 0.802 2.114 WFTS-365 5.000 159.076 0.031 16.806 406.160 0.024 128.960 2.519 0.008 0.798 0.802 2.114 WFTS-366 3.000 575.532 0.118 1.307 74.129 0.032 76.996 9.068 0.013 0.677 0.693 2.557 WFTS-367 5.000 476.187 0.091 22.698 250.230 0.044 187.390 9.974 0.012 0.901 0.910 1.590 WFTS-368 3.000 286.112 0.058 2.820 56.105 0.041 117.640 5.772 0.014 0.829 0.838 1.658 WFTS-369 5.000 319.476 0.068 10.479 180.230 0.028 158.300 5.165 0.010 0.826 0.832 1.915 WFTS-370 3.000 573.307 0.144 1.469 65.767 0.036 78.420 9.200 0.013 0.733 0.750 2.224 WFTS-371 2.000 315.717 0.067 0.935 11.981 0.049 89.305 7.762 0.017 0.888 0.897 0.868 WFTS-372 2.000 316.402 0.067 0.906 12.008 0.050 91.350 7.695 0.017 0.856 0.867 0.888 WFTS-373 5.000 316.754 0.065 8.361 104.520 0.024 125.590 4.884 0.010 0.765 0.773 1.026 WFTS-374 5.000 159.101 0.046 21.806 496.540 0.049 156.360 2.509 0.010 0.819 0.822 2.473 WFTS-375 1.000 95.364 0.021 0.166 7.114 0.065 59.760 3.499 0.025 0.907 0.911 1.971 WFTS-376 1.000 95.960 0.021 0.152 6.859 0.064 58.071 3.421 0.025 0.876 0.882 1.947 WFTS-377 3.000 285.693 0.073 1.718 29.056 0.037 93.162 5.447 0.015 0.734 0.741 0.988 WFTS-378 3.000 191.990 0.046 2.360 56.963 0.037 115.390 3.621 0.013 0.794 0.799 1.880 236 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) h (W/m².K) Nu (-) j (-) η (-) ηo (-) NTU (-) WFTS-379 2.000 189.157 0.043 0.702 18.093 0.043 95.090 4.425 0.017 0.794 0.801 1.661 WFTS-380 5.000 470.927 0.111 8.075 163.820 0.029 143.430 6.529 0.010 0.780 0.787 1.937 WFTS-381 1.000 31.893 0.006 0.478 37.062 0.030 51.390 1.006 0.012 0.931 0.934 3.145 WFTS-382 3.000 471.789 0.110 1.847 20.449 0.037 103.720 7.980 0.013 0.786 0.797 0.774 WFTS-383 5.000 792.875 0.184 6.136 229.880 0.028 157.840 10.257 0.010 0.650 0.668 3.337 WFTS-384 2.000 319.989 0.076 0.638 10.691 0.043 86.141 6.990 0.017 0.817 0.826 1.008 WFTS-385 1.000 191.064 0.046 0.103 3.021 0.060 62.533 6.132 0.025 0.826 0.836 1.295 WFTS-386 2.000 63.618 0.023 1.334 545.400 0.058 9.162 0.174 0.002 0.972 0.973 3.080 WFTS-387 5.000 157.089 0.055 8.550 2099.300 0.025 17.450 0.318 0.001 0.945 0.945 3.424 WFTS-388 5.000 157.669 0.055 16.044 491.030 0.047 128.680 1.882 0.008 0.753 0.756 2.515 WFTS-389 3.000 94.978 0.023 3.335 834.680 0.031 13.914 0.270 0.002 0.957 0.958 2.820 WFTS-390 3.000 191.457 0.037 2.202 52.171 0.023 98.077 3.843 0.012 0.758 0.766 1.505 WFTS-391 1.000 158.943 0.039 0.094 3.550 0.057 64.476 5.053 0.025 0.795 0.803 1.646 WFTS-392 1.000 158.442 0.039 0.092 3.491 0.057 65.989 5.012 0.025 0.771 0.781 1.656 WFTS-393 5.000 159.979 0.037 14.117 758.220 0.025 80.488 1.581 0.006 0.814 0.817 2.986 WFTS-394 1.000 189.436 0.047 0.091 2.923 0.057 64.028 5.934 0.025 0.787 0.797 1.389 WFTS-395 1.000 189.043 0.047 0.092 2.959 0.057 63.218 5.929 0.025 0.798 0.808 1.394 WFTS-396 3.000 479.490 0.123 1.810 22.614 0.039 95.427 7.397 0.012 0.781 0.790 0.796 WFTS-397 3.000 479.471 0.123 1.842 34.510 0.040 99.550 7.666 0.012 0.776 0.785 1.238 WFTS-398 1.000 31.741 0.006 0.355 31.909 0.022 42.088 0.820 0.009 0.924 0.928 2.968 WFTS-399 1.000 31.741 0.006 0.355 31.909 0.022 42.088 0.820 0.009 0.924 0.928 2.968 WFTS-400 1.000 31.741 0.006 0.355 31.909 0.022 42.088 0.820 0.009 0.924 0.928 2.968 WFTS-401 1.000 94.851 0.021 0.128 7.286 0.054 50.587 2.946 0.022 0.846 0.851 2.074 WFTS-402 5.000 786.727 0.198 5.590 245.320 0.029 173.630 10.022 0.010 0.581 0.598 3.849 WFTS-403 2.000 191.489 0.045 0.602 18.010 0.037 71.136 4.181 0.016 0.773 0.780 1.403 WFTS-404 1.000 191.945 0.048 0.084 2.771 0.055 66.459 5.914 0.025 0.743 0.755 1.399 WFTS-405 5.000 960.203 0.242 4.546 165.990 0.024 191.290 13.108 0.011 0.561 0.581 3.432 WFTS-406 5.000 958.903 0.243 4.983 182.210 0.026 197.130 13.384 0.011 0.556 0.577 3.515 WFTS-407 5.000 955.639 0.243 5.422 198.950 0.029 202.850 13.623 0.012 0.552 0.572 3.602 WFTS-408 1.000 31.782 0.007 0.346 256.370 0.051 4.611 0.090 0.001 0.988 0.988 2.858 WFTS-409 1.000 31.782 0.007 0.346 256.370 0.051 4.611 0.090 0.001 0.988 0.988 2.858 WFTS-410 3.000 95.985 0.024 4.061 404.030 0.036 43.410 0.853 0.005 0.864 0.866 3.163 WFTS-411 5.000 798.896 0.201 4.804 222.010 0.025 100.540 9.862 0.010 0.564 0.580 2.278 WFTS-412 3.000 282.385 0.071 1.304 30.404 0.027 78.116 4.514 0.012 0.678 0.685 1.055 WFTS-413 3.000 190.640 0.037 1.866 52.781 0.020 88.609 3.457 0.011 0.713 0.722 1.529 WFTS-414 1.000 191.305 0.049 0.084 3.066 0.052 47.686 5.601 0.023 0.805 0.813 1.196 WFTS-415 5.000 158.531 0.034 14.608 588.820 0.016 111.490 2.170 0.007 0.812 0.816 3.100 WFTS-416 5.000 158.391 0.041 8.871 1585.000 0.017 22.456 0.437 0.002 0.929 0.930 3.155 WFTS-417 2.000 382.560 0.097 0.408 7.775 0.034 61.939 7.274 0.015 0.637 0.652 0.650 WFTS-418 2.000 127.626 0.024 0.814 30.678 0.019 75.803 2.970 0.012 0.790 0.798 1.929 WFTS-419 5.000 799.181 0.201 3.995 36.673 0.021 81.233 7.971 0.008 0.578 0.592 0.373 WFTS-420 1.000 31.460 0.008 0.260 228.310 0.042 3.999 0.077 0.001 0.985 0.985 2.927 237 8.3.1.3Round Finless Tube Surface (RFTS) Figure 145. RFTS Segment. Table 52. RFTS Optimum designs dimensions. TAG Type (-) Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nt (-) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) Ao/V (cm²/cm³) RFTS-001 1 0.50 1.37 1.58 1.15 4 0.37 0.50 2.73 7.9E-04 2.9E-04 6.3E-03 29.11 RFTS-002 1 0.50 1.37 1.58 1.15 4 0.37 0.50 2.73 7.9E-04 2.9E-04 6.3E-03 29.11 RFTS-003 1 0.50 1.37 1.58 1.15 4 0.37 0.50 2.73 7.9E-04 2.9E-04 6.3E-03 29.11 RFTS-004 1 0.50 1.36 1.57 1.15 4 0.36 0.50 2.73 7.9E-04 2.9E-04 6.3E-03 29.30 RFTS-005 1 0.50 1.36 1.57 1.15 3 0.36 0.50 2.04 7.9E-04 2.9E-04 4.7E-03 29.30 RFTS-006 1 0.50 1.36 1.57 1.15 2 0.36 0.50 1.36 7.9E-04 2.9E-04 3.1E-03 29.30 RFTS-007 1 0.50 1.37 1.58 1.15 4 0.37 0.50 2.73 7.9E-04 2.9E-04 6.3E-03 29.11 d l=1.0mTube Banks (Nr) Tube Banks (Nr) Tube Rows (Nt) 2Pl 238 TAG Type (-) Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nt (-) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) Ao/V (cm²/cm³) RFTS-008 1 0.50 1.37 1.58 1.15 4 0.37 0.50 2.73 7.9E-04 2.9E-04 6.3E-03 29.11 RFTS-009 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.11 RFTS-010 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.11 RFTS-011 1 0.50 1.36 1.57 1.15 3 0.36 0.50 2.04 7.9E-04 2.9E-04 4.7E-03 29.30 RFTS-012 1 0.50 1.36 1.57 1.15 3 0.36 0.50 2.04 7.9E-04 2.9E-04 4.7E-03 29.30 RFTS-013 1 0.50 1.36 1.57 1.15 3 0.36 0.50 2.04 7.9E-04 2.9E-04 4.7E-03 29.30 RFTS-014 1 0.50 1.37 1.58 1.15 2 0.37 0.50 1.37 7.9E-04 2.9E-04 3.1E-03 29.11 RFTS-015 1 0.50 1.37 1.58 1.15 2 0.37 0.50 1.37 7.9E-04 2.9E-04 3.1E-03 29.11 RFTS-016 1 0.50 1.36 1.57 1.15 2 0.36 0.50 1.36 7.9E-04 2.9E-04 3.1E-03 29.30 RFTS-017 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.11 RFTS-018 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.21 RFTS-019 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.21 RFTS-020 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.21 RFTS-021 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.21 RFTS-022 1 0.50 1.37 1.58 1.15 2 0.37 0.50 1.37 7.9E-04 2.9E-04 3.1E-03 29.11 RFTS-023 1 0.50 1.37 1.58 1.15 2 0.37 0.50 1.37 7.9E-04 2.9E-04 3.1E-03 29.11 RFTS-024 1 0.50 1.37 1.58 1.15 2 0.37 0.50 1.37 7.9E-04 2.9E-04 3.1E-03 29.11 RFTS-025 1 0.50 1.37 1.58 1.15 2 0.37 0.50 1.37 7.9E-04 2.9E-04 3.1E-03 29.11 RFTS-026 1 0.50 1.36 1.57 1.15 2 0.36 0.50 1.36 7.9E-04 2.9E-04 3.1E-03 29.30 RFTS-027 1 0.50 1.37 1.58 1.15 40 0.37 0.50 27.34 7.9E-04 2.9E-04 6.3E-02 29.11 RFTS-028 1 0.50 1.36 1.57 1.15 40 0.36 0.50 27.26 7.9E-04 2.9E-04 6.3E-02 29.30 RFTS-029 1 0.50 1.36 1.57 1.15 40 0.36 0.50 27.26 7.9E-04 2.9E-04 6.3E-02 29.30 RFTS-030 1 0.50 1.37 1.58 1.15 5 0.37 0.50 3.42 7.9E-04 2.9E-04 7.9E-03 29.11 RFTS-031 1 0.50 1.37 1.58 1.15 5 0.37 0.50 3.42 7.9E-04 2.9E-04 7.9E-03 29.11 RFTS-032 1 0.50 1.37 1.58 1.15 5 0.37 0.50 3.42 7.9E-04 2.9E-04 7.9E-03 29.11 RFTS-033 1 0.50 1.37 1.58 1.15 5 0.37 0.50 3.42 7.9E-04 2.9E-04 7.9E-03 29.11 RFTS-034 1 0.50 1.37 1.58 1.15 3 0.37 0.50 2.05 7.9E-04 2.9E-04 4.7E-03 29.11 RFTS-035 1 0.50 1.36 1.57 1.15 3 0.36 0.50 2.04 7.9E-04 2.9E-04 4.7E-03 29.30 RFTS-036 1 0.50 1.36 1.57 1.15 2 0.36 0.50 1.36 7.9E-04 2.9E-04 3.1E-03 29.30 RFTS-037 1 0.50 1.68 1.94 1.15 5 0.49 1.01 4.20 9.7E-04 4.7E-04 7.9E-03 19.24 RFTS-038 1 0.50 1.68 1.94 1.15 4 0.49 1.01 3.36 9.7E-04 4.7E-04 6.3E-03 19.24 RFTS-039 1 0.50 1.68 1.93 1.15 4 0.48 1.00 3.35 9.7E-04 4.7E-04 6.3E-03 19.39 RFTS-040 1 0.50 1.68 1.94 1.15 3 0.49 1.01 2.52 9.7E-04 4.7E-04 4.7E-03 19.24 RFTS-041 1 0.50 1.68 1.94 1.15 3 0.49 1.01 2.52 9.7E-04 4.7E-04 4.7E-03 19.24 RFTS-042 1 0.50 1.68 1.93 1.15 3 0.48 1.00 2.51 9.7E-04 4.7E-04 4.7E-03 19.39 RFTS-043 1 0.50 1.68 1.93 1.15 3 0.48 1.00 2.51 9.7E-04 4.7E-04 4.7E-03 19.39 RFTS-044 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-045 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-046 1 0.50 1.68 1.93 1.15 2 0.48 1.00 1.68 9.7E-04 4.7E-04 3.1E-03 19.39 RFTS-047 1 0.50 1.68 1.94 1.15 4 0.49 1.01 3.36 9.7E-04 4.7E-04 6.3E-03 19.24 RFTS-048 1 0.50 1.68 1.93 1.15 4 0.48 1.00 3.35 9.7E-04 4.7E-04 6.3E-03 19.39 RFTS-049 1 0.50 1.68 1.94 1.15 3 0.49 1.01 2.52 9.7E-04 4.7E-04 4.7E-03 19.24 RFTS-050 1 0.50 1.68 1.94 1.15 3 0.49 1.01 2.52 9.7E-04 4.7E-04 4.7E-03 19.24 RFTS-051 1 0.50 1.67 1.93 1.15 3 0.48 0.99 2.51 9.7E-04 4.7E-04 4.7E-03 19.44 RFTS-052 1 0.50 1.67 1.93 1.15 3 0.48 0.99 2.51 9.7E-04 4.7E-04 4.7E-03 19.44 RFTS-053 1 0.50 1.67 1.93 1.15 3 0.48 0.99 2.51 9.7E-04 4.7E-04 4.7E-03 19.44 RFTS-054 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-055 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-056 1 0.50 1.67 1.93 1.15 2 0.48 0.99 1.67 9.7E-04 4.7E-04 3.1E-03 19.44 RFTS-057 1 0.50 1.68 1.94 1.15 4 0.49 1.01 3.36 9.7E-04 4.7E-04 6.3E-03 19.24 239 TAG Type (-) Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nt (-) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) Ao/V (cm²/cm³) RFTS-058 1 0.50 1.68 1.94 1.15 4 0.48 1.00 3.35 9.7E-04 4.7E-04 6.3E-03 19.34 RFTS-059 1 0.50 1.68 1.94 1.15 3 0.49 1.01 2.52 9.7E-04 4.7E-04 4.7E-03 19.24 RFTS-060 1 0.50 1.68 1.94 1.15 3 0.49 1.01 2.52 9.7E-04 4.7E-04 4.7E-03 19.24 RFTS-061 1 0.50 1.67 1.93 1.15 3 0.48 0.99 2.51 9.7E-04 4.7E-04 4.7E-03 19.44 RFTS-062 1 0.50 1.67 1.93 1.15 3 0.48 0.99 2.51 9.7E-04 4.7E-04 4.7E-03 19.44 RFTS-063 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-064 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-065 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-066 1 0.50 1.67 1.93 1.15 2 0.48 0.99 1.67 9.7E-04 4.7E-04 3.1E-03 19.44 RFTS-067 1 2.00 1.35 1.29 0.95 40 0.22 0.99 108.26 2.6E-03 5.8E-04 2.5E-01 9.01 RFTS-068 1 2.00 1.33 1.30 0.97 40 0.23 1.00 106.51 2.6E-03 5.9E-04 2.5E-01 9.11 RFTS-069 1 2.00 1.65 1.24 0.75 40 0.19 1.00 132.34 2.5E-03 4.8E-04 2.5E-01 7.67 RFTS-070 1 2.00 1.65 1.24 0.75 40 0.19 1.00 132.34 2.5E-03 4.8E-04 2.5E-01 7.67 RFTS-071 1 2.00 1.30 1.30 1.00 40 0.23 1.01 103.88 2.6E-03 6.1E-04 2.5E-01 9.28 RFTS-072 1 2.00 1.30 1.30 1.00 40 0.23 1.01 103.88 2.6E-03 6.1E-04 2.5E-01 9.28 RFTS-073 1 2.00 1.74 1.23 0.70 40 0.19 1.01 139.35 2.5E-03 4.5E-04 2.5E-01 7.35 RFTS-074 1 0.50 1.68 1.94 1.15 4 0.49 1.01 3.36 9.7E-04 4.7E-04 6.3E-03 19.24 RFTS-075 1 0.50 1.68 1.94 1.15 4 0.49 1.01 3.36 9.7E-04 4.7E-04 6.3E-03 19.24 RFTS-076 1 0.50 1.68 1.94 1.15 3 0.49 1.01 2.52 9.7E-04 4.7E-04 4.7E-03 19.24 RFTS-077 1 0.50 1.68 1.94 1.15 3 0.48 1.00 2.52 9.7E-04 4.7E-04 4.7E-03 19.29 RFTS-078 1 0.50 1.67 1.93 1.15 3 0.48 0.99 2.51 9.7E-04 4.7E-04 4.7E-03 19.44 RFTS-079 1 0.50 1.67 1.93 1.15 3 0.48 0.99 2.51 9.7E-04 4.7E-04 4.7E-03 19.44 RFTS-080 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-081 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-082 1 0.50 1.68 1.94 1.15 2 0.49 1.01 1.68 9.7E-04 4.7E-04 3.1E-03 19.24 RFTS-083 1 0.50 1.67 1.93 1.15 2 0.48 0.99 1.67 9.7E-04 4.7E-04 3.1E-03 19.44 RFTS-084 1 2.00 1.53 1.39 0.90 40 0.28 1.51 122.71 2.8E-03 7.7E-04 2.5E-01 7.39 RFTS-085 1 0.50 1.93 2.23 1.15 4 0.55 1.51 3.86 1.1E-03 6.2E-04 6.3E-03 14.57 RFTS-086 1 0.50 1.93 2.23 1.15 4 0.55 1.51 3.86 1.1E-03 6.2E-04 6.3E-03 14.57 RFTS-087 1 0.50 1.93 2.23 1.15 3 0.55 1.51 2.90 1.1E-03 6.2E-04 4.7E-03 14.57 RFTS-088 1 0.50 1.93 2.22 1.15 3 0.55 1.50 2.89 1.1E-03 6.1E-04 4.7E-03 14.67 RFTS-089 1 0.50 1.92 2.22 1.15 3 0.55 1.49 2.88 1.1E-03 6.1E-04 4.7E-03 14.74 RFTS-090 1 0.50 1.92 2.22 1.15 3 0.55 1.49 2.88 1.1E-03 6.1E-04 4.7E-03 14.74 RFTS-091 1 0.50 1.93 2.23 1.15 2 0.55 1.51 1.93 1.1E-03 6.2E-04 3.1E-03 14.57 RFTS-092 1 0.50 1.93 2.23 1.15 2 0.55 1.51 1.93 1.1E-03 6.2E-04 3.1E-03 14.57 RFTS-093 1 0.50 1.93 2.23 1.15 2 0.55 1.51 1.93 1.1E-03 6.2E-04 3.1E-03 14.57 RFTS-094 1 0.50 1.92 2.22 1.15 2 0.55 1.49 1.92 1.1E-03 6.1E-04 3.1E-03 14.77 RFTS-095 1 0.50 2.33 2.69 1.15 25 0.63 2.51 29.13 1.3E-03 8.5E-04 3.9E-02 10.02 RFTS-096 1 0.50 2.33 2.69 1.15 25 0.63 2.50 29.08 1.3E-03 8.4E-04 3.9E-02 10.06 RFTS-097 1 0.50 2.33 2.69 1.15 25 0.63 2.50 29.08 1.3E-03 8.4E-04 3.9E-02 10.06 RFTS-098 1 0.50 2.33 2.70 1.15 5 0.63 2.52 5.84 1.3E-03 8.5E-04 7.9E-03 9.98 RFTS-099 1 0.50 2.33 2.70 1.15 5 0.63 2.52 5.84 1.3E-03 8.5E-04 7.9E-03 9.98 RFTS-100 1 0.50 2.33 2.70 1.15 5 0.63 2.52 5.84 1.3E-03 8.5E-04 7.9E-03 9.98 RFTS-101 1 0.50 2.33 2.69 1.15 4 0.63 2.50 4.65 1.3E-03 8.4E-04 6.3E-03 10.06 RFTS-102 1 0.50 2.33 2.69 1.15 3 0.63 2.50 3.49 1.3E-03 8.4E-04 4.7E-03 10.06 RFTS-103 1 0.50 2.33 2.70 1.15 2 0.63 2.52 2.33 1.3E-03 8.5E-04 3.1E-03 9.98 RFTS-104 1 0.50 2.33 2.69 1.15 2 0.63 2.50 2.33 1.3E-03 8.4E-04 3.1E-03 10.06 RFTS-105 1 0.50 2.33 2.69 1.15 25 0.63 2.51 29.13 1.3E-03 8.5E-04 3.9E-02 10.02 RFTS-106 1 0.50 2.32 2.68 1.15 25 0.63 2.48 28.99 1.3E-03 8.4E-04 3.9E-02 10.11 RFTS-107 1 0.50 2.32 2.68 1.15 25 0.63 2.48 28.99 1.3E-03 8.4E-04 3.9E-02 10.11 240 TAG Type (-) Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nt (-) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) Ao/V (cm²/cm³) RFTS-108 1 0.50 2.32 2.68 1.15 25 0.63 2.48 28.99 1.3E-03 8.4E-04 3.9E-02 10.11 RFTS-109 1 0.50 2.33 2.69 1.15 4 0.63 2.52 4.67 1.3E-03 8.5E-04 6.3E-03 10.00 RFTS-110 1 0.50 2.33 2.69 1.15 4 0.63 2.52 4.67 1.3E-03 8.5E-04 6.3E-03 10.00 RFTS-111 1 0.50 2.33 2.69 1.15 4 0.63 2.52 4.67 1.3E-03 8.5E-04 6.3E-03 10.00 RFTS-112 1 0.50 2.33 2.69 1.15 4 0.63 2.50 4.66 1.3E-03 8.4E-04 6.3E-03 10.04 RFTS-113 1 0.50 2.32 2.68 1.15 4 0.63 2.48 4.64 1.3E-03 8.4E-04 6.3E-03 10.11 RFTS-114 1 0.50 2.32 2.68 1.15 3 0.63 2.48 3.48 1.3E-03 8.4E-04 4.7E-03 10.11 RFTS-115 1 0.50 2.33 2.69 1.15 25 0.63 2.52 29.16 1.3E-03 8.5E-04 3.9E-02 10.00 RFTS-116 1 0.50 2.33 2.69 1.15 25 0.63 2.50 29.10 1.3E-03 8.4E-04 3.9E-02 10.04 RFTS-117 1 0.50 2.33 2.69 1.15 25 0.63 2.50 29.10 1.3E-03 8.4E-04 3.9E-02 10.04 RFTS-118 1 0.50 2.33 2.69 1.15 4 0.63 2.52 4.67 1.3E-03 8.5E-04 6.3E-03 10.00 RFTS-119 1 0.50 2.33 2.69 1.15 4 0.63 2.52 4.67 1.3E-03 8.5E-04 6.3E-03 10.00 RFTS-120 1 0.50 2.33 2.69 1.15 4 0.63 2.50 4.65 1.3E-03 8.4E-04 6.3E-03 10.06 RFTS-121 1 0.50 2.32 2.68 1.15 3 0.63 2.48 3.48 1.3E-03 8.4E-04 4.7E-03 10.11 RFTS-122 1 0.50 2.32 2.68 1.15 3 0.63 2.48 3.48 1.3E-03 8.4E-04 4.7E-03 10.11 RFTS-123 1 0.50 2.33 2.69 1.15 2 0.63 2.52 2.33 1.3E-03 8.5E-04 3.1E-03 10.00 RFTS-124 1 0.50 2.32 2.68 1.15 2 0.63 2.49 2.32 1.3E-03 8.4E-04 3.1E-03 10.08 RFTS-125 1 0.50 2.33 2.70 1.15 3 0.63 2.52 3.50 1.3E-03 8.5E-04 4.7E-03 9.98 RFTS-126 1 0.50 2.32 2.68 1.15 3 0.63 2.48 3.48 1.3E-03 8.4E-04 4.7E-03 10.09 RFTS-127 1 0.50 2.32 2.68 1.15 3 0.63 2.48 3.48 1.3E-03 8.4E-04 4.7E-03 10.09 RFTS-128 1 0.50 2.32 2.68 1.15 3 0.63 2.48 3.48 1.3E-03 8.4E-04 4.7E-03 10.09 RFTS-129 1 0.50 2.33 2.69 1.15 2 0.63 2.52 2.33 1.3E-03 8.5E-04 3.1E-03 10.00 RFTS-130 1 0.50 2.33 2.69 1.15 2 0.63 2.52 2.33 1.3E-03 8.5E-04 3.1E-03 10.00 RFTS-131 1 0.50 2.33 2.69 1.15 2 0.63 2.50 2.33 1.3E-03 8.4E-04 3.1E-03 10.06 RFTS-132 1 0.50 2.33 2.69 1.15 2 0.63 2.50 2.33 1.3E-03 8.4E-04 3.1E-03 10.06 RFTS-133 1 0.50 2.33 2.69 1.15 10 0.63 2.52 11.66 1.3E-03 8.5E-04 1.6E-02 10.00 RFTS-134 1 0.50 2.33 2.69 1.15 10 0.63 2.50 11.63 1.3E-03 8.4E-04 1.6E-02 10.06 RFTS-135 1 0.50 2.51 2.90 1.15 25 0.65 3.03 31.36 1.4E-03 9.5E-04 3.9E-02 8.65 RFTS-136 1 0.50 2.49 2.88 1.15 25 0.65 2.98 31.14 1.4E-03 9.4E-04 3.9E-02 8.77 RFTS-137 1 0.50 2.49 2.88 1.15 25 0.65 2.98 31.14 1.4E-03 9.4E-04 3.9E-02 8.77 RFTS-138 1 0.50 2.50 2.89 1.15 4 0.65 3.02 5.01 1.4E-03 9.5E-04 6.3E-03 8.68 RFTS-139 1 0.50 2.50 2.89 1.15 4 0.65 3.02 5.01 1.4E-03 9.5E-04 6.3E-03 8.68 RFTS-140 1 0.50 2.50 2.89 1.15 4 0.65 3.02 5.01 1.4E-03 9.5E-04 6.3E-03 8.68 RFTS-141 1 0.50 2.49 2.88 1.15 4 0.65 2.98 4.98 1.4E-03 9.4E-04 6.3E-03 8.77 RFTS-142 1 0.50 2.49 2.88 1.15 3 0.65 2.98 3.74 1.4E-03 9.4E-04 4.7E-03 8.75 RFTS-143 1 0.50 2.51 2.90 1.15 2 0.65 3.03 2.51 1.4E-03 9.5E-04 3.1E-03 8.65 RFTS-144 1 0.50 2.49 2.88 1.15 2 0.65 2.98 2.49 1.4E-03 9.4E-04 3.1E-03 8.77 RFTS-145 1 0.50 2.50 2.88 1.15 4 0.65 3.00 5.00 1.4E-03 9.4E-04 6.3E-03 8.72 RFTS-146 1 0.50 2.49 2.88 1.15 4 0.65 2.98 4.99 1.4E-03 9.4E-04 6.3E-03 8.75 RFTS-147 1 0.50 2.50 2.89 1.15 3 0.65 3.02 3.76 1.4E-03 9.5E-04 4.7E-03 8.68 RFTS-148 1 0.50 2.50 2.88 1.15 3 0.65 2.99 3.74 1.4E-03 9.4E-04 4.7E-03 8.74 RFTS-149 1 0.50 2.49 2.88 1.15 3 0.65 2.98 3.74 1.4E-03 9.4E-04 4.7E-03 8.75 RFTS-150 1 0.50 2.49 2.88 1.15 3 0.65 2.98 3.74 1.4E-03 9.4E-04 4.7E-03 8.75 RFTS-151 1 0.50 2.51 2.90 1.15 2 0.65 3.03 2.51 1.4E-03 9.5E-04 3.1E-03 8.65 RFTS-152 1 0.50 2.51 2.90 1.15 2 0.65 3.03 2.51 1.4E-03 9.5E-04 3.1E-03 8.65 RFTS-153 1 0.50 2.51 2.90 1.15 2 0.65 3.03 2.51 1.4E-03 9.5E-04 3.1E-03 8.65 RFTS-154 1 0.50 2.49 2.88 1.15 2 0.65 2.98 2.49 1.4E-03 9.4E-04 3.1E-03 8.75 RFTS-155 1 0.50 2.51 2.90 1.15 25 0.65 3.03 31.36 1.4E-03 9.5E-04 3.9E-02 8.65 RFTS-156 1 0.50 2.49 2.88 1.15 25 0.65 2.98 31.14 1.4E-03 9.4E-04 3.9E-02 8.77 RFTS-157 1 0.50 2.49 2.88 1.15 25 0.65 2.98 31.14 1.4E-03 9.4E-04 3.9E-02 8.77 241 TAG Type (-) Do (mm) Pl/Do (-) Pt/Do (-) Pt/Pl (-) Nt (-) σ (-) Dh (mm) d (mm) Af (m²) Ac (m²) Ao (m²) Ao/V (cm²/cm³) RFTS-158 1 0.50 2.51 2.89 1.15 4 0.65 3.02 5.01 1.4E-03 9.5E-04 6.3E-03 8.66 RFTS-159 1 0.50 2.50 2.89 1.15 4 0.65 3.00 5.00 1.4E-03 9.4E-04 6.3E-03 8.71 RFTS-160 1 0.50 2.51 2.90 1.15 3 0.65 3.03 3.76 1.4E-03 9.5E-04 4.7E-03 8.65 RFTS-161 1 0.50 2.49 2.88 1.15 3 0.65 2.98 3.74 1.4E-03 9.4E-04 4.7E-03 8.77 RFTS-162 1 0.50 2.49 2.88 1.15 3 0.65 2.98 3.74 1.4E-03 9.4E-04 4.7E-03 8.77 RFTS-163 1 0.50 2.51 2.90 1.15 2 0.65 3.03 2.51 1.4E-03 9.5E-04 3.1E-03 8.65 RFTS-164 1 0.50 2.49 2.88 1.15 2 0.65 2.98 2.49 1.4E-03 9.4E-04 3.1E-03 8.77 RFTS-165 1 0.50 2.51 2.90 1.15 3 0.65 3.03 3.76 1.4E-03 9.5E-04 4.7E-03 8.65 RFTS-166 1 0.50 2.49 2.88 1.15 3 0.65 2.98 3.74 1.4E-03 9.4E-04 4.7E-03 8.77 RFTS-167 1 0.50 2.49 2.88 1.15 3 0.65 2.98 3.74 1.4E-03 9.4E-04 4.7E-03 8.77 RFTS-168 1 0.50 2.51 2.89 1.15 2 0.65 3.02 2.51 1.4E-03 9.5E-04 3.1E-03 8.66 RFTS-169 1 0.50 2.49 2.88 1.15 2 0.65 2.98 2.49 1.4E-03 9.4E-04 3.1E-03 8.77 RFTS-170 1 0.50 2.51 2.90 1.15 9 0.65 3.03 11.29 1.4E-03 9.5E-04 1.4E-02 8.65 RFTS-171 1 0.50 2.50 2.89 1.15 9 0.65 3.00 11.25 1.4E-03 9.4E-04 1.4E-02 8.71 RFTS-172 1 0.50 2.49 2.88 1.15 9 0.65 2.98 11.21 1.4E-03 9.4E-04 1.4E-02 8.77 RFTS-173 1 0.50 2.51 2.90 1.15 10 0.65 3.03 12.54 1.4E-03 9.5E-04 1.6E-02 8.65 RFTS-174 1 0.50 2.49 2.88 1.15 10 0.65 2.98 12.46 1.4E-03 9.4E-04 1.6E-02 8.77 Table 53. RFTS optimum designs performance. TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) NTU (-) h (W/m².K) Nu (-) j (-) RFTS-001 1.000 86.453 0.001 3.273 26.051 0.274 2.720 404.240 7.923 0.101 RFTS-002 1.000 86.453 0.001 3.273 26.051 0.274 2.720 404.240 7.923 0.101 RFTS-003 1.000 86.453 0.001 3.273 26.051 0.274 2.720 404.240 7.923 0.101 RFTS-004 1.000 86.940 0.001 3.318 26.498 0.273 2.738 405.600 7.854 0.100 RFTS-005 1.000 86.940 0.001 3.409 20.416 0.281 2.198 434.060 8.405 0.107 RFTS-006 1.000 86.940 0.001 3.599 14.371 0.296 1.635 484.440 9.381 0.120 RFTS-007 3.000 259.360 0.003 65.509 173.820 0.203 1.333 594.280 11.647 0.049 RFTS-008 3.000 259.360 0.003 65.509 173.820 0.203 1.333 594.280 11.647 0.049 RFTS-009 3.000 259.360 0.003 65.966 131.270 0.204 1.047 622.500 12.200 0.052 RFTS-010 3.000 259.360 0.003 65.966 131.270 0.204 1.047 622.500 12.200 0.052 RFTS-011 3.000 260.820 0.003 66.862 133.490 0.204 1.054 624.620 12.095 0.052 RFTS-012 3.000 260.820 0.003 66.862 133.490 0.204 1.054 624.620 12.095 0.052 RFTS-013 3.000 260.820 0.003 66.862 133.490 0.204 1.054 624.620 12.095 0.052 RFTS-014 3.000 259.360 0.003 67.658 89.759 0.210 0.756 674.220 13.214 0.056 RFTS-015 3.000 259.360 0.003 67.658 89.759 0.210 0.756 674.220 13.214 0.056 RFTS-016 3.000 260.820 0.003 68.568 91.261 0.209 0.761 676.590 13.101 0.056 RFTS-017 5.000 432.270 0.005 263.790 314.960 0.177 0.750 743.180 14.566 0.037 RFTS-018 5.000 433.500 0.005 265.550 317.590 0.176 0.753 744.420 14.501 0.037 RFTS-019 5.000 433.500 0.005 265.550 317.590 0.176 0.753 744.420 14.501 0.037 RFTS-020 5.000 433.500 0.005 265.550 317.590 0.176 0.753 744.420 14.501 0.037 RFTS-021 5.000 433.500 0.005 265.550 317.590 0.176 0.753 744.420 14.501 0.037 RFTS-022 5.000 432.270 0.005 266.840 212.400 0.179 0.533 791.520 15.513 0.039 RFTS-023 5.000 432.270 0.005 266.840 212.400 0.179 0.533 791.520 15.513 0.039 RFTS-024 5.000 432.270 0.005 266.840 212.400 0.179 0.533 791.520 15.513 0.039 RFTS-025 5.000 432.270 0.005 266.840 212.400 0.179 0.533 791.520 15.513 0.039 242 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) NTU (-) h (W/m².K) Nu (-) j (-) RFTS-026 5.000 434.700 0.005 270.380 215.920 0.178 0.536 794.230 15.379 0.039 RFTS-027 2.000 172.910 0.002 20.987 835.280 0.220 10.252 304.690 5.972 0.038 RFTS-028 2.000 173.880 0.002 21.274 849.440 0.219 10.314 305.550 5.917 0.038 RFTS-029 2.000 173.880 0.002 21.274 849.440 0.219 10.314 305.550 5.917 0.038 RFTS-030 2.000 172.910 0.002 21.602 107.470 0.226 2.085 495.840 9.718 0.062 RFTS-031 2.000 172.910 0.002 21.602 107.470 0.226 2.085 495.840 9.718 0.062 RFTS-032 2.000 172.910 0.002 21.602 107.470 0.226 2.085 495.840 9.718 0.062 RFTS-033 2.000 172.910 0.002 21.602 107.470 0.226 2.085 495.840 9.718 0.062 RFTS-034 2.000 172.910 0.002 21.972 65.586 0.230 1.369 542.510 10.633 0.068 RFTS-035 2.000 173.880 0.002 22.273 66.700 0.229 1.378 544.380 10.541 0.067 RFTS-036 2.000 173.880 0.002 23.091 46.100 0.238 1.008 596.920 11.559 0.074 RFTS-037 1.000 65.340 0.001 1.654 13.378 0.321 2.204 322.330 12.646 0.106 RFTS-038 1.000 65.340 0.001 1.670 10.808 0.324 1.830 334.410 13.120 0.110 RFTS-039 1.000 65.614 0.001 1.686 10.956 0.323 1.843 335.490 13.005 0.110 RFTS-040 1.000 65.340 0.001 1.716 8.327 0.333 1.453 354.020 13.889 0.117 RFTS-041 1.000 65.340 0.001 1.716 8.327 0.333 1.453 354.020 13.889 0.117 RFTS-042 1.000 65.614 0.001 1.732 8.442 0.332 1.463 355.250 13.771 0.117 RFTS-043 1.000 65.614 0.001 1.732 8.442 0.332 1.463 355.250 13.771 0.117 RFTS-044 1.000 65.340 0.001 1.818 5.884 0.353 1.064 388.860 15.256 0.128 RFTS-045 1.000 65.340 0.001 1.818 5.884 0.353 1.064 388.860 15.256 0.128 RFTS-046 1.000 65.614 0.001 1.836 5.965 0.352 1.072 390.340 15.131 0.128 RFTS-047 2.000 130.680 0.002 11.158 36.105 0.270 1.163 425.160 16.680 0.070 RFTS-048 2.000 131.230 0.002 11.265 36.594 0.270 1.171 426.520 16.534 0.070 RFTS-049 2.000 130.680 0.002 11.336 27.510 0.275 0.914 445.460 17.477 0.073 RFTS-050 2.000 130.680 0.002 11.336 27.510 0.275 0.914 445.460 17.477 0.073 RFTS-051 2.000 131.410 0.002 11.482 28.010 0.274 0.923 447.480 17.277 0.073 RFTS-052 2.000 131.410 0.002 11.482 28.010 0.274 0.923 447.480 17.277 0.073 RFTS-053 2.000 131.410 0.002 11.482 28.010 0.274 0.923 447.480 17.277 0.073 RFTS-054 2.000 130.680 0.002 11.813 19.112 0.286 0.660 482.310 18.923 0.079 RFTS-055 2.000 130.680 0.002 11.813 19.112 0.286 0.660 482.310 18.923 0.079 RFTS-056 2.000 131.410 0.002 11.964 19.457 0.285 0.666 484.690 18.714 0.079 RFTS-057 3.000 196.020 0.003 33.964 73.266 0.244 0.899 493.220 19.351 0.054 RFTS-058 3.000 196.570 0.003 34.178 73.922 0.243 0.904 494.260 19.236 0.054 RFTS-059 3.000 196.020 0.003 34.269 55.443 0.246 0.701 512.800 20.119 0.056 RFTS-060 3.000 196.020 0.003 34.269 55.443 0.246 0.701 512.800 20.119 0.056 RFTS-061 3.000 197.110 0.003 34.703 56.439 0.245 0.708 515.080 19.887 0.056 RFTS-062 3.000 197.110 0.003 34.703 56.439 0.245 0.708 515.080 19.887 0.056 RFTS-063 3.000 196.020 0.003 35.348 38.126 0.254 0.501 549.280 21.550 0.060 RFTS-064 3.000 196.020 0.003 35.348 38.126 0.254 0.501 549.280 21.550 0.060 RFTS-065 3.000 196.020 0.003 35.348 38.126 0.254 0.501 549.280 21.550 0.060 RFTS-066 3.000 197.110 0.003 35.793 38.808 0.253 0.506 551.920 21.309 0.060 RFTS-067 5.000 2837.600 0.015 892.760 17426.000 0.135 11.975 725.690 27.986 0.022 RFTS-068 5.000 2776.500 0.015 847.550 16439.000 0.137 11.650 710.480 27.725 0.022 RFTS-069 5.000 3293.600 0.015 1249.900 25368.000 0.121 14.433 841.150 32.856 0.022 RFTS-070 5.000 3293.600 0.015 1249.900 25368.000 0.121 14.433 841.150 32.856 0.022 RFTS-071 5.000 2718.700 0.015 808.860 15590.000 0.139 11.344 696.210 27.231 0.022 RFTS-072 5.000 2718.700 0.015 808.860 15590.000 0.139 11.344 696.210 27.231 0.022 RFTS-073 5.000 3421.100 0.015 1367.000 27991.000 0.118 15.137 874.430 34.320 0.022 RFTS-074 5.000 326.700 0.006 138.280 178.980 0.214 0.655 598.340 23.475 0.039 RFTS-075 5.000 326.700 0.006 138.280 178.980 0.214 0.655 598.340 23.475 0.039 243 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) NTU (-) h (W/m².K) Nu (-) j (-) RFTS-076 5.000 326.700 0.006 138.280 134.230 0.214 0.505 615.290 24.140 0.041 RFTS-077 5.000 327.150 0.006 138.700 134.810 0.214 0.506 615.950 24.070 0.041 RFTS-078 5.000 328.520 0.006 140.000 136.610 0.214 0.510 617.950 23.859 0.040 RFTS-079 5.000 328.520 0.006 140.000 136.610 0.214 0.510 617.950 23.859 0.040 RFTS-080 5.000 326.700 0.006 140.770 91.099 0.218 0.355 649.020 25.463 0.043 RFTS-081 5.000 326.700 0.006 140.770 91.099 0.218 0.355 649.020 25.463 0.043 RFTS-082 5.000 326.700 0.006 140.770 91.099 0.218 0.355 649.020 25.463 0.043 RFTS-083 5.000 328.520 0.006 142.500 92.701 0.217 0.359 652.020 25.174 0.043 RFTS-084 5.000 2275.400 0.016 483.510 8767.000 0.142 8.962 584.640 34.308 0.022 RFTS-085 5.000 287.140 0.007 104.850 118.100 0.240 0.515 540.380 31.850 0.041 RFTS-086 5.000 287.140 0.007 104.850 118.100 0.240 0.515 540.380 31.850 0.041 RFTS-087 5.000 287.140 0.007 104.900 88.617 0.240 0.394 552.240 32.549 0.041 RFTS-088 5.000 287.940 0.007 105.500 89.429 0.239 0.397 553.640 32.319 0.041 RFTS-089 5.000 288.470 0.007 105.910 89.979 0.239 0.398 554.580 32.168 0.041 RFTS-090 5.000 288.470 0.007 105.910 89.979 0.239 0.398 554.580 32.168 0.041 RFTS-091 5.000 287.140 0.007 107.050 60.289 0.245 0.275 577.210 34.021 0.043 RFTS-092 5.000 287.140 0.007 107.050 60.289 0.245 0.275 577.210 34.021 0.043 RFTS-093 5.000 287.140 0.007 107.050 60.289 0.245 0.275 577.210 34.021 0.043 RFTS-094 5.000 288.750 0.007 108.280 61.400 0.243 0.278 580.440 33.558 0.043 RFTS-095 1.000 50.432 0.002 0.621 18.123 0.262 5.421 219.710 21.448 0.094 RFTS-096 1.000 50.489 0.002 0.625 18.265 0.262 5.434 219.820 21.354 0.094 RFTS-097 1.000 50.489 0.002 0.625 18.265 0.262 5.434 219.820 21.354 0.094 RFTS-098 1.000 50.375 0.002 0.943 5.496 0.399 1.272 258.300 25.339 0.110 RFTS-099 1.000 50.375 0.002 0.943 5.496 0.399 1.272 258.300 25.339 0.110 RFTS-100 1.000 50.375 0.002 0.943 5.496 0.399 1.272 258.300 25.339 0.110 RFTS-101 1.000 50.489 0.002 0.950 4.445 0.399 1.045 264.170 25.662 0.113 RFTS-102 1.000 50.489 0.002 0.971 3.408 0.408 0.811 273.540 26.572 0.117 RFTS-103 1.000 50.375 0.002 1.024 2.387 0.433 0.571 289.960 28.445 0.124 RFTS-104 1.000 50.489 0.002 1.029 2.407 0.432 0.575 290.880 28.257 0.124 RFTS-105 2.000 100.860 0.003 5.558 81.111 0.293 3.694 299.410 29.228 0.064 RFTS-106 2.000 101.150 0.003 5.621 82.417 0.294 3.717 299.900 28.919 0.064 RFTS-107 2.000 101.150 0.003 5.621 82.417 0.294 3.717 299.900 28.919 0.064 RFTS-108 2.000 101.150 0.003 5.621 82.417 0.294 3.717 299.900 28.919 0.064 RFTS-109 2.000 100.810 0.003 6.415 14.963 0.339 0.663 336.170 32.898 0.072 RFTS-110 2.000 100.810 0.003 6.415 14.963 0.339 0.663 336.170 32.898 0.072 RFTS-111 2.000 100.810 0.003 6.415 14.963 0.339 0.663 336.170 32.898 0.072 RFTS-112 2.000 100.920 0.003 6.429 15.024 0.338 0.665 336.580 32.777 0.072 RFTS-113 2.000 101.150 0.003 6.457 15.147 0.337 0.669 337.400 32.535 0.072 RFTS-114 2.000 101.150 0.003 6.545 11.515 0.342 0.516 346.960 33.457 0.074 RFTS-115 3.000 151.210 0.005 19.421 188.760 0.304 3.011 366.460 35.863 0.052 RFTS-116 3.000 151.380 0.005 19.493 189.820 0.304 3.019 366.710 35.712 0.052 RFTS-117 3.000 151.380 0.005 19.493 189.820 0.304 3.019 366.710 35.712 0.052 RFTS-118 3.000 151.210 0.005 19.709 30.649 0.308 0.515 391.590 38.322 0.056 RFTS-119 3.000 151.210 0.005 19.709 30.649 0.308 0.515 391.590 38.322 0.056 RFTS-120 3.000 151.470 0.005 19.771 30.834 0.308 0.517 392.290 38.108 0.056 RFTS-121 3.000 151.720 0.005 19.989 23.447 0.310 0.398 401.580 38.724 0.057 RFTS-122 3.000 151.720 0.005 19.989 23.447 0.310 0.398 401.580 38.724 0.057 RFTS-123 3.000 151.210 0.005 20.552 15.980 0.321 0.274 417.550 40.863 0.059 RFTS-124 3.000 151.550 0.005 20.640 16.110 0.321 0.276 418.790 40.583 0.059 RFTS-125 5.000 251.880 0.008 81.177 56.754 0.275 0.286 483.680 47.449 0.041 244 TAG u (m/s) Re (-) Cmin (W/K) Ẇ" (W/m²) ΔP (Pa) f (-) NTU (-) h (W/m².K) Nu (-) j (-) RFTS-126 5.000 252.720 0.008 81.678 57.428 0.274 0.289 485.510 46.935 0.041 RFTS-127 5.000 252.720 0.008 81.678 57.428 0.274 0.289 485.510 46.935 0.041 RFTS-128 5.000 252.720 0.008 81.678 57.428 0.274 0.289 485.510 46.935 0.041 RFTS-129 5.000 252.020 0.008 83.080 38.759 0.281 0.197 498.560 48.790 0.043 RFTS-130 5.000 252.020 0.008 83.080 38.759 0.281 0.197 498.560 48.790 0.043 RFTS-131 5.000 252.440 0.008 83.334 38.989 0.280 0.198 499.620 48.534 0.043 RFTS-132 5.000 252.440 0.008 83.334 38.989 0.280 0.198 499.620 48.534 0.043 RFTS-133 5.000 252.020 0.008 95.109 221.850 0.321 1.002 507.950 49.709 0.043 RFTS-134 5.000 252.440 0.008 95.461 223.310 0.321 1.006 508.710 49.417 0.043 RFTS-135 1.000 48.399 0.002 0.495 13.418 0.236 4.940 215.520 25.403 0.096 RFTS-136 1.000 48.580 0.002 0.506 13.805 0.238 4.984 215.890 24.997 0.096 RFTS-137 1.000 48.580 0.002 0.506 13.805 0.238 4.984 215.890 24.997 0.096 RFTS-138 1.000 48.444 0.002 0.876 3.807 0.417 0.926 251.970 29.569 0.112 RFTS-139 1.000 48.444 0.002 0.876 3.807 0.417 0.926 251.970 29.569 0.112 RFTS-140 1.000 48.444 0.002 0.876 3.807 0.417 0.926 251.970 29.569 0.112 RFTS-141 1.000 48.580 0.002 0.881 3.848 0.415 0.934 252.810 29.272 0.112 RFTS-142 1.000 48.557 0.002 0.898 2.941 0.424 0.720 260.240 30.201 0.115 RFTS-143 1.000 48.399 0.002 0.945 2.050 0.451 0.501 273.220 32.204 0.121 RFTS-144 1.000 48.580 0.002 0.952 2.079 0.449 0.507 274.800 31.819 0.122 RFTS-145 2.000 97.024 0.003 5.967 13.000 0.353 0.593 321.970 37.530 0.071 RFTS-146 2.000 97.113 0.003 5.978 13.045 0.353 0.595 322.320 37.406 0.071 RFTS-147 2.000 96.887 0.003 6.027 9.822 0.358 0.453 328.860 38.592 0.073 RFTS-148 2.000 97.069 0.003 6.048 9.891 0.358 0.456 329.660 38.342 0.073 RFTS-149 2.000 97.113 0.003 6.053 9.908 0.357 0.456 329.860 38.281 0.073 RFTS-150 2.000 97.113 0.003 6.053 9.908 0.357 0.456 329.860 38.281 0.073 RFTS-151 2.000 96.799 0.003 6.282 6.813 0.375 0.315 343.430 40.479 0.076 RFTS-152 2.000 96.799 0.003 6.282 6.813 0.375 0.315 343.430 40.479 0.076 RFTS-153 2.000 96.799 0.003 6.282 6.813 0.375 0.315 343.430 40.479 0.076 RFTS-154 2.000 97.113 0.003 6.321 6.897 0.373 0.318 345.100 40.049 0.076 RFTS-155 3.000 145.200 0.005 16.899 152.730 0.299 2.732 357.560 42.145 0.053 RFTS-156 3.000 145.740 0.005 17.121 155.830 0.299 2.757 358.360 41.494 0.053 RFTS-157 3.000 145.740 0.005 17.121 155.830 0.299 2.757 358.360 41.494 0.053 RFTS-158 3.000 145.260 0.005 18.308 26.497 0.323 0.458 374.580 44.054 0.055 RFTS-159 3.000 145.470 0.005 18.353 26.632 0.322 0.460 375.180 43.832 0.056 RFTS-160 3.000 145.200 0.005 18.422 19.979 0.325 0.349 380.700 44.872 0.056 RFTS-161 3.000 145.740 0.005 18.547 20.257 0.324 0.353 382.500 44.289 0.056 RFTS-162 3.000 145.740 0.005 18.547 20.257 0.324 0.353 382.500 44.289 0.056 RFTS-163 3.000 145.200 0.005 19.065 13.785 0.337 0.241 394.780 46.532 0.059 RFTS-164 3.000 145.740 0.005 19.194 13.976 0.335 0.244 396.900 45.956 0.059 RFTS-165 5.000 242.000 0.009 75.595 49.192 0.288 0.254 461.480 54.394 0.041 RFTS-166 5.000 242.900 0.009 76.085 49.860 0.287 0.257 463.580 53.677 0.041 RFTS-167 5.000 242.900 0.009 76.085 49.860 0.287 0.257 463.580 53.677 0.041 RFTS-168 5.000 242.110 0.009 77.383 33.599 0.295 0.174 472.770 55.602 0.042 RFTS-169 5.000 242.900 0.009 77.820 33.998 0.294 0.175 474.900 54.988 0.042 RFTS-170 5.000 242.000 0.009 85.687 167.280 0.327 0.793 480.580 56.645 0.043 RFTS-171 5.000 242.440 0.009 85.933 168.340 0.326 0.797 481.310 56.231 0.043 RFTS-172 5.000 242.900 0.009 86.184 169.430 0.325 0.801 482.050 55.816 0.043 RFTS-173 5.000 242.000 0.009 87.036 188.790 0.332 0.898 489.460 57.691 0.044 RFTS-174 5.000 242.900 0.009 87.743 191.670 0.331 0.907 491.170 56.872 0.044 245 Appendix G - Performance Evaluation Criteria Analysis Excerpt from Purdue publication: Bacellar, D., Aute, V., Radermacher, R., Performance Evaluation Criteria Analysis of Compact Air-to-Refrigerant Heat Exchangers and Selection Utility Function for Single Phase Applications, 16th International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016. Introduction The research on heat transfer augmentation (HTA) relentlessly seeks developing highly compact heat exchangers (CHX) with high performance surfaces. A CHX is the definition of high surface-to-volume ratio [4]. The definition of high-performance surface, however, is more subject to interpretations, particularly when evaluating a full-sized HX. The sole evaluation of the thermal- hydraulic ratio of a surface do not necessarily portray the broader characteristics in the context of the HX, including overall size, face area and degradation aspects. The literature on HX Performance Evaluation Criteria (PEC) is quite extensive. There are two main approaches to assess the HX PEC: a) energy-based (first law of thermodynamics); b) entropy-based (second law of thermodynamics). Cowell (1990) revised the main categories within the energy-based PEC. The first, known as “area goodness” factor, is a typical way of evaluating surfaces and HX’s, and is simply defined as the ratio of j and f factors (equation 1). The main advantage of such metric is the non-dimensional aspect, which allows one to 246 compare surfaces regardless the geometrical scale, particularly the surface hydraulic diameter. Although it well represents the surface characteristics, it leads to potential skewed evaluation of the HX or even biasing the search made by an optimizer. The simplified form shows the dependency to the thermal conductance and the inverse of the pressure drop and the square of the minimum free flow area. In other words, this metric can only have some meaning either if the thermal hydraulic ratio is fixed or if the minimum free flow area is fixed. Furthermore, the general knowledge is that this factor is inversely proportional to the Reynolds number, which is not necessarily desired to be relatively low. The reason for this is that the pressure drop and face area (assuming constant flow rate) terms are more sensitive to the variation in velocity than for the thermal conductance. If one uses this metric as an optimization objective there is a possibility the optimizer will search for either low- pressure drop and/or small face area designs instead of lower thermal resistance. 2 2/3 2/3 2 2 1 Pr2 Pr , 2 tuc c p o c c Nj mA Ph K K u c A uf A P                  (96) 1, 1.0; ,0.0 1.0; m nc c c cP u m h u n A u        (97) The second category is the “volume goodness”, also described by London (1964) but discussed in other relevant publications including Kays and London (1984), Webb and Kim (2005) and Shah (1978). This category evaluates the dimensioned heat transfer coefficient and pressure drop (in the form of pumping power per surface area) (equation 3). The common observation with regards to 247 these metrics is their dependency to the hydraulic diameter, thus in order for one to make a fair comparison between two or more designs they must have the same hydraulic diameters [90, 92, 93, 94]. Additionally, the reduction in pressure drop is usually simpler to obtain instead of improving the heat transfer coefficient, thus normally resulting in large face area designs. 2 23 3 2/3 2 3 2 2/3 2" 2Re Re Pr 2 Pr Re/ p p h h ho c j c Dh h j f D D fW P V A                     (98) The third main category identified by Cowell (1990) include the 12 scenario design method [95] , which are at most limited to one or more fixed parameters, in addition to fixed hydraulic diameters. Such category was not intended to be applied to actual variable geometry HX’s, much less comparing multiple HX’s with very different surface types. The fourth category, and Cowell’s (1990) own method, account for methods that are either of diffusive interpretation, very particular or by any means extendable to a more general method, or a variation of the previous categories. In spite of the particular issues and limitations, the common denominator to all energy-based PEC metrics is the premise that the performance degradation is solely due to the hydraulic resistance. When one thinks of degradation, it can be flatly interpreted as the direct energy cost for driving the fluid through the HX. Alternatively, the degradation can be interpreted as everything that can cause a 248 negative impact not only on the overall HX performance but also to a larger control volume including a system of sub components (Shah, 2006). For the second interpretation, the entropy-based PEC (or thermodynamic) approach is more appropriate. Additionally, in many cases the entropy generation due to the finite temperature difference is significantly larger than it is for the pressure drop. McClintock (1951) introduced the concept of irreversibility to HX design, which was later formalized by Bejan (1977) where he defined the concept of Number of Entropy Generation Units (NS) as an evaluation metric. His work culminated in the idealization of the Entropy Generation Minimization (EGM) for broad applications of finite-size systems and finite-time processes (Bejan et al., 1996). min gen S S N C  (99) According to the literature, it is well established that the tradeoff between energy-based and entropy-based approaches comprises balancing out the HX size and production costs directly for savings in energy degradation (irreversibilities) (Bejan, 1977) further down the process. It is also a common sense that a larger and “more expensive” HX is more thermodynamically efficient (Bejan, 1977), and better heat transfer performance does not lead to minimum entropy generation (Bejan & Pfister, 1980; Seculik & Herman, 1986). The evolution of computational tools (such as CFD), optimization algorithms, storage capacities, processing speed and manufacturing technologies enable a large number of novel ideas and concepts establishing new frontiers. 249 Unfortunately, while the more novel heat transfer types and shapes are being developed the less clear their consequences are to a full HX design. Furthermore, it is becoming harder to compare and select an optimum HX on a fair basis. In this paper, we propose the use of a set of comprehensive metrics attempting to address the challenges from the common PEC approaches. We show how the optimization outcomes can be shifted when using different objectives and demonstrate why one metric should be chosen over the other. HX Evaluation Criteria Performance-Degradation Number Considering the brief literature review in the previous section, it should be clear that we want to find a metric that, not only carries quantitative and qualitative information regarding the performance and degradation aspects, but also it has to be sufficiently general so one can compare multiple HX types fairly. Bejan (1982) first studied the relationship between the Number of Entropy Generation Units (Ns) and the Number of Transfer Units (Ntu) for a balanced counter flow HX with no pressure drop. He encountered what was called the “entropy generation paradox” when the Ns went to zero for either Ntu = 0 or ∞, but reached a maximum at an intermediate Ntu. Shah & Skiepko (2004) interpreted such behavior as the irreversibility tend to zero whenever the heat transfer potential is zero; i.e. at NTU = 0 there is no heat flow thus, from the Second Law, Sgen has to be zero for it cannot be negative. When NTU  ∞ the hot and cold stream temperatures approach to the same value, thus nulling the heat transfer potential. Ogiso (2003) defined the dimensionless “entropy generation index” (Ns/Ntu) and 250 showed that the Bejan’s paradox can be Shah & Skiepko (2004) since the index is not defined at NTU = 0 or NTU  ∞. This metric satisfies the criteria we looked for since it provides the information on the thermal performance (Ntu), the degradation factors (Ns) and is non-dimensional. In this paper, we use the inverse and call it the performance- degradation number (equation 5). The reason is merely convenience; to have a number, which higher values are better. tu s N N   (100) For purposes of this paper, all analysis will focus on the airside. With this assumption, we can use the ideal gas model to calculate ψ. ln lno ogen gen p i i T Pq q s s s c R T T T P                    (101) , , , , , ,, ln , ln gen T gen Po tu ml o s s T s P s T s P i o S sT N T P P N N N N N C T T R P                           (102)     maxln ln tu tu o o o otu ml i o i o N N T P P T P PN T T T P T T P T                    (103) 251 On equation (8) it is clear that the performance degradation number has on its denominator, in addition to the pressure drop, the finite temperature difference contribution. HX Compactness and Face Area Typically, when using EGM or any other entropy-based PEC for designing a HX the trade-off between size and low entropy generation is always an issue. In reality, the larger HX’s actually have larger heat transfer surfaces in order to reduce the overall thermal resistance. For conventional surface types and dimensions, larger area will naturally result in larger volumes, thus the reference to the HX size. However, the next generation of HX’s is shifting to novel shapes and towards smaller tube sizes, which result in surfaces that are more compact. Additionally, smaller sized surfaces have higher heat transfer coefficients. In other words, these novel HX’s have the potential to reduce thermal resistance in a smaller envelope compared to conventional HX’s, but not proportionally increasing the surface area once the heat transfer coefficient is higher. Additionally, the term “size” is normally used loosely, i.e. most studies do not qualify what aspect of the size is the most relevant. In many applications, the envelope volume is not much of an issue as long as the design can satisfy potential limitations on tube length, face area and/or aspect ratio. The face area can be more critical since it can affect the cross section of an air duct, size of an equipment casing, or the size of the front of a car. Ultimately, the metrics that better evaluate the geometrical aspects of a HX are the face area and the surface hydraulic diameter (equation 9), since it represents the inverse of compactness. 252 4 4h c o oD A A d V A  (104) HX Design In this paper, we study the design of a 1.0 kW air-to-water HX in cross flow. We investigate two different HX surfaces: a) round bare tubes in staggered arrangement with diameters below 2.0mm (RTHX), b) Webbed NURBS tube (NURBS shaped channels connected by a longitudinal web) (WTHX). Here we investigate how the different performance metrics affect the optimization results. For this study, we solve three multi-objective optimization problems targeting minimizing face area and maximizing ψ, j/f, and h/ΔP, respectively for each problem. Figure 146: HX surface types: a) RTHX; b) WTHX. Table 54: Optimization Problem. Optimization OPT01 OPT02 OPT03 Objectives min Af min Af min Af max h/ΔP max j/f max ψ Constraints 1.0 < Q < 1.01kW VHX ≤ VHX, baseline ΔPair ≤ ΔPair, baseline ΔPwater ≤ ΔPwater 0.61