ABSTRACT Title of Document: FORCE FED MICROCHANNEL HIGH HEAT FLUX COOLING UTILIZING MICROGROOVED SURFACES Edvin Cetegen, Doctor of Philosophy, 2010 Directed By: Michael Ohadi, Professor Department of Mechanical Engineering Among other applications, the increase in power density of advanced electronic components has created a need for high heat flux cooling. Future processors have been anticipated to exceed the current barrier of 1000 W/cm2, while the working temperature of such systems is expected to remain more or less the same. Currently, the well known cooling technologies have shown little promise of meeting these demands. This dissertation investigated an innovative cooling technology, referred to as force-fed heat transfer. Force-fed microchannel heat sinks (FFMHS) utilize certain enhanced microgrooved surfaces and advanced flow distribution manifolds, which create a system of short microchannels running in parallel. For a single-phase FFMHS, a numerical model was incorporated in a multi-objective optimization algorithm, and the optimum parameters that generate the maximum heat transfer coefficients with minimum pumping power were identified. Similar multi-objective optimization procedures were applied to Traditional Microchannel Heat Sinks (TMHS) and Jet Impingement Heat Sinks (JIHS). The comparison study at optimum designs indicates that for a 1 x 1 cm2 base heat sink area, heat transfer coefficients of FFMHS can be 72% higher than TMHS and 306% higher than JIHS at same pumping power. For two-phase FFMHS, three different heat sink designs incorporating microgrooved surfaces with microchannel widths between 21 ?m and 60 ?m were tested experimentally using R-245fa, a dielectric fluid. It was demonstrated that FFMHS can cool higher heat fluxes with lower pumping power values when compared to conventional methods. The flow and heat transfer characteristics in two-phase mode were evaluated using a visualization test setup. It was found that at low hydraulic diameter and low mass flux, the dominant heat transfer mechanism is dynamic rapid bubble expansion leading to an elongated bubble flow regime. For high heat-flux, as well as combination of high heat flux and high hydraulic diameters, the flow regimes resemble the flow characteristics observed in conventional tubes. The present research is the first of its kind to develop a better understanding of single-phase and phase-change heat transfer in FFMHS through flow visualization, numerical and experimental modeling of the phenomena, and multi-objective optimization of the heat sink. FORCE FED MICROCHANNEL HIGH HEAT FLUX COOLING UTILIZING MICROGROOVED SURFACES By Edvin Cetegen 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 2010 Advisory Committee: Professor Michael Ohadi, Chair/Advisor Professor Avram Bar-Cohen Professor Marino di Marzo Professor Jungho Kim Professor Gary Pertmer Research Professor Serguei Dessiatoun ? Copyright by Edvin Cetegen 2010 ii Dedication To my wife, Basak, my son, Alp, and to my parents for their endless encouragement and support that helped me complete this work iii Acknowledgments First and foremost I would like to express my deepest appreciation to Dr. Serguei Dessiatoun for his guidance, encouragement, help and support. What I learned from him, I will always carry with me throughout the rest of my life. I am grateful to my advisor, Dr. Michael Ohadi not only for his dedication, intellectual guidance and support but also for teaching me how to push further my limits and capabilities. I also wish to thank to Dr. Avram Bar-Cohen for his help and technical guidance. His invaluable experience, comments and feedback helped me to see the light at end of the tunnel. I would like to take this opportunity to thank Dr. Amir Shooshtari for his help and support throughout the course of this research project. I am also grateful for my friends at Smart and Small Thermal Systems Laboratory for providing a stimulating, constructive and peaceful working environment. It was a pleasure to work beside Dr. Parisa Foroughi, Dr. Sourav Chowdhury, Dr. Ebrahim Al-Hajri, Dr. Mohammed Al Shehhi, Mr. Tim McMillin, Mr. Thomas Baummer, Ms. Elnaz Kermani and Mr. Ratnesh Tiwari. Finally, the acknowledgements would not be complete without thanks to the Office of Naval Research and the Center for Environmental Energy Engineering, Advanced Heat Exchangers Consortium who provided the financial support and made this research possible. iv Table of Contents List Of Tables ............................................................................................................ VII List Of Figures ......................................................................................................... VIII List Of Acronyms .................................................................................................... XIII Nomenclature ........................................................................................................... XIV CHAPTER 1: INTRODUCTION ................................................................................. 1 1.1. Motivation of the Study ............................................................................. 1 1.2. Research Objectives ................................................................................... 5 1.3. Dissertation Organization .......................................................................... 6 CHAPTER 2: WORKING PRINCIPLES AND THEORETICAL BACKGROUND . 8 2.1. Force Fed Microchannel Heat Sinks (FFMHS) ......................................... 8 2.2. The Microgrooved Surfaces ..................................................................... 11 2.3. FFMHS for Single-Phase Heat Transfer .................................................. 13 2.3.1. Heat Transfer and Pumping Power in Short Channels .................. 14 2.3.2. Heat Transfer and Pressure Drop for Thermally and Hydrodynamically Developing Flow ...................................................... 18 2.3.3. Heat Transfer and Pressure Drop in Turning Bends ..................... 20 2.3.4. Literature Survey on Single-Phase FFMHS .................................. 22 2.4. FFMHS for Two Phase Heat Transfer ..................................................... 31 2.4.1. Flow Boiling in Conventional Channels ....................................... 33 2.4.2. Flow Boiling in Microchannels ..................................................... 35 2.4.3. Effect of Channel Hydraulic Diameter on Inception of Nucleate Boiling ..................................................................................................... 42 2.4.4. Critical Heat Flux in Microchannels ............................................. 44 2.4.5. Literature Survey on Two-Phase Heat Transfer in Microchannels 46 2.4.6. Literature Survey on High Heat Flux Cooling Using Dielectric Working Fluids ........................................................................................ 50 2.1. Summary .................................................................................................. 54 CHAPTER 3: SINGLE-PHASE NUMERICAL STUDY .......................................... 55 3.1. Computational Domain ............................................................................ 55 3.2. Single-Phase Modeling with Computational Fluid Dynamics................. 58 3.3. Numerical Simulation of a Sample FFMHS ............................................ 61 3.3.1. Grid Generation and Numerical Mesh .......................................... 61 3.3.2. Boundary Conditions and Output Parameters ............................... 62 3.3.3. Grid Independency Test ................................................................ 65 3.3.4. Numerical Results ......................................................................... 66 3.4. Parametric Numerical Study .................................................................... 78 3.4.1. Practical Geometrical Range of Microgrooved Surfaces Fabricated by Micro Deformation Technology ......................................................... 80 3.4.2. Effect of Fin Thickness and Fin Height ........................................ 80 3.4.3. Effect of Microchannel Width ....................................................... 85 3.4.4. Effect of Inlet and Outlet Feed Channel Widths ........................... 87 3.4.5. Effect of Microchannel Length ..................................................... 89 3.4.6. Effects of Microgrooved Surface Base Thickness and Manifold Height ...................................................................................................... 91 v 3.5. Conclusions .............................................................................................. 91 CHAPTER 4: MULTI-OBJECTIVE OPTIMIZATION OF SINGLE-PHASE FFMHS ..................................................................................................................................... 93 4.1. Heat Sink Design and Optimization ........................................................ 93 4.2. Parametric CFD Simulation Interface ...................................................... 95 4.3. Approximation Assisted Optimization .................................................... 98 4.3.1. Design of Experiment .................................................................... 99 4.3.2. Metamodeling .............................................................................. 100 4.3.3. Metamodeling Validation ............................................................ 102 4.3.4. Multi-Objective Optimization ..................................................... 103 4.4. Selection of Optimization Parameters ................................................... 104 4.5. Single-Phase Optimization Results of FFMHS ..................................... 107 4.5.1. Analysis of Optimum FFMHS Geometry ................................... 110 4.6. Single-Phase Cooling Technology Comparison Study .......................... 116 4.6.1. Single-Phase Optimization of TMHS .......................................... 116 4.6.2. Single-Phase Optimization of JIHS ............................................. 118 4.6.3. Performance Comparison of FFMHS, TMHS and JIHS ............. 122 4.7. Conclusions ............................................................................................ 127 CHAPTER 5: EXPERIMENTAL TEST SETUP ..................................................... 130 5.1. Experimental Test Setup ........................................................................ 130 5.2. Test Chamber ......................................................................................... 133 5.2.1. Flow Distribution Header ............................................................ 137 5.2.2. The Heater Assembly .................................................................. 139 5.3. Working Fluid Selection ........................................................................ 141 5.4. Calculation of Heat Losses .................................................................... 144 5.4.1. Heat Loss Evaluation and Calculation for a Sample Case .......... 151 5.5. Uncertainty Propagation Calculations ................................................... 153 5.6. Summary ................................................................................................ 154 CHAPTER 6: EXPERIMENTAL RESULTS ON FFMHS THERMAL PERFORMANCE ..................................................................................................... 155 6.1. Experimental Procedure ......................................................................... 155 6.2. Data Reduction....................................................................................... 158 6.3. Single Phase Heat Transfer and Pressure Drop ..................................... 163 6.4. Two-Phase Heat Transfer and Pressure Drop ........................................ 168 6.4.1. Surface #17 .................................................................................. 172 6.4.2. Surface #12 .................................................................................. 178 6.4.3. Surface #C ................................................................................... 182 6.5. Comparison of Experimental Data with Convective Saturated Boiling Correlations ................................................................................................... 185 6.5.1. Chen correlation .......................................................................... 190 6.5.2. Kandlikar correlation ................................................................... 191 6.5.3. Tran correlation ........................................................................... 193 6.5.4. Lazarek and Black correlation ..................................................... 193 6.5.5. Warrier correlation ...................................................................... 194 6.5.6. Results ......................................................................................... 194 6.6. Critical Heat Flux Results ...................................................................... 199 vi 6.7. Performance Comparison of FFMHS with Other High Heat Flux Cooling Technologies ................................................................................................. 203 6.8. Conclusions ............................................................................................ 205 CHAPTER 7: VISUALIZATION STUDY .............................................................. 208 7.1. Introduction to Visualization Study ....................................................... 208 7.2. Visualization Test Section ..................................................................... 211 7.3. Heat Loss Calculations and Data Reduction .......................................... 217 7.4. Visualization Results for Gap of 225 ?m and G=200 kg/m2s ............... 221 7.5. Visualization Results for Gap of 70 ?m and G=240 kg/m2s ................. 230 7.6. Visualization Results for Gap of 70 ?m and G=780 kg/m2s ................. 236 7.7. Conclusions ............................................................................................ 240 CHAPTER 8: CONCLUSIONS AND FUTURE WORK RECOMMENDATIONS ................................................................................................................................... 251 8.1. Conclusions Summary ........................................................................... 251 8.2. Future Work Recommendations ............................................................ 254 CHAPTER 9: APPENDICES ................................................................................... 259 9.1. Appendix A ............................................................................................ 259 9.1.1. Test chamber assembly ............................................................... 260 9.1.2. Test Chamber Flow Distribution Header .................................... 261 9.1.3. Test Chamber Top Flange ........................................................... 262 9.1.4. Test Chamber Bottom Flange ...................................................... 263 9.1.5. Test Chamber Heater Assembly .................................................. 264 9.1.6. Test Chamber Microgrooved Surface ......................................... 265 9.1.7. Visualization Test Section Assembly .......................................... 266 9.1.8. Visualization Test Section Base .................................................. 267 9.1.9. Visualization Test Section Heat Conductor ................................ 268 9.1.10. Visualization Test Section Teflon Layer 2 ................................ 269 9.1.11. Visualization Test Section Teflon Layer 1 ................................ 270 9.2. Appendix B ............................................................................................ 271 9.3. Appendix C ............................................................................................ 274 9.3.1. TMHS Model Used in Optimization ........................................... 274 9.3.2. TMHS Optimization Results ....................................................... 279 9.3.3. JIHS Optimum Results ................................................................ 282 9.4. Appendix D ............................................................................................ 284 REFERENCES ......................................................................................................... 286 vii List of Tables Table 2-1. Dimensions of tested microgrooved surface and feed channels (all dimensions in microns) ................................................................................... 13 Table 2-2. Summary of related work on single phase FFMHS?s ............................... 29 Table 2-3. Publication list of recent work performed for boiling in microchannels ... 48 Table 2-4. Summary of technologies used for high heat flux cooling ........................ 53 Table 3-1. The boundary conditions applied to computational domain ..................... 63 Table 3-2. Results of grid independency test .............................................................. 66 Table 3-3. Numerical simulation results for reference cases ...................................... 68 Table 4-1.The curve fit coefficients for Equations (4-7),(4-8) and (4-9) ................. 125 Table 5-1. List of system components used in the experimental test setup .............. 131 Table 5-2. Properties of common refrigerants at 30?C saturated liquid phase ......... 144 Table 6-1. Experimental test conditions for FFMHS utilizing microgrooved Surface #12................................................................................................................. 170 Table 6-2. Experimental test conditions for FFMHS utilizing microgrooved Surface #17................................................................................................................. 170 Table 6-3. Experimental test conditions for FFMHS utilizing microgrooved Surface #C .................................................................................................................. 171 Table 7-1. Summary of parameters used for visualization tests ............................... 221 Table 9-1. Optimum results obtained for the 1 x 1 cm2 TMHS ................................ 279 Table 9-2. Optimum results obtained for the 2 x 2 cm2 TMHS ................................ 280 Table 9-3. Optimum results obtained for JIHS ......................................................... 282 viii List of Figures Figure 2-1. Schematic flow representation of a typical FFMHS .................................. 9 Figure 2-2. (a) Picture of a typical microgrooved surface profile fabricated with MDT, (b) Profile of three microgrooved surfaces selected for present study 13 Figure 2-3. Schematic of flow in (a) single long channel and (b) multiple short channels........................................................................................................... 15 Figure 2-4. Flow and heat transfer regimes in a uniformly heated horizontal circular tube (adopted from (Ghiaasiaan, 2008)) ......................................................... 33 Figure 2-5. Major flow regimes for flows in microchannels observed by (Cornwell & Kew, 1992) ...................................................................................................... 36 Figure 2-6. Flow boiling regimes proposed by (Kandlikar, 2003) ............................. 39 Figure 2-7. Rapid bubble growth in 200 micron square microchannels observed by (Steinke & Kandlikar, 2003)-Each image is 8 milliseconds apart .................. 40 Figure 2-8. Diagram illustrating a liquid slug, an elongated bubble and a vapor slug of model developed by (Thome et al., 2004) ...................................................... 41 Figure 2-9. Cyclic variation in heat transfer coefficient with time (adopted from (Thome et al., 2004)) ...................................................................................... 42 Figure 3-1. Numerical computational domain ............................................................ 56 Figure 3-2. (a) Front view and (b) perspective view for grid generated for Hch=480 ?m, wch/2=36 ?m, tfin/2 = 24 ?m, L=800 ?m, wl/2=200 ?m, wv/2=200 ?m, Lman=2 mm, Hbase = 400 ?m ............................................................................ 63 Figure 3-3. (a) Variation of effective heat transfer coefficient with Reynolds number, (b) Variation of pumping power with Reynolds number ................................ 67 Figure 3-4. Velocity vectors and velocity magnitude distribution at z=0 for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K .......................................................................................... 69 Figure 3-5. Static pressure distribution at z=0 for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K ................. 69 Figure 3-6. Velocity vectors created by secondary flows at several cross sections in the computational domain for Case #3 at h=250,000 W/m2K and De=61 ..... 73 Figure 3-7. Pathlines at z=0 plane for (a) Case #1 at h=50,000 W/m2K and De=2, (b) Case #2 at h=150,000 W/m2K and De=16, (c) Case #3 at h=250,000 W/m2K and De=61 ....................................................................................................... 74 Figure 3-8. Working fluid temperature distribution at z=0 for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K ......................................................................................................................... 75 Figure 3-9. Fin feat flux distribution for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K ............................... 75 Figure 3-10. Temperature contours of fin surface, microchannel bottom wall and base material for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K ..................................................... 77 ix Figure 3-11. Effect of fin and microchannel height (Hch) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K ......................................................................................................................... 82 Figure 3-12. Schematic of flow and a typical streamline for (a) high channel height (b) low channel height FFMHS configuration ................................................ 83 Figure 3-13. Effect of fin thickness (tfin) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K .......... 83 Figure 3-14. Effect of microchannel width (wch) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K .......... 86 Figure 3-15. Effect of inlet feed channel width (wl) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K .......... 88 Figure 3-16. Effect of outlet feed channel width (wv) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K ......................................................................................................................... 88 Figure 3-17. Effect of microchannel length (Lch) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K .......... 90 Figure 4-1. Flow diagram for Parametric CFD Simulation Interface ......................... 97 Figure 4-2. Example of Kriging (adopted from (Wikipedia?, 2009)) ..................... 102 Figure 4-3. Distribution of objective functions for sampling points obtained for FFMHS optimization study........................................................................... 108 Figure 4-4. Distribution of objective functions for sampling and validation points obtained for FFMHS optimization study ...................................................... 109 Figure 4-5. Distribution of objective functions for sampling and optimal points obtained for FFMHS optimization study ...................................................... 109 Figure 4-6. Variation of Reynolds and Dean numbers with pumping power ........... 114 Figure 4-7.Variation of microchannel height with pumping power ......................... 114 Figure 4-8. Variation of microchannel width and fin thickness with pumping power ....................................................................................................................... 114 Figure 4-9.Variation of inlet and outlet feed channel widths with pumping power . 114 Figure 4-10. Variation of fin density with pumping power ...................................... 115 Figure 4-11. Variation of manifold number per cm with pumping power ............... 115 Figure 4-12. Variation of surface temperature uniformity with pumping power ..... 115 Figure 4-13. Variation of channel velocity with pumping power ............................. 115 Figure 4-14. TMHS model used in optimization study ............................................ 117 Figure 4-15. Optimum Pareto solutions of TMHS at 1 x 1 cm2 and 2 x 2 cm2 base areas .............................................................................................................. 118 Figure 4-16. Jet impingement heat sink (JIHS) developed by (Meyer et al., 2005) . 119 Figure 4-17. (a) Schematic of flow in a typical JIHS, (b) Computational domain ... 120 Figure 4-18. Sampling, optimum and validation point distribution for optimization process of JIHS ............................................................................................. 122 Figure 4-19. Optimum Pareto solution for three cooling technologies for 1 x 1 cm2 base area heat sink ........................................................................................ 124 Figure 4-20. Optimum Pareto solution for three cooling technologies for 2 x 2 cm2 base area heat sink ........................................................................................ 124 Figure 4-21. Optimum heat transfer coefficients for three cooling technologies at constant pumping power (a) 1 x 1 cm2 heat sink, (b) 2 x 2 cm2 heat sink .... 126 x Figure 4-22. Optimum pumping power values for three cooling technologies at constant heat transfer coefficient (a) 1 x 1 cm2 heat sink, (b) 2 x 2 cm2 heat sink ................................................................................................................ 126 Figure 5-1. Experimental test setup used for single-phase and two-phase thermal performance tests .......................................................................................... 132 Figure 5-2. Flow diagram of experimental test setup ............................................... 133 Figure 5-3. Picture of the experimental test chamber ............................................... 135 Figure 5-4. Schematic of the experimental test chamber .......................................... 136 Figure 5-5. (a) 3D view of flow distribution header, (b) picture of the actual flow distribution header ........................................................................................ 137 Figure 5-6. (a) Flow distribution in the header, (b) Position of thermocouples ....... 138 Figure 5-7. The heater assembly (a) exploded schematic view, (b) actual picture and schematic of assembled view ........................................................................ 141 Figure 5-8. Thermocouple locations on the back of the microgrooved surface ....... 141 Figure 5-9. Resistance analogy for heat transfer in heater assembly ........................ 145 Figure 5-10. Temperature distribution on the bottom part of the heater assembly for a thin-film resistor temperature of 320 K and 300K fluid temperature ........... 147 Figure 5-11. Thermal resistance network between microgrooved surface base and ambient fluid ................................................................................................. 147 Figure 5-12. Thermal resistance network between the microgrooved surface base and the fluid in the microchannel and manifold channel ..................................... 149 Figure 5-13. Experimentally measured Rmm values .................................................. 151 Figure 5-14. Percentage of parasitic heat loss distribution and boiling curve for FFMHS using microgrooved Surface #17 at G=1000 kg/m2s constant mass flux ................................................................................................................ 152 Figure 6-1. Schematic of microgrooved surface and manifold configuration .......... 159 Figure 6-2. Single-phase results of experimental and numerical heat transfer coefficients .................................................................................................... 165 Figure 6-3. Single-phase results of experimental and numerical pressure drop values ....................................................................................................................... 165 Figure 6-4. Velocity and static pressure distribution in the center plane for (a) Surface #12, G=200 kg/m2s, (b) Surface #17, G=200 kg/m2s, (c) Surface #C, G=200 kg/m2s, (a) Surface #12, G=1000 kg/m2s, (a) Surface #17, G=1000 kg/m2s, (a) Surface #C, G=1000 kg/m2s, ........................................................................ 167 Figure 6-5 Boiling curves for FFMHS Surface #17 for (a) 200 < G <600 kg/m2s and (b) 700 < G < 1400 kg/m2s ........................................................................... 173 Figure 6-6. (a) Heat transfer coefficient based on base area versus base heat flux and (b) heat transfer coefficient based on wetted area versus outlet quality for FFMHS Surface #17 ..................................................................................... 176 Figure 6-7. Pressure drop values versus outlet quality for FFMHS Surface #17 ..... 177 Figure 6-8. Boiling curves for FFMHS Surface #12 ................................................ 179 Figure 6-9. Heat transfer coefficient based on base area versus base heat flux and (b) heat transfer coefficient based on wetted area versus outlet quality for FFMHS Surface #12 ................................................................................................... 180 Figure 6-10. Pressure drop values versus outlet quality for FFMHS Surface #12 ... 181 Figure 6-11. Boiling curves for FFMHS Surface #C ................................................ 183 xi Figure 6-12. Heat transfer coefficient based on base area versus base heat flux and (b) heat transfer coefficient based on wetted area versus outlet quality for FFMHS Surface #C ..................................................................................................... 184 Figure 6-13. Pressure drop values versus outlet quality for FFMHS Surface #C .... 185 Figure 6-14. Flow schematic in (a) an FFMHS (b) a straight microchannel ............ 188 Figure 6-15. Heat transfer coefficient comparison for single-phase convective heat transfer for selected microgrooved surfaces ................................................. 190 Figure 6-16. Comparison of saturated convective boiling heat transfer correlations with experimental data of FFMHS Surface #12, (a) G=300 kg/m2s and Re=100, (a) G = 1200 kg/m2s and Re=400 ................................................... 196 Figure 6-17. Comparison of saturated convective boiling heat transfer correlations with experimental data of FFMHS Surface #17, (a) G=300 kg/m2s and Re=70, (a) G = 1400 kg/m2s and Re=320 ................................................................. 198 Figure 6-18. Comparison of saturated convective boiling heat transfer correlations with experimental data of FFMHS Surface #C, (a) G=400 kg/m2s and Re=50, (a) G = 1000 kg/m2s and Re=130 ................................................................. 198 Figure 6-19. Critical heat flux based on wet channel area versus channel mass flux data obtained for Surface #17 ....................................................................... 200 Figure 6-20. Variation of surface temperature and inlet fluid temperature with time at critical heat flux condition for Surface #17, G=300 kg/m2s and q?wall = 72.1 W/cm2, ?Tsubcool = 2.6 ?C .............................................................................. 202 Figure 6-21. Variation of surface temperature and inlet fluid temperature with time at critical heat flux condition for Surface #17, G=1400 kg/m2s and q?wall = 154.9 W/cm2, ?Tsubcool = 8.5 ?C .............................................................................. 203 Figure 6-22. Thermal performance comparison of different high heat flux cooling technologies .................................................................................................. 204 Figure 7-1. Schematic of visualization test section (a) front isometric view (b) back isometric view ............................................................................................... 212 Figure 7-2. Exploded view of visualization test section components ....................... 214 Figure 7-3. Picture of the visualization test section .................................................. 215 Figure 7-4. Test surface and area of interest for the visualization study .................. 216 Figure 7-5. (a) Heat conduction paths in the test set section, (b) Location of thermocouples ............................................................................................... 218 Figure 7-6. Calculated total heat losses for the test surface with a gap of 70 ?m .... 219 Figure 7-7. Calculated total heat losses for the test surface with a gap of 225 ?m .. 220 Figure 7-8. Single-phase velocity vectors and static pressure distribution in test section for 225 ?m gap and G=200 kg/m2s mass flux .................................. 222 Figure 7-9. Two-phase flow regimes for gap of 225 ?m and mass flux of G=200 kg/m2s at (a) q?wall= 3.1 W/cm2, (b) q?wall= 4.6 W/cm2, (c) q?wall= 9.3 W/cm2 ....................................................................................................................... 224 Figure 7-10. Two-phase flow regimes for gap of 225 ?m and mass flux of G=200 kg/m2s at (a) q?wall= 15.5 W/cm2, (b) q?wall= 23.8 W/cm2 (c) q?wall= 32.8 W/cm2 ........................................................................................................... 226 Figure 7-11. Two-phase flow regimes for gap of 225 ?m and mass flux of G=200 kg/m2s at (a) q?wall= 46.2 W/cm2 (b) q?wall= 88.9 W/cm2 ............................. 227 xii Figure 7-12. Two-phase flow instability observed for gap of 225 ?m, G=200 kg/m2s, q?wall= 103.1 W/cm2 ...................................................................................... 229 Figure 7-13. Single-phase velocity vectors and static pressure distribution in test section for 70 ?m gap and G=240 kg/m2s mass flux .................................... 231 Figure 7-14. Two-phase flow regimes for gap of 70 ?m and mass flux of G=240 kg/m2s at (a) q?wall= 9.8 W/cm2 (b) q?wall= 13.4 W/cm2 (c) q?wall= 15.1 W/cm2 (d) q?wall= 18.2 W/cm2 .................................................................................. 234 Figure 7-15. Two-phase flow instability observed for gap of 70 ?m, G=240 kg/m2s, q?wall= 40.9 W/cm2 ........................................................................................ 235 Figure 7-16 Single-phase velocity vectors and static pressure distribution in test section for 70 ?m gap and G=780 kg/m2s mass flux .................................... 236 Figure 7-17. Two-phase flow regimes for gap of 70 ?m and mass flux of G=780 kg/m2s at (a) q?wall= 17.7 W/cm2 (b) q?wall= 24.1 W/cm2 (c) q?wall= 31.8 W/cm2 (d) q?wall= 46.7 W/cm2 ...................................................................... 239 Figure 7-18. Two-phase flow regimes for gap of 70 ?m and mass flux of G=780 kg/m2s at (a) q?wall= 61.9 W/cm2 (b) q?wall= 81.4 W/cm2 (c) q?wall= 92.0 W/cm2 ........................................................................................................... 240 Figure 7-19. Variation of experimental heat transfer coefficients with stability criteria for Surface #12 .............................................................................................. 246 Figure 7-20. Variation of experimental heat transfer coefficients with stability criteria for Surface #17 .............................................................................................. 246 Figure 7-21. Variation of experimental heat transfer coefficients with stability criteria for Surface #C ............................................................................................... 247 Figure 7-22. Schematic of flow model in the inlet region for (a) Half FFMHS unit cell (a) Flow between parallel plates with constant wall heat flux ...................... 247 Figure 7-23. Local heat transfer coefficients versus non dimensional entrance length for (a) Surface #C, (b) Surface #12 ............................................................... 248 Figure 7-24. Onset of Nucleate Boiling (ONB) and wall and liquid superheats calculated for (a) Surface #C, (b) Surface #12 ............................................. 250 Figure 8-1. Low profile FFMHS with zigzag manifold design ................................ 258 Figure 9-1. Boundary conditions and computational domain ................................... 271 Figure 9-2. The meshed geometry used in numerical model .................................... 272 Figure 9-3. Total thermal resistance versus mass flow rate for the bottom part of the heater assembly ............................................................................................. 273 Figure 9-4. Mathematical model of TMHS .............................................................. 274 xiii List of Acronyms 1D One Dimensional 2D Two Dimensional 3D Three Dimensional AAO Approximation Assisted Optimization CFC Chlorofluorocarbon CFD Computational Fluid Dynamics CHF Critical Heat Flux DOE Design of Experiment EDM Electron Discharge Machining EES Engineering Equation Solver FFMHS Force Fed Microchannel Heat Sink FPI Fins Per Inch GA Genetic Algorithm HCF Hydrofluorocarbons HVAC Heating Ventilation and Air Conditioning JIHS Jet Impingement Heat Sink MDT Micro Deformation Technology MED Maximum Entropy Design MOGA Multi Objective Genetic Algorithm ONB Onset of Nucleate Boiling OTEC Ocean Thermal Energy Conversion PCFDSI Parametric CFD Simulation Interface PTFE Polytetrafluoroethylene RMSE Root Mean Square Error RRMSE Relative RMSE MSFCVT Multi-response Space Filling Cross Validation Tradeoff TMHS Traditional Microchannel Heat Sink xiv Nomenclature A Heat transfer area, m2 Br Brinkman number: ( )2 /?= ?sBr V k T T Pc Specific heat at constant pressure, J/kgK D Diameter, m f Friction loss coefficient g Gravitational acceleration, m/s2 G Mass flux (mass velocity), kg/m2s; Geometrical parameter, mm h Heat transfer coefficient, W/m2K; Enthalpy, J/kg h Average heat transfer coefficient, W/m2K H Height, mm I Current, Amp K Local pressure loss coefficient k Thermal conductivity, W/mK L Length, mm Mass flow rate, kg/s n Number of channels/tubes N Number of computational cells Nu Nusselt number: /= hNu hD k Nu Average Nusselt number P Pressure, Pa; Power, W; Perimeter, m P Average pressure Pr Prandtl number: Pr /? ?= q Heat transfer rate, W q? Heat flux, W/cm2 R Curvature radius, mm; Thermal resistance, K/W Re Reynolds number: Re /? ?= VD S Source term t Thickness, mm T Temperature, K; Constant temperature T Average temperature v Specific volume, m3/kg V Fluid velocity, m/s; Voltage, V Volumetric flow rate, m 3/s w Width, mm We Webber number: 2e /? ?=W V D xv Greek symbols: ? Thermal diffusivity, m2/s ? Aspect ratio ? Difference ? Film thickness ? Density, kg/m3 ? Fin efficiency ? Relative rate of change of geometrical parameters ? Mass flow rate per unit depth, kg/sm ? Kinematic viscosity, m2/s ? Shear stress vector, Pa ? Surface tension, N/m; Area expansion ratio ? Relative rate of change of pumping power ? Viscosity, Pa-s Subscripts: AlNi Aluminum nitride app Apparent base Base c Contraction; Curvature; Conductive h Channel e Expansion f Film fd Fully developed film Film fin Fin h Hydraulic diameter; hydrodinamically; heated hab Bottom part of heater assembly heater Heater i Inlet; index inf Ambient l Liquid lam Laminar lv Liquid-vapor m Mean (average) max Maximum mg Microgrooved surface to fluid min Minimum mm Microgrooved surface to manifold o Outlet pump Pumping ref Reference s Heated surface xvi sat Saturation solder Solder t Thermally; Thermocouple; Total v Vapor wall Heat transfer wet area x Local 1 CHAPTER 1: INTRODUCTION 1.1. Motivation of the Study Active thermal management is required in many applications such as power electronics, plasma facing components, high heat load optical components, laser diode arrays, X-ray medical devices, and power electronics in hybrid vehicles. In general, the exposed area that needs to be cooled for these systems is limited, and the amount of heat that needs to be removed is extremely high, thus requiring cooling of high heat fluxes. More importantly, the performance of many of these systems is often directly related to their cooling capacity and heat transfer efficiency. While high heat flux cooling is essential, to create an efficient cooling system there are usually also other system requirements, such as low thermal resistance, surface temperature uniformity, low pumping power, compact design, suitability for large area cooling and compatibility for use with dielectric fluids. For example, the power electronics capacity and functionality has grown significantly during the past decade. Currently, most of the advanced electronic components already generate heat fluxes exceeding 100 W/cm2, while some future microprocessors and power-electronic components, such as high power laser and electronic radar systems, have been projected to generate heat fluxes over 1000 W/cm2 (Mudawar, 2001), (Kandlikar, 2005), (Kandlikar & Bapat, 2007). The increase in power density of the components has also created a need for advanced cooling technologies to achieve high heat dissipation rates in order to keep the electronic system at desired working temperatures. At this point, traditional and well 2 known cooling methods such as conduction and natural/forced air convection will prove insufficient for such high heat fluxes leaving the possibility open for the introduction of new competitive technologies. Depending on whether single-phase or phase-change cooling is selected, the two options generally accepted as the most effective active cooling methods for next- generation high heat-flux systems are; single phase liquid cooling and two phase convective boiling, respectively. Single-phase cooling systems are currently used to cool power electronics usually by directly forcing liquid water over the heat transfer surface of a heat sink. These cooling systems can yield very high heat transfer coefficients when combined with microchannels. However, this technique requires high pumping power to sustain the very large pressure drops associated with driving the single-phase flow through the typical micro-channels with small hydraulic diameters. But one particular design advantage of single-phase systems is that the heat transfer and fluid flow physical mechanisms are relatively well understood and well established, and a large variety of numerical simulation CFD tools can be used to simulate flow in complex geometries. Two-phase cooling systems are generally more accepted as the ultimate solution to meet demanding cooling requirements of future power electronics in terms of heat transfer efficiency, compactness, and weight and energy consumption. For the same heat sink geometry and flow conditions, the transfer coefficients generated during phase change can be expected to be several times higher than those for convective liquid cooling. Two-phase systems benefit from the large latent heat capacity of the working fluid, which is much higher than the sensible heat of a single 3 phase cooling system. But although they are superior to single-phase systems in several aspects, two-phase systems also present certain challenges, including the complexity of two-phase flow regimes and heat transfer phenomena. The complexity is even more pronounced when phase-change occurs in small hydraulic diameter channels such as microchannels. Also, the two-phase flow instabilities and the difficulty of mathematical modeling are other issues that need to be considered when designing two-phase flow systems. Several cooling systems for both single-phase and two-phase active cooling have been proposed for cooling high heat fluxes. The current leading options are systems such as microchannel, jet impingement and spray cooling systems. A detailed overview of these technologies, along with a discussion of their fundamental physics, can be found in reviews of (Bar-Cohen, Arik, & Ohadi, 2006), (Agostini, Fabbri et al., 2007), (Kandlikar & Bapat, 2007) and for spray cooling alone, (J. H. Kim, 2007). In general, jet impingement and spray cooling techniques use high-pressure liquid jets and shattered liquid droplets aimed directly at the electronic device being cooled or at a heat spreader in contact with the electronic device. Spray cooling systems can provide good isothermal surface temperature and can remove high heat fluxes, but due to small nozzle diameters and the high pressure required to produce small droplets, spray nozzles are more prone to clogging, inconsistent spray characteristics and erosion, while also representing high pressure drops. The heat transfer performance of Jet Impingement Heat Sinks (JIHS) mostly depends on the jet velocity, which can be highly non-uniform over the cooled surface, so using a heat spreader may be necessary to improve the temperature uniformity. This in turn results 4 in additional thermal resistance to the heat sink. Traditional Microchannel Heat Sinks (TMHS) are constructed using microchannels running in parallel connected by an inlet and outlet manifold. This technology has demonstrated the ability to generate high heat transfer coefficients. However, the issues of high pressure drops, and two- phase flow instabilities accompanied by flow maldistribution, suppress the cooling limits and applicability ranges of microchannel heat sinks. All the current active thermal management systems, whether working in single-phase or two-phase mode, have their own applicability advantages and challenges, and none of these systems have been accepted yet as the universal cooling technology. Therefore, the field is open for the introduction of new cooling systems that can remove heat fluxes exceeding 1000 W/cm2 with higher heat transfer coefficients and reasonable pumping power requirements. To meet all of these requirements, innovative technologies and concepts have been proposed in several publications. Single phase Force Fed Microchannel Heat Sink (FFMHS) concept (also known as the manifold microchannel heat sink) was first introduced by (Harpole & Eninger, 1991), and later studies reported that FFMHS can achieve heat transfer coefficients of 30% (Y. I. Kim, Chun, Kim, Pak, & Baek, 1998) to 50% (Ryu, Choi, & Kim, 2003) higher than TMHS at same pumping power. However, due to flow and geometrical complexities, FFMHS have received less attention, and the optimum geometry and flow conditions have not been studied in detail yet. Moreover, all available published data is based on microgrooved surfaces created on silicon substrates, while similar enhanced surfaces created from metal substrates such as copper have several advantages. For two-phase heat transfer, the fundamentals of 5 FFMHS have not been investigated, but a few experimental results performed at the University of Maryland?s, Smart and Small Thermal Systems Laboratory through the earlier phases of current study showed that force-fed cooling has the ability to cool heat fluxes up to 925 W/cm2 with heat transfer coefficient of 130,000 W/m2K using the non aqueous refrigerant HFE 7100. These results demonstrated that FFMHS is a promising candidate for applications that require high heat-flux cooling with high efficiency. The present work therefore represents a focus on exploring and pushing the technological boundaries of FFMHS working in both single-phase and two-phase heat transfer modes. 1.2. Research Objectives The main research objectives and contributions of this dissertation are as follows: ? To develop a better understanding of single-phase and phase-change heat transfer in FFMHS through experimental and numerical modeling of the phenomena, multi-objective optimization of the heat sink and its comparison with widely known cooling technologies, and flow visualization studies that all contributed to advance the basic understanding of the complex physics involved in a force-fed micro channel heat sinks. ? To formulate metamodels that can predict single-phase heat transfer coefficients and pumping power for FFMHS at given geometrical and flow conditions, and to validate the metamodel prediction capability and demonstrate its efficiency. 6 ? To optimize the single-phase FFMHS using a multi-objective optimization algorithm by selecting the most important and relevant geometrical parameters as optimization variables and objective functions. ? To compare the single-phase thermal performance of FFMHS with the performance of other well-known high heat-flux cooling systems such as TMHS and JIHS to better quantify major advantages and limitation of the force-fed micro channel cooling technique ? To apply the force-fed cooling principle to two-phase cooling and to identify the parameters that most significantly affect the heat transfer performance. ? To determine the two-phase flow regimes and to understand the heat transfer and critical heat flux (CHF) mechanisms that control two-phase FFMHS. 1.3. Dissertation Organization Chapter 2 explains the working principles of FFMHS in both single-phase and two-phase heat transfer modes. Fluid flow and heat transfer fundamentals are covered, including the relevant literature survey. Chapter 3 discusses the single-phase numerical modeling strategy for FFMHS and the effects of several geometrical and flow parameters on heat transfer coefficients and pressure drops. In Chapter 4, the FFMHS is optimized by the Approximation Assisted Optimization technique, and then the thermal performance at optimum conditions is compared to TMHS and JIHS. The experimental test setup, test section and the test procedure are explained in detail in Chapter 5, and the single-phase and two-phase results are presented and analyzed in Chapter 6. In order to visualize the flow patterns in a unit FFMHS cell, a visualization test section was fabricated. The design procedure of the test section and 7 the resulting visualization results are presented in Chapter 7. The dissertation concludes with Chapter 8, where the conclusions are summarized, followed by the recommended future work. 8 CHAPTER 2: WORKING PRINCIPLES AND THEORETICAL BACKGROUND This chapter begins with an introduction to the working concepts of Force Fed Microchannel Heat Sinks (FFMHS). The design and geometrical properties of the microgrooved surfaces that provide the heat transfer area enhancement of FFMHS, are described next. The chapter concludes with review of fundamental aspects of fluid flow and heat transfer mechanisms that appear to govern thermal performance of FFMHS. Both single-phase and two-phase heat transfer modes are analyzed, and relevant literature survey is presented. 2.1. Force Fed Microchannel Heat Sinks (FFMHS) An FFMHS is a combination of a microgrooved surface and a system of manifolds. The flow schematic of a typical FFMHS is shown in Figure 2-1. The flat side of the microgrooved surface is attached to the heat source, while the fins and microchannels on the other side are in contact with the working fluid. On the top of the microchannels is a series of manifolds, usually aligned perpendicularly to the fins and microchannels. The manifolds do not contribute to heat transfer, significantly and their role is mainly to distribute the fluid and to provide structural integrity of FFMHS. Each gap between two neighboring manifolds forms a feed channel, which is used to direct the fluid in (inlet feed channel) or out (outlet feed channel) of the microchannels. This gap can have similar or different dimensions for inlet and outlet feed channels, depending on the desired design configuration. From a design stand 9 point, compared with microchannels, the feed channels have much greater hydraulic diameters and lower flow velocities. The manifolds and the microgrooved surface are usually attached to each other by use of compressive force that seals the tip of the fins to the bottom of the manifolds. Figure 2-1. Schematic flow representation of a typical FFMHS Generally, all the inlet feed channels are connected to a larger common volume, such as a reservoir, which supplies the fluid and pressure needed to drive the flow. Thus, being fed from the same pressure source, each inlet feed channel will deliver same amount of fluid. The flow in the feed channels can be considered as flow between two parallel plates due to the usually high aspect ratio of feed channels. Heat Manifolds Microgrooved surface base Microchannel Fin Feed channels y z x 10 After entering and flowing along the feed channel, the fluid will encounter the microchannels and fins of the microgrooved surface. Here the fluid will be forced to enter the microchannel from the top, perpendicularly to the microchannel direction. This entrance will create a flow area reduction and in turn will increase the flow velocity and decrease the static pressure at the entrance region of the microchannel. After entering the microchannel area, the flow will start to develop until it flows down to the bottom of the channel, eventually creating an impingement zone. After the stagnation point, the fluid splits in two streams, each stream turning 90? and flowing in the opposite direction in the microchannel. The fluid continues to flow a short distance in the microchannel, where the flow and heat transfer occurs similar to that in a typical TMHS. This distance of the straight microchannel is defined by the thickness of the manifolds. At the end of the straight microchannel, the fluid will make a second 90? turn, joining with the counter stream and leaving the area through the corresponding outlet feed channel. The exit from the microchannel to the outlet feed channel creates a pressure increase and velocity reduction due to an increase in flow area. This flow configuration is repetitive and results in the formation of arrays of short microchannels working in parallel. The key geometrical arrangements and flow distributions that make FFMHS an effective heat transfer cooling system are listed as follows: - The system pressure drop is decreased significantly due to the short flow length of a turning path in the microchannels. The system, in fact, is a network of short microchannels working in parallel, and therefore the total system pressure drop is the pressure drop of a single microchannel flow turn. 11 - FFMHS is suitable for cooling of large areas and can be easily expandable in the x-y directions (Figure 2-1). By increasing the flow rate proportional to the base area expansion rate, the system pressure drop and effective heat transfer coefficient remain constant. - FFMHS benefits from multiple inlet entrance effects. The area in the microchannel flow inlet region is very effective and can yield very high heat transfer coefficients. This effect is the result of thermally developing flow in this region, which is associated with very thin boundary layers and low thermal resistance values. Having multiple inlet regions enhances the overall heat transfer coefficient of the heat sink. - Generally, chips that need to be cooled are spaced close together on the substrate, and there is limited space in the x-y direction for including additional equipment such as flow distributing manifolds. In this case, it could be more convenient to include additional parts in the z-direction, which makes FFMHS design favorable. 2.2. The Microgrooved Surfaces As shown in Figure 2-1, the FFMHS design requires enhanced surfaces with alternating fins and channels, also known as microgrooved surfaces. Depending on the substrate material and geometric features, several fabrication methods are currently used for this purpose. For example, the silicon microfabrication technique can create very fine surfaces with microchannels having hydraulic diameters in the order of microns. Micromachining is another process that can create microchannels using methods such as Electron Discharge Machining (EDM) or micro-milling. These 12 methods are the most suitable for metal substrates. The microgrooved surfaces selected and used in this study were fabricated using Micro Deformation Technology (MDT). This relatively new fabrication method allows fabrication of enhanced surfaces with very high aspect ratios from a wide range of metals. MDT was initially developed to produce enhanced heat transfer tubes and was later adopted for flat surfaces. The fabrication principle of MDT is based on a continuous process of skiving and bending material on the top of a metal substrate. The major advantage of MDT is that it can be cost effective when adapted for mass production. Detailed information on MDT can be found in (Thors & Zoubkov, 2009). A cross section of a typical microgrooved surface fabricated using MDT is shown in Figure 2-2 (a). The fin geometry created by MDT is usually slightly different from the fin structure of a traditional microgrooved surface fabricated usually by silicon microfabrication technique. Based on the cutting tool geometry used during fabrication, MDT microgrooved surfaces have an unconventionally sharp fin-tip and a slightly bent fin geometry. For the present work, three types of microgrooved surfaces with different geometries have been selected and fabricated by MDT. All three samples were fabricated from copper, and the experimental test procedure is described in detail in Chapter 5. The cross-sectional profile of selected samples is shown in Figure 2-2, while dimensions are given in Table 2-1. 13 Figure 2-2. (a) Picture of a typical microgrooved surface profile fabricated with MDT, (b) Profile of three microgrooved surfaces selected for present study Table 2-1. Dimensions of tested microgrooved surface and feed channels (all dimensions in microns) Sample Name Fin Density [FPI] Fin Pitch [?m] Channel Height ? Hch [?m] Channel Width ? wch [?m] Fin Thickness ? tfin [?m] Channel Aspect Ratio Surface #12 143 178 406 60 118 6.8 Surface #17 200 127 483 42 85 11.5 Surface #C 409 62 415 22 40 18.7 2.3. FFMHS for Single-Phase Heat Transfer It is expected that the flow pattern and geometrical configuration of a typical FFMHS have the potential to enhance single-phase thermal performance compared to (a) (b) Surface #17 Surface #C Surface #12 wch tfin Hch tbase 14 other conventional high heat flux cooling technologies. But first, the basic mechanisms and flow regimes behind the possible heat transfer enhancement need to be demonstrated. The following sections address these issues. 2.3.1. Heat Transfer and Pumping Power in Short Channels A simple analysis can demonstrate the thermal performance advantages of FFMHS in comparison to traditional microchannel single-phase flow. To simplify the analysis, consider the two flow configurations shown in Figure 2-3 (a) and (b). The first case, Case 1, shown in Figure 2-3 (a), depicts flow in a single long tube with hydraulic diameter of Dh, tube length L, mass flow rate &m , constant surface temperature Ts and inlet temperature of Ti. This case is analogous to a single channel in a traditional microchannel heat sink with a highly conductive microgrooved surface base material. The second case, Case 2, shown in Figure 2-3 (b), represents the same tube divided into n equal length, short tube segments. This case is analogous to FFMHS flow configuration formed for a single microchannel. The mass flow rate running in each tube is divided equally, resulting in a mass flow rate of /&m n in each single short tube. All other parameters, such as hydraulic diameter and inlet, outlet and surface temperatures, were kept constant. At this stage, to further simplify the problem, the ratio of channel length to hydraulic diameter L/Dh for both cases was assumed to be high; therefore, entrance effects were neglected and flow was assumed to be fully developed. The flow in microchannels is generally in laminar flow regime; therefore, Reynolds number was assumed to be always below Re 2300< . Also, the major pressure losses were assumed to be dominantly higher, and inlet and outlet 15 minor losses were neglected. Heat was applied to the surface at constant temperature Ts. Figure 2-3. Schematic of flow in (a) single long channel and (b) multiple short channels Usually the most important performance parameters considered in a heat sink design are overall heat transfer coefficient and pumping power. While the overall heat transfer coefficient is desired to be as high as possible to increase heat transfer efficiency, the pumping power values need to be minimized. Since these parameters conflict, a reasonable comparison can be made by keeping one parameter constant and performing the comparison based on the other one. Here, the overall heat transfer coefficients for Case 1 and Case 2 will be kept constant and the pumping power will be evaluated. Dh Constant Temperature Ts L Inlet Temperature Ti L/n n small tubes Mass flow rate m Mass flow rate m/n (a) (b) Inlet Temperature Ti Case 1 Case 2 single tube 16 It can be shown that with constant surface temperature assumption, the outlet fluid temperature To,1 for Case 1 can be calculated from (Incropera & DeWitt, 2002) as: (2-1) where h is the average heat transfer coefficient. For the current case this value is constant along the tube and is equal to: 3.66= = =z T h h k kh h Nu D D (2-2) Here 3.66=TNu is the Nusselt number defined for fully developed flow in a tube (Incropera & DeWitt, 2002), and k denotes the thermal conductivity of the working fluid. The heat transfer to the fluid is then calculated based on logarithmic mean temperature difference: ( )( ) ( ),11 ,1ln ? ? ? ?= ? ? s o s i Case h s o s i T T T Tq h D L T T T T (2-3) Similarly, for each short tube defined in Case 2 the outlet fluid temperature To,2 can be calculated as: (2-4) The right-hand side of Equations (2-1) and (2-4) are identical which concludes that for two cases the outlet temperatures are equal. The total heat transfer in Case 2 is then evaluated by substituting ,1 ,2=o oT T and summing the heat transfer surface as: 17 ( )( ) ( ) ( )( ) ( ),2 ,12 ,2 ,11 ln ln ? ? = ? ? ? ? ? ?= = ? ? ? ? ?n s o s i s o s iCase h h s o s oi s i s i T T T T T T T TLq h D h D L n T T T T T T T T (2-5) Equations (2-3) and (2-5) are equal, which demonstrates that the heat transferred from both the single-tube configuration of Case 1 and multiples tubes with the same hydraulic diameter and heat transfer area of Case 2 is the same. A common practice for identifying single-phase heat transfer performance for heat sinks is to calculate effective heat transfer coefficient. This parameter is defined as the ratio of heated surface heat flux and temperature difference between inlet and heated surface temperature. Since inlet temperature is constant and equal for both cases, the effective heat transfer coefficient will be the same as well. The isentropic pumping power for a control volume is the product of volumetric flow rate and pressure drop: (2-6) The major pressure losses for laminar flow in a tube can be calculated as: 2 2?? = h L VP f D (2-7) where is the mean fluid velocity in the tube and the pressure loss coefficient for fully developed laminar flow is defined as: 64 64 Re ? ?= = hf VD (2-8) Substituting Equations (2-7) and (2-8) into Equation (2-6), the total pumping power required for Case 1 and Case 2 can be calculated as: 18 (2-9) (2-10) Based on these two equations the pumping power reduction can be calculated as: ,2 2 ,1 1=pump pump P P n (2-11) Equation (2-11) demonstrates that for the same overall heat transfer coefficient, the split-flow configuration with multiple inlet and outlets has the potential to decrease the pumping power proportional to the square of number of divisions. However, it should be noted that tube hydraulic diameter and total tube length was assumed to be the same for both cases, and no optimization study was performed. More realistic performance comparison would be to compare pumping powers for two cases at optimum channel dimensions and at the same heat transfer. 2.3.2. Heat Transfer and Pressure Drop for Thermally and Hydrodynamically Developing Flow For the analysis performed in the previous section, it was assumed that the flow is fully developed along the whole tube. This assumption is not valid when the tube length over the tube hydraulic diameter ratio (L/Dh) becomes small. In this case, the heat transfer and momentum transfer occur mostly in the entrance region, where the hydrodynamic and thermal boundary layers are developing. Therefore, the heat transfer coefficient and friction factor in the entrance region depend on distance from entrance, Reynolds number and fluid physical properties and are not constant 19 anymore. This may have a significant impact on thermal performance of FFMHS where the heat transfer occurs mostly in the entrance region and the flow is hydrodynamically and thermally developing. Assuming uniform velocity profile at the inlet, the hydrodynamic entry length ,fd hL for laminar flow in a tube is obtained from the following relation given by (Langhaar, 1942): , 0.05Re? ? ?? ? ? ? fd h lam L D (2-12) The friction factors in the hydrodynamically developing region are higher than those defined for fully developing flow. Both the skin friction and additional momentum rate change due to change in the velocity profile are added together to define apparent friction coefficient. For circular tubes, (Shah & London, 1978) proposed the following correlation: ( ) ( ) ( )( ) 0.5 0.5 0.24 1.25 Re 3.44 Re 3.44 1 2.12 10 ?+ +?+ ?? + + ? = + + ? fd app f xx f x x (2-13) where ( )Re 64=fdf is defined for fully developed flow and +x is the non- dimensional channel length defined as: Re + = Lx D (2-14) For thermally developing laminar flows, (Kays & Crawford, 1980) proposed the following equation to calculate the thermal entry length ,fd tL : , 0.05 Re Pr? ? ?? ? ? ? fd t lam L D (2-15) 20 For combined hydrodynamically developing region and thermal entry region for laminar flow in a circular tube, the average Nusselt number is given by (Sieder & Tate, 1936): 0.141/3Re Pr 1.86 / ??? ?? ?= ? ?? ?? ? ? ?s Nu L D (2-16) Equations (2-13) and (2-16) demonstrate that in the entry region both heat transfer coefficients and pressure drop increase compared to fully developed flow. This result may have an important impact on thermal performance of FFMHS, where the length of channels is usually comparable to hydraulic diameters. When considering pumping power and heat transfer coefficients as the most important heat sink design parameters, both hydrodynamic and thermal entry effects need to be considered. At this point, a multi-objective optimization procedure can be useful in revealing the flow and geometrical conditions that maximize the heat transfer and minimize the pressure losses at the entry region. 2.3.3. Heat Transfer and Pressure Drop in Turning Bends In FFMHS, the fluid enters and exits the microgrooved surface from the top, perpendicular to the microchannel axis. This configuration creates a 180? flow turn which may have significantly different flow and heat transfer characteristics from straight channel flow. As the fluid makes the turn, centrifugal forces affect the flow field. The magnitude of the centrifugal forces that act on a fluid particle are proportional to 2 /V R where V is velocity and R is the curvature radius. For laminar flow in a tube or rectangular channel, due to no slip boundary conditions, the axial velocities in the vicinity of the channel walls are much smaller than those in the 21 center of the channel. This difference in axial velocity results in centrifugal forces acting with different magnitude on each fluid particle. A significant difference in centrifugal forces in turn can induce secondary flows. For flow in a helical circular tube, (Ujhidy, Nemeth, & Szepvolgyi, 2003) described the flow pattern as a double vortex that appears on the cross section of the tube and is superimposed on the axial velocity profile. Dean (Dean, 1927) was first to analyze the formation of secondary flows and concluded that the friction loss for laminar flow in a curved pipe is a function of a dimensionless parameter called the Dean number: Re 2= DDe R (2-17) where Re is the Reynolds number and D is tube diameter. Equation (2-17) shows that the Dean number represents the ratio of inertia and centrifugal forces to the viscous forces. The Dean number can also be interpreted as the measure of magnitude of secondary flows. The vortices created by secondary flows can enhance the heat transfer by disturbing the thermal boundary layer and by replacing the hotter fluid close to the heated wall with colder fluid in the fluid core. This mixing mechanism has been reported for flow in helical tubes by (Xin & Ebadian, 1997) who proposed the following correlation to calculate the average Nusselt number: ( )0.643 0.1772.153 0.318 Pr= +Nu De (2-18) The equation was validated for the parametrical range of 20 2000< conf h gN D (2-20) where is defined as the dimensionless confinement number confN , ? as the surface tension, ?? as the density difference between liquid and vapor phases, and hD as the hydraulic diameter. The confinement number was derived by correlations developed for pool boiling and represents the ratio of bubble departure diameter to the channel hydraulic diameter. For a confined two-phase flow, based on their observations, they also proposed a microchannel flow regime based on three distinctive flow regimes as shown in Figure 2-5. Figure 2-5. Major flow regimes for flows in microchannels observed by (Cornwell & Kew, 1992) The isolated bubble flow has small vapor bubbles mixed in the liquid phase flowing in the microchannel. Here, the characteristic diameter of the bubbles is smaller than the microchannel width and this flow regime is similar to the bubbly flow regime in conventional channels. The diameters of the bubbles can be very small, as (Kandlikar, 2002) reported presence of bubble diameters as small as 10-20 microns. The confined bubble flow consists of large bubbles that are created by the growth or coalescence of small bubbles and are confined with the microchannel walls. A thin liquid film 37 separates the bubble and the walls, and this flow regime is similar to the plug flow in flow boiling in conventional channels. The confined bubble flow regime ends when the confined bubbles grow significantly in the axial direction by destroying the liquid slugs/columns separating them and leading to an annular-like flow regime. Therefore, the third and last major flow regime is annular slug flow, which represents all flow patterns that occur after the termination of confined bubble regime. As seen, the proposed flow regime is similar to flow regime shown in Figure 2-4 for conventional channels. The major difference is the confinement effect, which results in only three major flow regimes and which can possibly shift the rate of transition between flow regimes eventually switching to annular flow at much lower vapor qualities. It should be noted, however that the confinement number confN is based on geometrical considerations only. It does not include the effects of heat flux and liquid and wall superheat. (Kandlikar, 2003) argued that the effect of gravity in microchannel flows is negligible and that the use confinement number needs to be reevaluated. He suggested that the new criteria should be defined considering relevant forces in microchannel flow. Based on force balance applied to a bubble, (Kandlikar, 2004)suggested using the following non-dimensional group: 2 1 ? ? ? ???= ? ?? ? l lv v qK Gh (2-21) The 1K number represents the ratio of evaporative momentum force to the inertia forces of incoming liquid. For large values, it indicates that the evaporative momentum forces dominate the inertia forces, and this may result in vapor pushing back the liquid, creating backflows. The reversed lows in microchannels have been 38 reported by many authors including (Steinke & Kandlikar, 2003), (Peles, Yarin, & Hestroni, 2001) and (Kandlikar & Balasubramanian, 2003). While the 1K number is useful in determining the dominant forces in microchannel boiling, it assumes that the vapor mass flux transferred to the bubble is equal to the idealized mass flux calculated based on wall heat flux as /?? lvq h and is not dependent on hydraulic diameter. However, hydraulic diameter in fact can be very important in determining the liquid superheat that contributes to vapor generation. Based on experimental observations, (Kandlikar, 2003) defined the heat transfer mechanism in microchannels based on the elongated bubble (also known as expanding bubble, and sometimes explosive bubble) model shown in Figure 2-6. Similarly to flow regime observed by (Cornwell & Kew, 1992), the heterogeneous nucleation starts from the wall crevices. However, the growth rate of the bubble is much higher, and the rapidly bubble growth process continues even after the bubble departs. This short period may not allow the bubble to interact with other bubbles and create slug/plug flow, but instead it is rapidly confined by channel walls. After the confinement period, the bubble experiences a fast expansion in the axial direction as shown in the picture. 39 Figure 2-6. Flow boiling regimes proposed by (Kandlikar, 2003) There are two important issues that need to be addressed here. First, the source of rapid bubble expansion is explained by Kandlikar, as the liquid and wall superheat build before nucleation. The high local heat transfer coefficients at small hydraulic diameters decrease the thermal boundary layer and can suppress nucleation. Utilizing microchannels with smooth walls and withouth nucleation cavities will also further suppress nucleation. When the conditions to nucleate the bubble are satisfied, the liquid around the bubble is largely superheated. Therefore, the energy stored in the liquid superheat is released into the bubble in the form of evaporation, and the large amount of vapor generation forces the rapid bubble growth. If the evaporative forces are much higher than the forces associated with liquid inertia, then the elongated bubble grows both upstream and downstream. For example, a set of images taken at 8 milliseconds apart observed by (Steinke & Kandlikar, 2003) is shown in Figure 2-7. The bubble is heated from the walls and starts to grow rapidly downstream, while the upstream also experiences the force created by evaporative momentum. Therefore the upstream liquid front is pushed back closer to the inlet, Bubble nucleation Flow direction Confined bubble Elongated bubble Thin liquid film Dryout 40 where it is more or less stationary until the vapor in the channel exits from the outlet and the next cycle with liquid front moving downstream is released again. Second, the process has a transient nature and is repeated for each cycle. During the elongated bubble regime, as the bubble front advances, a thin liquid film is created on the heated surface by the receding liquid vapor interface. As the bubbles become larger, the thin film will provide a very highly efficient heat transfer zone. This thin film will eventually start to dry if the bubbles become too large, and localized dryouts will induce reduction in heat transfer. Figure 2-7. Rapid bubble growth in 200 micron square microchannels observed by (Steinke & Kandlikar, 2003)-Each image is 8 milliseconds apart (Thome, Dupont, & Jacobi, 2004) developed a three-zone model to investigate the evaporation process of elongated bubbles in microchannels. The schematic of their heat transfer model is shown in Figure 2-8 and includes the heat transfer from three major zones: the liquid slug, the elongated bubble with thin liquid film on 41 heated surface and the dry zone with vapor in contact with walls. Due to the transient nature of the process, a time-averaged approach was adopted in calculating the heat transfer coefficients. Figure 2-8. Diagram illustrating a liquid slug, an elongated bubble and a vapor slug of model developed by (Thome et al., 2004) The calculated heat transfer coefficients for the three heat transfer zones at two cyclic variations are shown in Figure 2-9. As expected, the minimum heat transfer is observed at the dry zone where the thermal resistance between vapor and surface is very high. The heat transfer coefficients in the liquid zone are slightly higher than the vapor zone. In the elongated bubble zone, however, the heat transfer coefficients can achieve very high values, on the several orders of magnitude higher than the liquid and dry zones. However, as the resistance of the thin film is dictated by conduction, the heat transfer values change significantly as film thickness changes. It is also interesting to note that the ratio of the area occupied by each region may have a direct relation with averaged heat transfer values. When the dry and liquid slug regions are large compared to the elongated bubble region, the high heat transfer associate with thin-film evaporation becomes less effective when averaged over the whole heat transfer surface. Based on this model, (Thome et al., 2004) concluded that 42 the dominant heat transfer mechanism in microchannels is thin-film evaporation under the elongated bubble, and not nucleate or convective boiling alone. Figure 2-9. Cyclic variation in heat transfer coefficient with time (adopted from (Thome et al., 2004)) 2.4.3. Effect of Channel Hydraulic Diameter on Inception of Nucleate Boiling The effect of channel hydraulic diameter on initiation of nucleate boiling needs to be evaluated. This effect is particularly important in the development of the elongated bubble flow regime mentioned in the previous section. The suppression and delay of nucleate boiling can increase wall and liquid superheat that can result in the rapid bubble expansion phenomena. Let us assume that flow in the channel shown in Figure 2-4 at constant heat flux boundary condition. The flow at inlet is subcooled and as the fluid flows 43 downstream, both the wall and liquid temperatures increase. The onset of nucleate boiling will occur at a specific flow condition in crevices present on the heated tube wall that fall in a certain range of sizes. Assuming that the heated surface contains nucleation crevices of all sizes, (Hsu & Graham, 1961) proposed the following equation to calculate the minimum amount of wall superheat required to initiate nucleation: , 4 1 1 2 ? ? ? ??? = + + ? ?? ? ? ? sat lv x lv sub sat ONB lv sat lv x T v h kh TT kh T v h (2-22) where satT is saturation temperature in units of [K], ? is surface tension, lvv is liquid- vapor specific volume, k is fluid thermal conductivity, lvh is evaporation enthalpy, and xh is local heat transfer coefficient. The equation can be further simplified by assuming saturated inlet flow conditions by introducing 0? =subT and by using the definition of the Nusselt number of /=x x hNu h D k . The new form can be cast as: , 8?? = sat lv x sat ONB h lv T v NuT D h (2-23) One important observation in Equation (2-23) is the relation between the local Nusselt number, hydraulic diameter and wall superheat. Single-phase flow regime in microchannels and FFMHS is generally laminar. For long channels, where the entrance effects can be negligible, the Nusselt number is constant, and wall superheat is reversely proportional to hydraulic diameter. This in turn highlights that for smaller microchannel hydraulic diameter dimensions, higher wall superheat values are needed to initiate nucleation, and the expanding bubble flow regime is more likely to occur at smaller channel geometries. On the other hand, in FFMHS, the entrance effects can 44 be significant due to small values of channel length to hydraulic diameter ratios (L/Dh) which can result in large developing regions. Heat transfer coefficients in this thermally developing region are much higher than the fully developed flow and such difference can affect the initiation of nucleation by further increasing the required wall superheat given in Equation (2-23). In this case, (Kandlikar, Garimella, Colin, Li, & King, 2004) suggested using entry region correlations to calculate the local Nusselt number. For thermally developing laminar flow between two parallel plates and for constant heat flux boundary condition, (Shah & London, 1978) proposed the following correlation: ( ) ( ) ( ) * 1/3* * 1/3* * 0.5063 * 164 * 1.49 , 0.0002 1.49 0.4 ,0.0002 0.001 8.235 8.68 10 , 0.001 ? ? ? ? ? ? ? ?= + < ?? ? ? + >? x x x x Nu x x x e x (2-24) where * / Re Pr= hx L D is non-dimensional length. By substituting Equation (2-24) into Equation (2-23), one can calculate the minimum wall superheat required to initiate nucleation close to the inlet region of FFMHS at a given hydraulic diameter. 2.4.4. Critical Heat Flux in Microchannels One of the most important parameters that limit the system performance is the critical heat flux (CHF). CHF is the upper limit of safe operation of two-phase heat sinks, since the heat transfer coefficients of the post-CHF zone are extremely low. In most cases, the CHF represents the system burnout condition due to the large jump in surface temperature. The CHF process is very complex due to the strong coupling of flow and heat transfer phenomena in two-phase flow. For example, CHF mechanisms 45 are quite sensitive to flow regimes, orientation (when gravity is important) and flow path. Therefore, it is expected that the CHF mechanism for FFMHS will be different from that of straight microchannels where the flow is not affected by turning flow and impingement effects. Nevertheless, the correlations developed for CHF in straight microchannels can indicate some important aspects about the relevant, important parameters. (Bowers & Mudawar, 1994) developed a correlation to predict CHF in minichannels. The correlation, given as Equation (2-25) was validated based on experimental data obtained for square channels with a hydraulic diameter of 2 mm and using R-113 as the working fluid. 0.54 0.190.16 ? ? ? ??? = ? ? ? ?CHF lv h Lq Gh We D (2-25) where G is mass flux, lvh is evaporation enthalpy and We is the Webber number based on liquid properties. (Qu & Mudawar, 2004) followed a similar procedure and proposed their correlation based on experimental data obtained for rectangular microchannels with hydraulic diameters ranging from 0.78 mm to 3.63 mm. The working fluids used in their experiments were R-113 and water. The resulting CHF correlation was proposed as follows: 0.36 1.1 0.2133.43 ? ? ? ? ? ? ? ??? = ? ? ? ? ? ? ? ? v CHF lv h l Lq Gh We D (2-26) where ??? ?? ? ? ? v l is the ratio of vapor and liquid densities. 46 Equations (2-25) and (2-26) both show that CHF is reversely proportional to length to hydraulic diameter parameter L/Dh. This, in fact, suggests that FFMHS has the potential to increase CHF by decreasing this parameter alone. In a typical FFMHS design, the length of channel and hydraulic diameter are comparable in size. 2.4.5. Literature Survey on Two-Phase Heat Transfer in Microchannels The numerical modeling of two-phase flow is still in rudimentary stages and has been applied mostly for very simple geometries such as straight tubes and channels. Most of the related published literature consists of experimental work. A review of the recent literature on flow boiling in microchannels is given in Table 2-3. The reviewed publications contain recent studies performed with both HFC fluids and water. As shown in the table, the minimum hydraulic diameter investigated is the microchannels with 162-microns hydraulic diameters investigated by (P. S. Lee & Garimella, 2008). This value is almost eight times higher than the microchannel width of Surface #C, and three times higher than the microchannel width of Surface #12 (Table 2-1). It is also important to note that the maximum aspect ratio investigated in the publications listed in Table 2-3 is 5, much less than the aspect ratios of microgrooved surfaces investigated in this study (up to 18.7 for Surface #C). Another parameter of importance is the L/Dh ratio, which is the ratio of microchannel length to hydraulic diameter, whose importance was discussed in the previous section. As shown in the table, this value is over L/ Dh > 40 for almost all studies except for the work done by (Bertsch, Groll, & Garimella, 2008), in which they investigated channels with L/Dh = 8.74. The microgrooved surface and manifold combination used in the current study correspond to a range of 6.31.0 local Yes (J. Lee & Mudawar, 2005a, 2005b) 2005 R134a 713 3 25.3 72 over 20 350 53 rectangular -18 to +25 127?654 31.6?93.8 base area 0.2?0.9 local No (P. S. Lee, Garimella, & Liu, 2005) 2005 Water 884- 2910 5 25.4 79-28 NA 318? 903 10 rectangular 100 1000? 2400 4.5 base area Overall No (Lie & Lin, 2005) 2005 R134a - - 730 365- 183 NA 2000? 4000 1 annular 10, 15 200?300 0?5 wetted area ... Yes (Saitoh, Daiguji, & Hihara, 2005) 2005 R134a - - 1620- 3240 552- 3240 480 at G=300 kg/m2s 510, 1120, 3101 1 circular 5, 15 150?450 0.5?3.9 wetted area 0.2?1 local Yes (T. L. Chen & Garimella, 2006) 2006 FC-77 389 1 12.7 33 3.5 390 24 rectangular 97 160?275 5?70 base area <0?0.7 overall Yes 49 (Lie & Lin, 2006) 2006 R134a - - 730 365- 183 NA 2000? 4000 1 annular 10?15 200?300 0?5.5 wetted area Subcoole d overall Yes (Yen, Shoji, Takemura, Suzuki, & Kasagi, 2006) 2006 R123 214 1 100 467 NA 200? 214 1 rectangular and circular ... 100?800 0?5 wetted area 0?0.8 overall Yes (Yun, Heo, & Kim, 2006) 2006 R410A 1200 0.67- 0.76 NA NA over 40kPa/m 1360? 1440 7?8 rectangular 0, 5, 10 200?400 1.0?2.0 wetted area 0?0.85 overall No (D. Liu & Garimella, 2007) 2007 Water 636 - 1063 2.31- 2.61 25.4 66-32 1.2 at G=324 kg/m2s 384? 796 25 rectangular 100 221? 1283 Up to 129 base area 0?0.2 local No (Schneider, Kosar, & Peles, 2007) 2007 R123 264 1.32 10 44 NA 227 5 rectangular 38?80 622? 1368 0-213 base area Overall Yes (P. S. Lee & Garimella, 2008) 2007 Water 4 4-0.4 12.7 78- 22.3 40 162- 570 25 rectangular 100 368-738 10 - 340 base area 0-0.19 Overall No (Agostini, Thome et al., 2007a) 2007 R236fa 68 3 20 60 105 335 67 rectangular 25 280- 1500 3.6-221.7 base area 0.2-0.75 Local No (Agostini, Thome et al., 2007b) 2007 R245fa 68 3 20 60 125 335 67 rectangular 23.7 281- 1501 3.6-190 base area 0-0.78 Local No (Kuo & Peles, 2007) 2007 Water 253 1.26 10 44.8 NA 223 5 rectangular 100 83-303 0-643 base area 0-0.40 Local yes (Harirchian & Garimella, 2008) 2008 FC-77 400 0.06-4 12.7 79- 16.97 25 at G=700 kg/m2s 160- 748 2-60 rectangular 100 240- 1600 0-65 base area 0-1 No (Bertsch et al., 2008) 2008 R-134a 1900 2.5 9.53 8.74 0.3 1090 17 rectangular 8.9- 21 20-81 0-20 wetted area 0-0.9 No 50 2.4.6. Literature Survey on High Heat Flux Cooling Using Dielectric Working Fluids Since this work focuses on high heat flux cooling, the current position and level of technology advancement need to be determined. The objective of the following literature surveys was to define the technologies that proved to cool high heat fluxes using dielectric fluids. The resulting thermal performance of th technologiesvalues will be used in later chapters to compare them to those of FFMHS. (Agostini, Fabbri et al., 2007) presented a comprehensive review of high heat flux cooling technologies for literature published between 2003 and 2006. The highest heat flux achievable for TMHS was q?=93.8 W/cm2 using FC-72, reported by (J. Lee & Mudawar, 2005a, 2005b), and for jet impingement cooling was q?=161 W/cm2 using FC-72, from the work of (Fabbri et al., 2006). However, as will be seen in next paragraphs, the technological advancement in high heat flux cooling during the years since 2006 have generated more advanced technologies and higher heat flux values. (Agostini, Thome, Fabbri, & Michel, 2008) investigated boiling of refrigerant R-236fa in TMHS composed of 134 parallel channel of 67 microns wide, 680 microns high and 2 cm long. The maximum heat flux at the base of the heat sink was 255 w/cm2, corresponding to a pressure drop of 90 kPa and wall superheat of 25 ?C. To the best of this author?s knowledge, this value represents the highest heat flux achieved by a TMHS using a dielectric fluid and working in two phase heat transfer mode. Using an extrapolation technique on their experimental data, they argued that 51 the microchannel heat sink has the potential to keep the chip temperature 13?C lower than water liquid cooling at same pumping power. For these analyses they assumed a base heat flux of 350 W/cm2. (Kosar & Peles, 2007) performed two-phase experimental tests to analyze the thermal performance of a silicon heat sink with hydrofoil pin fins. The fins were 243 microns deep and equally spaced at 150 microns apart. The authors selected R-123 as working, fluid and the maximum critical heat flux of 312 W/cm2 was achieved at 2349 kg/m2s mass flux. The corresponding pressure drop was measured as 300 kPa. Finally, they concluded that the CHF mechanism is triggered by dryout and that CHF increases with increase in mass velocity and decreases with increase in vapor quality. (Visaria & Mudawar, 2008) studied the effect of subcooling on critical heat flux for spray-cooling systems. They utilized three different full-cone spray nozzles to spray FC-77, and a 1x1 cm2 heated copper surface was selected as test heated surface. They reported that enhancement of CHF at low subcooling values was mild but that at higher subcooling values it was significantly higher. Using a highly subcooled spray, they could achieve a maximum critical heat flux of 349 W/cm2 with a corresponding pressure drop of 174 kPa. They concluded that besides an increase in subcooling, CHF can also be increased by increasing volumetric flow rate and/or decreasing droplet diameter. (Sung & Mudawar, 2009) explored subcooled boiling and CHF in a novel heat sink designed by the authors and named ?hybrid microchannel and jet impingement cooling module.? They used a copper microgrooved surface with a base footprint area of 2x1 cm2 as the heat transfer surface. The fluid was HFE-7100 and was forced into 52 each microchannel from the top, using 14 small equally spaced orifices, each 0.39 mm in diameter. The highest critical heat flux achieved was 1127 W/cm2, which corresponds to a jet velocity of 6.5 m/s, pressure drop of 172 kPa and subcooling of 143 ?C. The authors argued that this is the highest ever heat flux achieved for a dielectric coolant at near atmospheric pressure. A summary of cooling technologies and the important parameters used in these studies is listed in Table 2-4. These values will be used as a basis for comparison with the performance of two-phase FFMHS in the next chapters. 53 Table 2-4. Summary of technologies used for high heat flux cooling Authors Cooling Technology Heat Sink Base Area [cm2] Fluid Pressure Drop [kPa] Subcooling [?C] Pumping Power / Cooling Capacity (x 103) ?Tsat [?C] Maximum Achievable Heat Flux [W/cm2] (Agostini et al., 2008) Microchannel 2x1 R236fa 90 10 1.97 27.0 250 (Kosar & Peles, 2007) Hydrofoil based micro pin fin 1x0.18 R-123 300 76 (1) 1.3 27.5 (1) 312 (Visaria & Mudawar, 2008) Spray Cooling 1x1 F-77 174 70 11.9 32.4 349 (Sung & Mudawar, 2009) Hybrid Microchannel and Jet Impingement 2x1 HFE-7100 172 114.3 (2) 4.5 104.6 (2) 1127 (1)-Calculated for Pout=500 kPa, and assuming a room temperature of Tamb=25 ?C (2)-Caluclated by assuming the outlet pressure to be Pout=Patm=101 kPa 54 2.1. Summary In this chapter working principles of FFMHS in single-phase and two-phase heat transfer modes are defined and the possible benefits of using such systems are highlighted. The fabrication methodology, advantages and manufacturing limitation of microgrooved surfaces adopted for this study are reviewed. The important fundamentals of flow and heat transfer mechanisms expected to dominate heat transfer in FFMHS are covered and relevant equations are given. The literature on single-phase FFMHS, two-phase saturated boiling in microchannels and high heat flux cooling systems are reviewed and important conclusions are tabulated. 55 CHAPTER 3: SINGLE-PHASE NUMERICAL STUDY The objective of this chapter is to analyze single phase Force Fed Microchannel Heat Sink (FFMHS) heat transfer and fluid flow and to determine the geometrical and flow parameters that affect the thermal performance. For this purpose a numerical model is introduced and the numerical simulation methodology is discussed in detail. Applying the numerical model, a typical FFMHS geometry is analyzed and important flow parameters are discussed. Finally, a parametric analysis is performed by changing several geometrical and flow variables and calculating the rate of change on heat transfer and pumping power. This study will create a base understanding that will help to determine the optimization variables discussed in Chapter 4. 3.1. Computational Domain Numerical modeling of a real scale complete heat sink show in Figure 2-1 using CFD tools is neither feasible nor practical and presents real challenges in terms of computational time. A practical solution for this problem is to define a computational domain consisting of a much smaller but repetitive part of the real- scale heat sink. For this study, the selected computational domain is shown in detail in Figure 3-1. Due to the repetitive nature of the computational domain over the entire heat sink on the Y-Z and X-Y planes, symmetry boundary conditions can be used at the boundary surfaces located at these planes. The model is a combination of the microgrooved surface modeled as solid material and the fluid that flows through the 56 feed channels and the microchannels. Because the microgrooved surface is symmetrical, it is modeled as the base and half of a fin, the microchannel consists of half of a channel, and similarly the inlet and outlet feed channels are considered only half of the channel width size. Figure 3-1. Numerical computational domain Selection of the computational domain shown in Figure 3-1 includes several assumptions: ? The flow rate in each feed channel is steady and equal. For an FFMHS the inlet feed channels have identical geometries and they are fed from the same pressure source. The outlet feed channels are formed by the gap between two neighboring manifolds, and therefore the pressure loss for each unit cell is constant. The only exception is the feed channels at the edges (the first L ch x y z 57 and last feed channels), where there is no counter-manifold to create symmetry. ? The fins and channels of the microgrooved surfaces are usually not straight and may have a slightly bent geometry, as shown in Figure 2-2 (a)-(b), and the fins may end with an unconventional sharp fin tip. The geometry of the surface is a function of the process and tools used for manufacturing. Here the microgrooved surface geometry was simplified by assuming straight fin geometry with flat fin tips. ? The heat flux applied from the bottom of the microgrooved surface is constant. A non-uniform heat flux distribution is not possible, since any variation in X and Z directions will violate the symmetry conditions. ? The thermal properties (thermal conductivity) of the metal substrate are isotropic. Similarly, the symmetry boundary condition can only be applied for solids with isotropic thermal properties in the X and Z directions. ? The heat transfer through the manifolds is neglected and the manifolds are adiabatic. There are two means of possible heat transfer in the manifolds. The first mechanism is the heat transfer through the incoming and outgoing fluid streams in the neighboring inlet and outlet feed channels. Here a temperature gradient forms due to the temperature difference in the fluid streams, where fluid leaving the heat sink is hotter than inlet steam due to the energy gained during heat transfer on the microgrooved surface. The heat transfer caused by this temperature gradient was neglected by assuming the manifolds to be made of poor conductive material such as low conductivity plastic. The 58 second possible heat transfer mechanism is the thermal conduction through the tip of the fins to the manifold. In many practical applications, the manifolds are not bonded to the microgrooved surface, but rather kept in place by compressive forces. This configuration allows the microgrooved surfaces to be cleaned by easily disassembling the heat sinks in case of fouling and microchannel clogging. As shown in Figure 2-2 (a)-(b), the fin tips usually have a sharp edge, which creates a line of contact when compressed with the manifold top face, therefore creating a relatively high thermal contact resistance. To further simplify the problem and eliminate uncertainties associated with linear thermal contact resistance, an adiabatic manifold was assumed for the numerical simulations. There are six distinctive heat transfer areas between the fluid and solid walls, and each was numbered as shown in Figure 3-1. The first zone is the fin tip under the inlet feed channel; the second zone is the side fin area under the inlet feed channel; the third zone is the base area; the fourth zone is the straight microchannel zone; the fifth zone is the side fin area under the outlet manifold; and the sixth zone is defined as the fin tip area under the outlet feed channel. The heat transfer characteristics of each of these zones will be analyzed in the next sections. 3.2. Single-Phase Modeling with Computational Fluid Dynamics Due to the complex three-dimensional geometry of the computational domain, an exact analytical solution for flow field and heat transfer cannot be obtained; therefore, a numerical approach needs to be considered. Modeling techniques 59 incorporating computational fluid dynamics (CFD) are based on numerically solving the flow field for a given geometry and given boundary conditions. The solver selected for this work is Fluent? 6.3.26, which is a CFD package well known for its capability to solve fluid flow and heat transfer problems. Fluent? uses the finite volume discretization method with implicit or explicit formulation to solve the Navier-Stokes equation. For flows involving heat transfer an additional equation of energy balance is solved. Additional detailed information about the finite volume method and solution procedure can be found in (Fluent-Inc, 2008), (LeVegue, 2002) and (Versteeg & Malalasekera, 2007). The continuity equation is shown in general form in Equation (3-1) : (3-1) For steady-state incompressible flow with no mass source term, the conservation equation can be further simplified by eliminating the first terms on the left-hand side and right-hand side, respectively. The conservation of momentum in a non-accelerating reference frame is given in Equation (3-2) where the stress tensor ? is given by Equation (3-3). The terms on the left-hand side represent the momentum change rate and convective momentum transfer rate, while the right-hand side represents pressure forces, diffusive momentum transfer rate, gravitational forces and external body forces, respectively. For incompressible and steady-state flow with zero body force, the first and last terms of Equation (3-2) will be neglected. For all numerical simulations performed in this study laminar flow regime was considered. (3-2) 60 (3-3) The general form of energy equation is given in Equation (3-4). The left-hand side represents the temporal energy change and convective energy transfer. The first three terms on the right hand-side represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively. hS includes the heat of chemical reaction, and any other defined volumetric heat sources. (3-4) The energy equation does not include the viscous dissipation effect, which is turned off by default in Fluent. The viscous dissipation can be important at high Brinkman numbers (Br > 1); the Brinkman number is defined as the ratio of viscous heating rate to the heat transferred through walls. The heat flux considered in the numerical simulations was fairly high, 1000 W/cm2 base heat flux for all cases. Therefore, for the calculated numerical cases Br << 1 was always satisfied and the viscous dissipation term was not calculated. However, based on authors experience from preliminary numerical simulations, special attention should be given in cases with low to moderate heat fluxes on the order of ~10 W/cm2,where viscous heating effect can be significant at small hydraulic diameters and high velocity flows. All fluid physical properties were calculated at 101 kPa pressure and 20 ?C using Engineering Equation Solver (F-Chart-Inc, 2009), and solid material properties were evaluated at the same temperature using property tables given in (Incropera & DeWitt, 2002). 61 3.3. Numerical Simulation of a Sample FFMHS A basic understanding of heat transfer and flow in FFMHS is needed before performing any design, optimization or modeling. Therefore, as the first step, a typical FFMHS was numerically simulated and analyzed. The purpose of these numerical simulations was to create an understanding of the working principle and to serve as the initial design concept that would later be used in the optimization process. The selected sample FFMHS configuration consisted of a microgrooved surface with channel height of Hch=480 ?m, fin thickness of tfin = 48 ?m, microchannel width of wch =72 ?m, base thickness of Hbase = 400 ?m and manifold system with inlet feed channel width of wl = 400 ?m, outlet feed channel width of wv = 400 ?m and total channel length of Lman=2 mm. These values were based on previous numerical and experimental experience: the microgrooved surface dimensions are close to those of Surface #17 given in Table 2-1, and the manifold and feed channel dimensions were based on the manifold designed for experimental tests, with equal inlet and outlet width of feed channels. The microgrooved surface material and working fluid were copper and water, respectively. 3.3.1. Grid Generation and Numerical Mesh Selection of the proper mesh for the computational domain is important due to the tradeoff between computational time and model accuracy. A mesh generated with fine grid spacing will have higher accuracy but will require higher computational time. Selection of an optimum mesh was even more important in the current 62 optimization procedure, in which several hundreds of numerical solutions were to be solved for different geometries and flow conditions. The first step in meshing process is the selection of mesh type which can be either structured or unstructured. The unstructured grids can be applied to almost any geometry but require more information to be stored furthermore, controlling the local grid resolution is difficult, and such grids are not suitable for automated grid generation. Therefore, as a general numerical strategy, structured grids are preferred when they are applicable. The computational domain shown in Figure 3-1 has a ?straight? geometry which does not include any round corners or bended angled edges. The geometry can be formed by combining different rectangular volumes, and therefore a structural grid can be successfully applied. The mesh generation was performed by Gambit?, which is a software package available in the Fluent? 6.3.26 package. The meshed computational domain consists of 68,850 structured hexahedral cells and is shown in Figure 3-2 (a) and (b), front view and isometric views, respectively. 3.3.2. Boundary Conditions and Output Parameters A complete list of applied boundary conditions is given in Table 3-1, based on the coordinate system shown in Figure 3-1. Boundaries not included in the table were selected as adiabatic wall as default. The specified inlet mass flow rate boundary condition uses flow rate as input and calculates the static pressure based on the flow field. Therefore, the inlet static pressure is not known as a priori until the convergence is obtained. Similarly, the outlet boundary condition is specified as static pressure and the total pressure is calculated after convergence is obtained. 63 Figure 3-2. (a) Front view and (b) perspective view for grid generated for Hch=480 ?m, wch/2=36 ?m, tfin/2 = 24 ?m, L=800 ?m, wl/2=200 ?m, wv/2=200 ?m, Lman=2 mm, Hbase = 400 ?m Table 3-1. The boundary conditions applied to computational domain Location of applied boundary condition Boundary Condition x = 0 Symmetry x=L Symmetry z=0 Symmetry z=tfin/2+wch/2 Symmetry y=0 Uniform Heat Flux of q?=1 kW/cm2 y=Hbase + Hch + Lman 0De a secondary vortex pair may be present, dependent on channel geometry. The development of secondary flows changes both heat transfer and flow characteristics. The vortices create continuous fluid mixing by moving the ?cold? fluid at the center to the side-walls of the microchannel, therefore enhancing the convective heat transfer. This process disturbs and decreases the thickness of the thermal boundary layer that started to develop at the inlet to the microchannel. On the pressure drop side, however, the flow energy associated with vortices will eventually dissipate into heat, and the pumping power required to drive the fluid in a curved pipe will be always higher compared with straight-tube and channel geometries at the same flow rate. These conflicting objectives of heat transfer efficiency and pumping power need to be considered for a clear evaluation of the possible benefits of secondary flows. Velocity vectors at several cross sections in the computational domain for Case #3 are shown in Figure 3-6. As the fluid starts to turn at both the first and second bends, vortex pairs are created in the microchannel as the fluid in the center is pushed down and forces the liquid close to the walls to move in the opposite direction. Due to symmetry conditions, only one half of the channel, and therefore only one vortex is shown in the figure. The pathlines and transition between flow regimes at different Reynolds number flows are shown in Figure 3-7 (a),(b) and (c). The corresponding Dean numbers were calculated as 2=De , 15=De and 61=De , 73 respectively. For Case #1, the low Reynolds number leads to low Dean numbers, and therefore the centrifugal forces are negligible, and the secondary flows are not present. The pathlines are uniform and almost symmetric, with no disturbance in the flow. As the Reynolds number is increased in Case #2 and later in Case #3 by achieving 10>De , the centrifugal forces start to become important. The vortices formed during flow turning disturb the flow, and the pathlines show a less uniform pattern. As seen in Figure 3-7 (c), due to secondary flows and the mixing effect, the pathlines can cross over each other on the plane of view. Figure 3-6. Velocity vectors created by secondary flows at several cross sections in the computational domain for Case #3 at h=250,000 W/m2K and De=61 74 Figure 3-7. Pathlines at z=0 plane for (a) Case #1 at h=50,000 W/m2K and De=2, (b) Case #2 at h=150,000 W/m2K and De=16, (c) Case #3 at h=250,000 W/m2K and De=61 The fluid temperature distribution at the symmetry plane of z=0 is shown in Figure 3-8 (a), (b) and (c) for Case #1, Case #2 and Case #3 respectively. Two different trends become important as the flow Reynolds number goes from low to high. First, the temperature rise of the fluid is significant at low flow rates. This is expected, since the mass flux is lower and fluid can be heated much more before exiting the microchannel. Second, the velocity stratification shown in Figure 3-4 also creates temperature stratification. The low velocity zones close to the bottom of the microchannel at low Reynolds number flows and ?dead zones? in the high Reynolds number cases create high temperature zones. Similarly, the relatively low velocities allow the liquid to be heated for longer times therefore a temperature difference is observed in these regions. (a) (b) (c) 75 Figure 3-8. Working fluid temperature distribution at z=0 for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K Figure 3-9. Fin feat flux distribution for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K (a) (b) (c) (a) (b) (c) 76 The heat flux distribution on the fin and microchannel base for the three cases is shown in Figure 3-9 (a),(b) and (c). Although the mass flux has a significant effect on heat flux distribution on the fin surface, the maximum heat flux always occurs at the inlet region to the microchannel. This global maximum is the result of the large temperature difference between the fluid and surface and the significant entrance region effects where thermal boundary layer is relatively thin and heat transfer resistance is low. At low Reynolds number flows (Figure 3-9 (a)) the heat sink efficiency decreases due to increase in non effective areas which do not contribute to heat transfer. The temperature difference between bulk liquid and surface is low in these regions. The heat transfer characteristic changes significantly with higher Reynolds number flows (Figure 3-9 (c)). First, the heat flux becomes more uniformly distributed along the fin surface with the heat flux gradient decreasing slightly along the microchannel length. However, local minimums are present at the heat transfer surfaces under the recirculation zones. The fluid trapped in the recirculation zones has high bulk temperatures, thereby decreasing the convective heat transfer efficiency. Second, the secondary local maxima starts to appear close to the impingement zones under the inlet and outlet feed channels. Similar local high heat transfer zones were reported by (Copeland, 1995b), (Copeland et al., 1997) and (Ng & Poh, 1999). Close to the impingement zones, the local fluid acceleration and vortices created during the flow turning have the effect of reducing the thermal boundary layer thickness and enhance heat transfer. These local high heat transfer zones are a strong function of Reynolds and Dean numbers. 77 Figure 3-10. Temperature contours of fin surface, microchannel bottom wall and base material for (a) Case #1 at h=50,000 W/m2K, (b) Case #2 at h=150,000 W/m2K, (c) Case #3 at h=250,000 W/m2K Finally, the surface temperature distributions on the fin surface, microchannel base and middle of base material are shown in Figure 3-10 (a),(b) and (c) for the selected three reference cases. The minimum fin temperature occurs close to the tip of the fin region, where the fluid enters the microchannel. Due to high heat transfer coefficients and relatively large temperature differences between the surface and fluid, the local fin temperature can decrease significantly. At low Reynolds number flows all the heat that is transferred to the fluid is localized at the inlet region with heat flowing from all directions, perpendicular to the isotherms shown in Figure 3-10 (a). Increasing the flow rate to higher Reynolds numbers (Figure 3-10 (a) and (b)) increases the heat transfer efficiency and significantly decreases the heat sink temperatures. On the other hand, the temperature isotherms become more horizontal, indicating a more uniform heat flow from the bottom of the base material to the fin heat transfer surface. (a) (b) (c) 78 3.4. Parametric Numerical Study In the previous section several numerical simulations were performed for a single geometry with various inlet flow conditions. The numerical simulation results indicated that flow regimes and thermal performance of FFMHS are a strong function of flow parameters or Reynolds number. In order to investigate the geometrical effects, a similar parametric study was initiated. The goal of this study was to identify the effects of each geometrical parameter on heat transfer and pumping power. The parametric analyses were performed by selecting and varying one of the geometrical parameters of interest while keeping other parameters constant. Each new design variation was simulated three times to yield heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K, respectively. This was accomplished by adjusting the flow inlet conditions until the desired heat transfer coefficient was obtained. The effect of selected geometrical parameter was then analyzed by calculating the pumping power rate of change compared with a selected benchmark reference case. The reference cases are the selected case studies shown in Table 3-3. The resulting pumping power values were compared with reference cases at similar heat transfer coefficient values. The geometrical variation of each parameter was calculated by evaluating: , ? = ii i ref G G (3-12) where iG represents the dimension of geometrical parameter i being studied (microchannel height, microchannel width, manifold dimensions, microchannel length and base thickness), and ,i refG is the reference value for the same parameter 79 taken from Table 3-3. The ?i value represents the relative change of the investigated parameters to the reference case. The relative change in pumping power was normalized similarly by dividing the resulting pumping power of the investigated parameter ??pumpP by the pumping power of the reference case at the same heat transfer coefficient, ,??pump refP , taken from Table 3-3: , ? ??= ??pumppp pump ref P P (3-13) The advantage of using a ?i versus a ? pp graph is the ease of showing the relative change in pumping power in terms of relative change in geometry at fixed heat transfer coefficients. For example, a ? pp value greater than one indicates an increase in pumping power compared with the benchmark reference case. The geometry variation was based on the practical fabrication range of microgrooved surfaces and manifolds. While increasing the ratio of the microgrooved enhanced heat transfer surface area to the base area by increasing the fin height or fin aspect ratio is highly desirable, fabrication limitations restrict the geometrical design ranges. These limitations also play an important role in defining the optimization parameters? lower and upper bounds and prevent heat transfer geometries that might be theoretically superior heat transfer surfaces but that are practically impossible to fabricate. Therefore, the lower and upper bounds of the geometrical parameters of microgrooved surfaces were defined before performing any parametrical study. 80 3.4.1. Practical Geometrical Range of Microgrooved Surfaces Fabricated by Micro Deformation Technology The copper microgrooved surfaces are fabricated by Micro Deformation Technology (MDT) and are designed to improve heat transfer by creating parallel microfins that enhance heat transfer area. Currently, MDT is under continuous development, but according to Wolverine Inc., which has patented this technology, the current practical limitations that can be applied for cost effective surfaces are as follows: 0.2 mm 5.0 mm? ?chH (3-14) 10?ch fin H t (3-15) 0.2 1.5? ?ch fin w t (3-16) The inequality shown in Equation (3-14) defines the practical minimum and maximum bounds for fin and microchannel height chH ; Equation (3-15) represents the maximum fin aspect ratio /ch finH t ; and Equation (3-16) defines the limits for channel width to fin thickness ratio /ch finw t . 3.4.2. Effect of Fin Thickness and Fin Height The effect of fin thickness fint and channel height chH on pressure drop is shown in Figure 3-11 and Figure 3-13, respectively. For each constant h value taken into consideration, the cases of 1? =tfin and 1? =Hch represent the reference cases and the corresponding fin aspect ratio at these values is / 10=ch finH t . It should be noted 81 that this value is actually equal to the practical limitation dimension defined by Equation (3-15). The parametric study was performed by increasing fin thickness or decreasing channel height which resulted in FFMHS designs utilizing microgrooved surfaces with fin aspect ratios lower than 10. As noted before, numerical results for these cases were obtained by variation of flow rate until desired heat transfer coefficient of 50,000 W/m2K, 150,000 W/m2K or 250,000 W/m2K was achieved. Two important results can be drawn from Figure 3-11. First, the pumping power variations are relatively small when the channel height is decreased up to 20% but increase drastically at small channel heights where the height is reduced up to 60%. The change in channel height affects active heat transfer area, microchannel cross-section flow area and the length of a typical streamline passing through the microchannel. Decreasing the fin height will decrease the heat transfer area and microchannel cross-section flow area; therefore, it will require higher flow rates to increase the convective heat transfer and keep the desired heat transfer coefficient constant. The high flow rate and smaller flow area in turn will rise the pumping power significantly at small ?Hch values. The second important result that can be obtained from Figure 3-11 is the decreasing trend of pumping power with decreasing channel height for constant heat transfer coefficient curve of 250,000 W/m2K between 0.6 0.8?? ?Hch . In this region the pumping power can be lowered by about 15% by decreasing the channel height. This effect can be explained by the flow schematic shown in Figure 3-12. For a high channel height case, a typical streamline passing through the middle of the channel is longer than the streamline passing through a microgrooved surface with shorter channel height; therefore, the flow 82 resistance decreases. On the other hand, convective heat transfer in the region close to the inlet into the microchannels is very high due to the thin thermal boundary layer of thermally developing flow. At high Reynolds numbers the local heat transfer coefficient in the region close to the tip of the fin is very high, and the fin efficiency in this region drops significantly. Decreasing the channel height will decrease the heat transfer area but in turn will increase fin efficiency by decreasing the fin height and therefore the fin thermal resistance as well. In summary, by decreasing channel height and thus shortening of the flow path and increasing fin efficiency, it is possible to enhance the heat sink performance by lowering the pumping power at heat transfer coefficients of 250,000 W/m2K. However, this trend is observed only at high heat transfer coefficients where the flow rate is relatively high and the decrease in pumping power is not more than 20%. Figure 3-11. Effect of fin and microchannel height (Hch) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ???? p p ?Hch h= 50 000 [W/m2K] h= 150 000 [W/m2K] h= 250 000 [W/m2K] 83 Figure 3-12. Schematic of flow and a typical streamline for (a) high channel height (b) low channel height FFMHS configuration Figure 3-13. Effect of fin thickness (tfin) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K The effect of fin thickness on pumping power is shown in Figure 3-13. Increasing the fin thickness will decrease the fin aspect ratio, will increase the fin efficiency and will decrease the flow area per unit base heat sink area. Therefore, a larger amount of fluid needs to pass through the microchannels to remove more heat 1 1.2 1.4 1.6 1.8 2 1 1.2 1.4 1.6 1.8 2 ???? p p ?tfin h= 50 000 [W/m2K] h= 150 000 [W/m2K] h= 250 000 [W/m2K] Base Half fin Half channel Feed channel (a) (b) 84 and to keep heat transfer constant at selected constant values. The resulting effect is a monotonic and almost linear increase in pumping power with increased fin thickness. An interesting observation seen in both Figure 3-11 and Figure 3-13 is that the pumping power increase for the intermediate heat transfer coefficient of 150,000 W/m2K is significantly higher than the values for 50,000 W/m2K and 250,000 W/m2K at the same ?i values. This trend results from the beneficiary effects of increase in mass flux by decreasing the fluid temperature close to the outlet region of the microchannel. For example, consider the fluid temperature variations calculated at fixed heat transfer coefficients shown in Figure 3-8 (a),(b) and (c). Here, going to higher heat transfer coefficients an increase in mass flow rates was required. For high mass fluxes (Figure 3-8 (c)) the fluid temperature that exits the microchannel is very close to the inlet temperature, therefore a moderate increase in mass flux will have a negligible impact on fluid temperature distribution. On the other hand, at low mass fluxes (Figure 3-8 (a)), there is a significant fluid temperature variation in the microchannel and a moderate increase in mass flux will have a significant impact on total heat transfer. The increase in fluid velocity will create higher temperature differences at microchannel outlet region and will decrease the less efficient heat transfer areas close to the microchannel bottom. When the channel height decreases or fin thickness increases, to balance the increase in heat dissipation and to keep the heat transfer coefficients at desired constant values, the mass flux in the microchannel needs to increase. This increase in mass flux in turn, will enhance the heat transfer efficiency much more significantly at low h values, when compared to high h values. This additional benefit in heat transfer will require less pumping power increase at 85 h=50,000 W/m2K, resulting in ?i values ending in intermediate region between curves of h=150,000 W/m2K and h=250,000 W/m2K. 3.4.3. Effect of Microchannel Width Varying the microchannel width while keeping other parameters constant has a significant effect on both heat transfer coefficient and pumping power. In fact, heat transfer coefficients and pumping power values conflict when the microchannel width is changed. A heat sink design with smaller microchannels can benefit from the increase of local heat transfer coefficients as it scales down. However the consequent decreases in the ratio of flow-area per unit heat-sink base area and the smaller hydraulic diameters are the parameters that decrease the heat sink performance. The variation of pumping power rate with microchannel width is shown in Figure 3-14. Here, the trend of pumping power rate curves is significantly dependent on the heat transfer coefficient. At low heat transfer coefficients (50,000 W/m2K), a decrease in channel width has a continuously increasing trend on pumping power rate. Here the flow rate is relatively low and the fluid temperature will rise rapidly along the channel. Most of the heat will be transferred in a small region close to the microchannel entrance, while the end part will not contribute much due to the relatively low temperature difference, similar to Figure 3-8 (a) and Figure 3-9 (a). Therefore, decreasing the microchannel width and hydraulic diameter will increase the local heat transfer coefficients, but will have little or negligible effect on overall heat transfer coefficient due to the small temperature differences between liquid and heated wall. On the other 86 hand, the increase in pumping power due to the decrease in hydraulic diameter will have a more dominant effect and will further increase the pumping power. Figure 3-14. Effect of microchannel width (wch) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K The opposite effect is dominant for high heat transfer coefficients. For a constant heat transfer coefficient of 250,000 W/m2K decreasing the channel width has a significant positive effect on pumping power, continuously decreasing it up to 60%. The local increase in heat transfer is much more effective here, where the flow rate is high and the rise in fluid temperature along the microchannel is less. Therefore, much less fluid needs to flow through the microchannels to compensate for the pressure increase due to hydraulic diameter and the lower flow area per unit base area. It is clear, however, that at a given heat transfer level, a further reduction in channel width 0 0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 ???? p p ?wch h= 50 000 [W/m2K] h= 150 000 [W/m2K] h= 250 000 [W/m2K] 87 will create very small gaps and flow areas, and pumping power will eventually rapidly increase. 3.4.4. Effect of Inlet and Outlet Feed Channel Widths The variations of the rate of pumping power per unit area with changes to inlet and outlet feed channel widths are given in Figure 3-15 and Figure 3-16, respectively. Changes in feed channel widths have a significant impact on both pumping power and heat transfer. As the inlet feed channel width decreases, the reduced inlet flow area will decrease inlet hydraulic diameter and therefore the inlet flow resistance will increase. On the other hand, the reduction in feed channel will reduce the base area of the unit cell and therefore the total heat input will decrease, requiring less heat to be cooled. This in turn will decrease the fluid temperature increase along the microchannel, and the end parts of the heat sink will work more efficiently due to the increased temperature difference between the microgrooved surface and working fluid. Another benefit of decreasing feed channel width may be the decrease in flow length which will decrease the characteristic flow length, and flow resistance. Interestingly, increasing the inlet and outlet feed channel widths at low to intermediate heat transfer coefficients of 50,000 W/m2K and 150,000 W/m2K have little effect on pumping power, while decreasing the width at the same values creates a sudden increase in pumping power rate. Further reductions in the feed channel width will eventually create a rapid increase in pumping power rate due to the excessive pressure drop caused by the inlet area restriction. 88 Figure 3-15. Effect of inlet feed channel width (wl) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K Figure 3-16. Effect of outlet feed channel width (wv) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K 0.5 1 1.5 2 2.5 0.5 1 1.5 2 ???? p p ?wl h= 50 000 [W/m2K] h= 150 000 [W/m2K] h= 250 000 [W/m2K] 0.5 1 1.5 2 2.5 0.5 1 1.5 2 ???? p p ?wv h= 50 000 [W/m2K] h= 150 000 [W/m2K] h= 250 000 [W/m2K] 89 At a high heat transfer coefficient of 250,000 W/m2K the pumping power shows a different trend with respect to variations in the inlet and outlet feed channels. Here, decreasing the inlet feed channel width has the beneficial effect of decreasing the pumping power significantly, while decreasing the outlet feed channel width produces a continuous rising trend in the pumping power curve. Again, the reduction in fin efficiency at the inlet regions has a negative effect on heat sink performance, and therefore the heat sink reduces this effect by decreasing the fin tip area under the inlet feed channel and increasing the heat transfer area close to the end of the channels under the outlet feed channel, where the fin efficiency is significantly higher. 3.4.5. Effect of Microchannel Length In the study of microchannel length effect, the dimension of inlet and outlet feed channels were kept constant and only the manifold length was varied. The case of 1? =Lch corresponds to a manifold thickness of 0.4=mant mm. In general, short manifolds are desired for typical FFMHS designs as suggested by (Copeland, 1995a), (Ryu et al., 2003) and (Copeland et al., 1997). Decreasing the manifold thickness will improve the heat sink performance by decreasing the flow length and therefore the flow resistance. Similarly, the base area will decrease, and less cooling will be required to cool the heat generated in a single FFMHS unit cell. Also shortening the channel will increase the effectiveness range of the inlet regions associated with high local heat transfer coefficients. 90 Figure 3-17. Effect of microchannel length (Lch) on pumping power at heat transfer coefficients of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K Here, there are two factors that limit the performance improvement resulting from the decrease of the manifold thickness. First, as the channel becomes shorter, the flow resistance of flow passing the channel through different pathlines will be significantly different. More specifically, the length of a pathline located close to the top of the microgrooved surface will be much shorter compared with a pathline passing all the way down to the bottom of the microchannel. The resulting difference will facilitate creation of a bypass of fluid in the regions close to the top of the microgrooved surface and the feed channels, and it will require an increase in flow rate to increase the fluid inertia enough to be pushed to the bottom of the channel. The bypass effect is clearly shown in Figure 3-17, where decreasing the microchannel length more than 25% forces the heat sink to go to higher flow rates to achieve desirable heat transfer coefficients, therefore increasing the pumping power. The 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.6 0.8 1 1.2 1.4 ???? p p ?Lch h= 50 000 [W/m2K] h= 150 000 [W/m2K] h= 250 000 [W/m2K] 91 second limitation is related to the fabrication and manufacturing of manifolds. Since the coupling of microgrooved surfaces and the manifold system was designed to be implemented using compression forces, the manifolds should be structurally sound and also easy to manufacture. Fabricating micron size manifolds is thus not always practical. 3.4.6. Effects of Microgrooved Surface Base Thickness and Manifold Height One particularly interesting parameter is the height/thickness of the microgrooved surface base (Hbase shown in Figure 3-1). The base thickness does not affect the pressure drop and does not conflict with heat transfer coefficient. In fact, it contributes to additional thermal resistance to heat transfer from the bottom of the microgrooved surface to the fins and it is generally desired to design it to be as thin as possible, especially for high heat flux cooling applications. A possible increase in base thickness is usually considered only in applications where the surface temperature uniformity is important and adding extra material will increase the heat spreading through the base. The surface temperature uniformity was not selected as a parameter in this study, but resulting temperature variations will be reported in next chapter. 3.5. Conclusions A sample FFMHS geometry was first investigated numerically at different inlet flow conditions. It was found that the flow Reynolds numbers have a significant effect on both flow regimes and heat transfer characteristics. At low Reynolds 92 number flows, the fluid stratifies uniformly by creating a bypass zone between the inlet and outlet feed channels at the top of the microchannel. This effect in turn creates inefficient dead zones with low fluid circulation and low heat transfer. Increasing the Reynolds number reverses the velocity stratification, with the higher fluid core close to the bottom of the microchannel and with fluid recirculation zones close to the top part. The increase in fluid velocity also initiates secondary flows manifested in the forms of vortex pairs in the microchannel cross section. The vortices and flow impingement in turn reduce the convective thermal resistance and create local heat transfer maximums. The effects of geometrical parameters on pumping power were analyzed for three different heat transfer coefficient values of 50,000 W/m2K, 150,000 W/m2K and 250,000 W/m2K. It was found that each geometrical parameter can affect the thermal performance in both positive and negative ways. Usually the change in geometrical parameters has conflicting effects on heat transfer and pressure drop, and an optimum point may exist at a specific flow condition. Here, the main difficulty in calculating optimal flow and geometrical conditions is due to the large number of parameters that affect the FFMHS performance. Therefore, the results of this study will be used in next chapter as a basis for selecting key optimization parameters and their lower and upper bounds. 93 CHAPTER 4: MULTI-OBJECTIVE OPTIMIZATION OF SINGLE-PHASE FFMHS This chapter discusses the optimization procedure for Force Fed Microchannel Heat Sinks (FFMHS). The chapter starts with an introduction to heat sink optimization and a description of the metamodeling and optimization algorithm and its implementation with a numerical Computational Fluid Dynamics (CFD) solver. Then the optimization procedure is applied for three different cooling technologies; Force Fed Microchannel Heat Sink (FFMHS), Traditional Microchannel Heat Sink (TMHS) and Jet Impingement Heat Sink (JIHS) for comparison purposes. A detailed analysis of the FFMHS metamodeling results and the effect of its variables on thermal performance is performed. The chapter concludes with a comparison between the investigated cooling technologies at their optimum designs. 4.1. Heat Sink Design and Optimization The design of heat sinks is a complicated process because the final thermal and hydraulic performance is dependent on many parameters such as geometrical dimensions, coolant fluid properties, flow conditions and heat sink material properties. Geometrical parameters can be channel dimensions through which the coolant fluid passes, extended surface dimensions such as rectangular fin thickness or pin fin diameter, and height or base-plate thickness. The coolant and material parameters depend on physical properties such as thermal conductivity, density, specific heat and fluid viscosity, and the flow condition that is generally specified as 94 the total fluid mass flux that passes through the heat sink. All those parameters are coupled, affecting performances of the heat sink and thus should be considered in the optimization. TMHS for high heat flux cooling applications using liquid cooling have been investigated extensively since their early introduction by (Tuckerman & Pease, 1981). Several authors performed optimization studies by numerically and analytically modeling TMHS?s with the objective of minimizing the overall thermal resistance (Khan, Culham, & Yovanovich, 2009), (Kandlikar & Upadhye, 2005), (D.-K. Kim, 2007), (S. J. Kim, 2004), (Dong Liu & Garimella, 2005), (Phillips, 1987), (Shao, Sun, & Wang, 2007). The analytically developed models have the advantage of eliminating the relatively time-consuming computational time and providing a functional form that can be easily implemented in any programming language. Along with simplifying assumptions, this method was successfully used in predicting heat transfer performance of TMHS?s, and it was demonstrated by (Dong Liu & Garimella, 2005) that analytical models offer sufficiently accurate predictions for practical designs, while being straightforward to use. On the other hand, the CFD based numerical models have the advantage of being applicable to more complex geometries and being able to simulate advanced physical phenomena such as conjugate heat transfer between fluid and solid surfaces, temperature and pressure dependent properties, and turbulence modeling as well as transient flow modeling. The CFD based models are particularly useful in modeling, designing and predicting heat sink performances where traditional heat transfer and pressure drop correlations cannot be applied, such as complex unconventional geometries. 95 The complex geometry and flow field encountered in FFMHS?s make it challenging to generate any analytical based models, and to date no such models have been published. At this point, CFD-based methods are more accurate and straightforward techniques to investigating FFMHS performance. Therefore, adopting a similar approach to that described in previous chapter, Fluent? was selected as the numerical solver for the optimization purposes. However, a direct implementation of CFD tools with any optimization algorithm can be prohibitively time expensive and not practical. As a practical solution at this point, Approximation Assisted Optimization (AAO) technique proved to be a successful candidate. AAO combines the advantages of CFD modeling with time efficient metamodeling methods. 4.2. Parametric CFD Simulation Interface Although AAO methods were developed to minimize the computational time, the number of CFD simulation evaluations that need to be performed is still large, mostly in the order of 100 runs. Manual mesh generation and numerical simulation for each case is not practical and may require continuous user interaction. This problem was eliminated by automating the process with the help of Parametric CFD Simulation Interface (PCFDSI). The code of PCDSI was written in Matlab and serves as a function that accepts optimization variables as inputs and generates the desired objective functions, temperature distribution, velocity field and wall heat flux distribution. The flow diagram of PCFDSI is shown in detail in Figure 4-1. The function accepts one set of variables as input. These variables, combined with constant parameters defined in the function, set the problem. In other words, the geometrical 96 dimensions, flow input conditions, material properties, grid distribution, boundary conditions and CFD solution procedure are set for the given input conditions. Based on these set values, the PCFDSI function creates Fluent? and Gambit? script files, also known as journal files. The journal file created for Gambit? contains commands for building the computational geometry, meshing the domain and setting up boundary conditions. The Fluent journal file incorporates command syntax that is used for mesh import, grid checking, scaling, initializing the energy model, applying the inlet and outlet boundary condition values, controlling and initializing the post- processing of the results, and saving the case and data files. The next process is initialization of Gambit? with the journal file created, which in turn generates the mesh file of the computational domain. After the end of this process, Fluent? is initiated and run with the input of the journal file and mesh file. The numerical solution procedure is performed at this stage, which mainly determines the period of a PCFDSI function evaluation. After the numerical convergence is achieved, post-processing is performed by generating the desired data such as velocity, temperature and pressure values at specified locations in the computational domain. Post-processing was also used to validate the numerical convergence in case of reaching maximum iteration number. (O. A. A. Abdelaziz, 2009) suggested tracking static pressure difference for a given number of last iterations and evaluating the solution by comparing standard deviations of this value. 97 In this study, the total pressure differences between the inlet and outlet boundaries and average base temperatures for the last recorded 100 iterations were recorded. In the case reaching the total iteration number, the standard deviations for these values were calculated and evaluated. The case was accepted if standard deviation values were less than 0.5%. Finally, the post-processing data were evaluated to generate the desired outputs, which were the objective functions used for Figure 4-1. Flow diagram for Parametric CFD Simulation Interface Start Read Parameters Generate journal files Gambit.jou Fluent.jou Run Gambit and generate Mesh Mesh.msh Run Fluent Post Processing Results.txt Case.cas Data.dat End Calculate output values 98 optimization, effective heat transfer coefficient and pumping power per unit base area. 4.3. Approximation Assisted Optimization Approximation is the process that uses metamodels (also known as surrogate models) to decrease the computational load and numerical evaluation time of CFD solvers. The reason approximation methods are particularly useful in optimization using CFD simulations is related to their ability to decrease the number of evaluations of design points required to achieve the optimum deigns by utilizing metamodels. The metamodels are functions or subroutines that mimic the response of the simulation model based on simulated sampling data. They are cheap in terms of computational time, and a large selection of available metamodels is available for this purpose. There are two types of responses in the approximation methods, the real response and the predicted response. The real response is the true value resulted from an experiment or CFD numerical simulation, while the predicted response is the response of the metamodel. The real responses are obtained in the Design of Experiment (DOE) stage, where the design space is sampled and the results in turn are used in metamodels to generate the predicted results. The obtained metamodel is then validated for goodness assessment and finally used in optimization. The steps involved in AAO are individually discussed below. For DOE data sampling process the Space Filling Cross Validation Tradeoff method developed by (Aute, Abdelaziz, Azarm, & Radermacher, 2008) and (O. Abdelaziz, Aute, & Radermacher, 2009) was used. Kriging was used for metamodeling and Multi 99 Objective Genetic Algorithm (MOGA) was applied for optimization of the metamodel. 4.3.1. Design of Experiment The sampling process is performed in the DOE stage and can be based on several strategies. (O. A. A. Abdelaziz, 2009) summarized and reviewed the DOE methods used in literature. There are three different methods of sampling: classical methods, space filling methods and adaptive methods. Classical methods are based on sampling the majority of the points from boundaries while leaving few sampling points in the center of the design space. Space filling methods tend to fill out the design space more uniformly based on a specific algorithm. Adaptive methods select the new samples by processing and modeling the available previously selected samples and by understanding the behavior of the model. While classical models and space filling methods offer a time-effective method of sampling, they do not capture the important changes and trends, and the metamodels based on these methods are usually less accurate. Adaptive methods on the other hand, can distribute the sampling more efficiently by increasing the sampling at regions with high gradients and large variations while coarsening the samples at regions where less variation is observed. In this study, a Matlab computer code developed at University of Maryland by a joint effort of Professor Shappour Azarm and Professor Reinhard Radermacher?s research groups was implemented for DOE sampling (Aute et al., 2008), (O. Abdelaziz et al., 2009). The algorithm and computer code uses a two-step combined process of the space filling and adaptive method for sampling. In the first step, the 100 design space is sampled using a space filling method, namely Maximum Entropy Design (MED). The MED principle is based on generating a natural probability distribution in the design space where the entropy is a measure of the amount of information contained in the distribution of a sampling dataset (Shewry & Wynn, 1987), (Johnson, Jones, & Fowler, 2008). Since MED is based on a probability distribution, it does not require any previous sampling knowledge. The second step of the DOE sampling consists of an adaptive methodology. The sampling technique called Multi-response Space Filling Cross Validation Tradeoff (MSFCVT) selects new samples based on the tradeoff between cross validation error and the space validation error. Here, a multi-objective optimization is applied to generate the tradeoff between space filling and cross validation. A more detailed explanation of the MED, MSFCVT methods and the DOE sampling algorithm can be found in (O. A. A. Abdelaziz, 2009). 4.3.2. Metamodeling Metamodeling is defined as the process of predicting unobserved points based on previously observed points. In different disciplines metamodels may have different names: response surface, compact model or emulator. (Van Beers, 2005). Classical metamodeling techniques use approximation methods based on least square fitting after the DOE stage. This approach was found to be not practical because it requires the fitting function type to be known as a priori. The solution for obtaining the right function type requires an iterative process and is time-consuming. At this point, stochastic techniques have the advantage of not having a functional form, which makes them more appropriate to be used in a design space with a large number of 101 parameters and samples. Among these stochastic techniques, Kriging has been successfully used in metamodeling of different engineering optimization designs (Sacks, Welch, Mitchell, & Wynn, 1989), (Park, Oh, & Lim, 2006), (O. A. A. Abdelaziz, 2009). Kriging metamodeling is very suitable with nonlinear problems and show a high degree of flexibility. Kriging method approximates the non-observed points by using spatial correlation information of known points. The formulation consists of a combination of linear regression and departure estimation (Park et al., 2006): ( ) ( ) ( )= +y x f x z x (4-1) where x is the design variable, ( )y x represents the unknown function of interest, ( )f x is the known linear regression function, and ( )z x is the departure represented by a stochastic function with mean zero and variance and nonzero covariance. The selection of the regression function and the stochastic correlation is generally dependent on the problem of interest, and the appropriate functions can be selected by investigating their fitness to the metamodel. The DACE? Toolbox for Matlab? developed by (Lophaven, Nielsen, & S?ndergaard, 2002) provides Kriging metamodeling by incorporating a series of optional linear regression functions and stochastic correlations. This toolbox was used in this work due to its programming flexibility and robust performance. The variance associated by Kriging can be useful in predicting the space filling criteria. For example, large spacing between neighboring points will create large variance and therefore a large uncertainty in response. 102 Figure 4-2. Example of Kriging (adopted from (Wikipedia?, 2009)) A simple Kriging example based on one parameter is shown in Figure 4-2. Kriging interpolation shown by red line was applied for several observed points, shown in blue squares. The 95% confidence interval shown between the green lines becomes smaller in regions where spacing of observed data is small and increases between points with large spacing. 4.3.3. Metamodeling Validation There is a tradeoff between the sampling number and the accuracy of the metamodel. A metamodel with a large number of samples will predict the desired points with less average error, but it will be time expensive in the DOE stage. The desired metamodel accuracy can be achieved by testing the metamodel for randomly selected points in the design space and by estimating the error. In case where the errors are high, the DOE step needs to be run for additional sampling. A few 103 iterations of trial and error may need to be run until the errors drop below a desired value. The Relative Root Mean Squared Error (RRMSE) and Relative Maximum Absolute Error (RMAE) are calculated as: 2 1 1 = = ? n i i RRMSE en (4-2) ( )max= iRMAE e (4-3) where ( ) ( ) ( ) ?= %i i i i y x y xe y x (4-4) 4.3.4. Multi-Objective Optimization Multi-objective optimization is the process of minimizing or maximizing several objective functions simultaneously with several equality and/or inequality constraints. At this point, the Multi Objective Genetic Algorithm (MOGA) offers several attractive features and has been applied successfully to several engineering optimization problems (Xie, Sunden, & Wang, 2008), (Hilbert, Janiga, Baron, & Th?venin, 2006), (Peng & Ling, 2007), (O. A. A. Abdelaziz, 2009). The main advantage of MOGA is that it always searches for the global minimum, and unlike gradient search techniques, it is less prone to get stuck at local minimum points. It is also very successful in solving combined continuous and discrete mixed problems. MOGA is a model of the machine learning process, which mimics nature?s evolutionary process. The model creates a population of points in the design space and characterizes every point by encoding it with a series of several genes. Then the algorithm manipulates the decision-making genes using operators such as mutation 104 and crossover to generate new design populations with the hope of getting better genes that are closer to the global minimum. The process is iteratively continued for every step (evolution). More detailed information about MOGA can be found in (Goldberg, 1989) and (Mitchell, 1998). 4.4. Selection of Optimization Parameters The selection of the right parameters for optimization needs to be clarified before continuing, since this procedure has several implications on the overall optimization process. There is a tradeoff between the number of parameters and computational time. In fact, the real challenge of an FFMHS optimization is the dependence of thermal performance on the large number of geometrical parameters, each affecting the heat transfer and pressure drop. The geometry of the computational domain shown in Figure 3-1 consists of eight possible geometrical parameters: microchannel width chw , microchannel and fin height chH , fin thickness fint , base material thickness baseH , inlet feed channel width lw , outlet feed channel width vw , microchannel length L and feed channel/manifold length manL . These parameters together with one flow parameter add up to a total of nine optimization variables. A model that includes many variables is more realistic. On the other hand, the large number of parameters can also inconveniently increase computational time and make the optimization process not practical. A more feasible solution for this problem is to select only the parameters that affect the objective functions the most, and setting the parameter number based on computational resources. The total of nine optimization variables is very high for the scope of this work, and therefore comparative analysis 105 needed to be done to identify the important ones. In terms of parameters numbers, the practical number was selected based on previous reported experience. For example, (O. A. A. Abdelaziz, 2009) performed multi-objective AAO for a heat exchanger model consisting of six variables and two objective functions. The model was numerically solved on a multi-cluster super computer. Therefore it was realistic to select five optimization parameters for an optimization done using a single PC with a dual core processor. The most important parameters selected for this study were based on the parametric numerical study performed in the previous chapter and considering the fabrication limitations of microgrooved surfaces and manifold systems. The selected five optimization parameters were: channel height chH , channel width to fin thickness ratio /ch finw t , inlet feed channel width lw , outlet feed channel width vw and Reynolds number. The fin aspect ratio /ch finH t was maximized by selecting a value of 10 as indicated by Equation (3-15). Although decreasing the fin aspect ratio may have a positive impact on FFMHS performance at high heat transfer coefficients, as shown in Figure 3-11, the effect is small and not present for low to medium heat transfer coefficients. The manifold thickness was selected constant at 0.4=mant mm. This value corresponds to 1? =Lch in Figure 3-17 where the pumping power has a decreasing trend for all three cases. A smaller manifold thickness has the potential to improve the heat sink performance, but fabrication of channels with such small features is not practical. Finally, the base thickness of the microgrooved surface baseH should be as small as possible to minimize the thermal resistance. Therefore the 106 minimum applicable and practical base thickness of 0.4=baseH mm was selected. Based on these analyses the optimization process was formulized as follows: maximize h minimize ??pumpP subject to: 0.2 1.0< baseq W/cm 2, the trend is reversed, and departures from the main trend are observed, for low to medium mass fluxes of 200 600< G kg/m2s and " 600> baseq W/cm 2, the boiling curves are almost overlapped and increase in a linear fashion. In contrast to the low mass flux cases, the CHF condition here is achieved along the straight overlapping part of the boiling curve and does not show an early performance degradation. The maximum achievable heat flux was " 1.23=baseq kW/cm2 corresponding to a wall superheat of 56.2? =satT ?C. For the same set of data, the heat transfer coefficients based on heat sink base area versus base heat flux variation are given in Figure 6-6 (a). This classification is more convenient for heat sink designers since the definitions are based on the targeted cooling area and are not dependent on enhanced area parameters such as channel aspect ratio or fin efficiency. Figure 6-6 (b) shows the heat transfer coefficients based on wet channel area versus outlet quality. This definition is useful in comparing the hydraulic and thermal performance of different microchannel geometries of microgrooved surfaces. It is important to note that these two graphs are not independent because for a fixed heat flux and mass flux there exists only one outlet quality. In other words, for a constant mass flux case, to change the outlet equilibrium quality the heat flux needs to be changed and vice versa. As shown in Figure 6-6 (a), at mass fluxes below 500G kg/m2s, the trend is shifted as seen in Figure 6-6 (a). As the mass flux increases, the peak previously seen at lower mass fluxes further decreases and diminishes after G=1000 kg/m2s. At the same time, the previously decreasing trend is also eliminated, and for high mass fluxes, both effects create a slow but monotonically increasing trend. More interestingly, all curves collapse altogether, forming a single line on the graph. This trend may suggest a convective boiling-dominated heat transfer regime since the heat transfer coefficients are slightly dependent on heat flux but are more dependent on outlet quality and mass flux (Figure 6-6 (b)). Another observation that results from these graphs is the trend of heat transfer coefficient before reaching CHF. For low mass fluxes and the bell curve-like trend the CHF always occurs when the heat transfer coefficients have a decreasing trend. On the other hand, at high mass fluxes, the boiling crisis phenomenon occurs on the curve shown in Figure 6-6 (a) where all the heat transfer coefficients are overlapped and have a slightly increasing trend. 176 Figure 6-6. (a) Heat transfer coefficient based on base area versus base heat flux and (b) heat transfer coefficient based on wetted area versus outlet quality for FFMHS Surface #17 50000 70000 90000 110000 130000 150000 170000 190000 210000 230000 0 200 400 600 800 1000 1200 1400 hba se [W /m 2K ] q"base[W/cm2] 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 1400 [kg/m2s] (a) (b) +G + G 15000 20000 25000 30000 35000 40000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 hw all [W /m 2K ] xout 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 1400 [kg/m2s] 177 Figure 6-7. Pressure drop values versus outlet quality for FFMHS Surface #17 The pressure drop variation versus outlet equilibrium quality are shown in Figure 6-7. As expected, the pressure drop of the FFMHS is a function of both mass flux and outlet quality. For a constant mass flux, the pressure drop values show an exponential-like increase at low outlet quality values and a linear trend at higher outlet qualities. At the lowest tested mass flux of G=200 kg/m2s the system pressure drop reads less than 10 kPa, corresponding to a saturation temperature change of less than 1.5?C. On the other hand, when the system works at high mass fluxes the saturation temperature change can be significant and should be carefully considered in the design stages. A very large saturation temperature difference can increase the surface temperature non-uniformity of the heat sink base. For example, for G=1400 kg/m2s the maximum pressure drop was 60.4 kPa, which corresponds to a saturation temperature variation of 7.8 ?C. 0 10 20 30 40 50 60 70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ????P [k Pa ] xout 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 1400 [kg/m2s] 178 6.4.2. Surface #12 The second set of experimental tests was performed on FFMHS microgrooved Surface #12. As shown in Table 2-1, all tested surfaces had similar microchannel heights and had the same fin-thickness-to-microchannel-width ratio of 2. The fin thickness and microchannel width of Surface #12 were about 1.5 times larger than those of Surface #17, which decreased the active enhanced surface area created by the microgrooved surface. To protect the heater assembly, no CHF tests were performed for this set of data. The wall superheat was kept below 45 ?C for all tests. For Surface #12, boiling curves for the tested mass fluxes are shown in Figure 6-8. For a given mass flux, the general trend is increased wall superheat with increase in heat flux. At heat fluxes below 300 W/cm2 the boiling curves show little deviation, and for a constant heat flux, slightly higher wall superheats are achieved at higher mass fluxes. Above 300 W/cm2 the curves come closer again, and starting with lower mass fluxes, separation from the trend occurs. Each curve departs from the main trend, making a smaller slope on the boiling curve, indicating performance degradation, which will eventually lead to CHF conditions. The maximum heat flux achievable for this data set was " 666.7=baseq W/m2 corresponding to a wall superheat of 43.8 ?C. 179 Figure 6-8. Boiling curves for FFMHS Surface #12 The heat transfer coefficients defined for the base area and for the wet microchannel area are given in Figure 6-9 (a) and (b). First, for the tested mass flux range, all heat transfer coefficient curves show a similar trend. As seen in Figure 6-9 (a), the general trend of heat transfer coefficients with increase in base heat flux is a gradual increase until a mild decrease begins. The curves have very similar slopes, and heat transfer coefficient values do not deviate much from each other. Also, the heat transfer maximum points observed for Surface #17 that occurred at low outlet qualities were not so distinguished here. 0 100 200 300 400 500 600 700 800 0 10 20 30 40 50 q" ba se [W /cm 2] ?Tsat[?C] 300 [kg/m2s] 400 [kg/m2s] 600 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 180 Figure 6-9. Heat transfer coefficient based on base area versus base heat flux and (b) heat transfer coefficient based on wetted area versus outlet quality for FFMHS Surface #12 0 20000 40000 60000 80000 100000 120000 140000 160000 0 100 200 300 400 500 600 700 800 hb as e[ W/ m2 K] q"base[W/cm2] 300 [kg/m2s] 400 [kg/m2s] 600 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 0 5000 10000 15000 20000 25000 30000 35000 40000 0 0.1 0.2 0.3 0.4 0.5 hw all [W /m 2K ] xout 300 [kg/m2s] 400 [kg/m2s] 600 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] (a) (b) 181 The heat transfer coefficients versus outlet quality curves shown in Figure 6-9 (b) indicate that the heat transfer coefficient curves are almost similar in trend but start to shift to higher values when going to higher mass fluxes. For example, the corresponding heat transfer coefficient at quality of 10% for G=300 kg/m2s is 23,000 W/m2K, while increasing the mass flux to G=1200 kg/m2s at the same outlet quality generates a heat transfer coefficient of h=30,000 W/m2K. This may be the result of an increase in convective boiling due to the increase in vapor velocity. The effect of velocity increase is more pronounced in pressure drop curves given in Figure 6-10. Interestingly, the curves tend to show an almost linear trend with increase in outlet quality. Also, as expected, the slope of the curve increases as the mass fluxes increase. Figure 6-10. Pressure drop values versus outlet quality for FFMHS Surface #12 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 ????P [k Pa ] xout 300 [kg/m2s] 400 [kg/m2s] 600 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 182 6.4.3. Surface #C The last FFMHS that was tested experimentally utilizes microgrooved Surface #C, which is the surface with the highest channel aspect ratio and smallest channel width. As seen in Table 2-1, the channel width and fin thickness for Surface #C is about twice as small as that for Surface #17 and three times smaller than Surface #12. The corresponding boiling curve for the tested mass flux range is given in Figure 6-11. For low to medium base heat fluxes, less superheat is needed at low mass fluxes to achieve the same heat flux. In other words, the high mass flux values in this region are shifted to the right on boiling curve, which represents a decrease in heat transfer efficiency. By increasing the heat flux to higher values, two trends are visible. First, the boiling curves will start to come closer and eventually overlap at high mass fluxes. This trend is similar to the results obtained for FFMHS utilizing Surface #17 at high mass fluxes and Surface #12 at all major mass fluxes. The second trend departs from this trend starting from lower mass fluxes. The departing curves have a lower slope, indicating higher wall superheat for less base heat flux. Although no CHF tests were performed for the current case, the decrease in curve slope may indicate CHF conditions were aproached. The maximum base heat flux achieved with this configuration was " 926=baseq W/cm2, which was obtained for a mass flux of G=600 kg/m2s at a wall superheat of 41.4 ?C. It should be noted, however, that higher heat fluxes are expected to be achieved with higher mass fluxes. All tests performed for mass fluxes exceeding G=600 kg/m2s were stopped before reaching a pressure drop value of about DP=60 kPa to protect the pressure transducer. 183 The heat transfer coefficients are given in Figure 6-12 (a) and (b) versus base heat flux and outlet quality values, respectively. Again, two different trends are present. For most of the tested mass fluxes the heat transfer coefficients show a bell- like shape with a sharp increase at lower heat fluxes and then a decreasing trend after reaching a maximum. The maximum heat transfer increasex with increasing mass flux until G=500 kg/m2s and then starts to decrease for higher mass fluxes. The monotonic decrease in heat transfer coefficient may represent a partial dryout condition in the microgrooves which deteriorates the heat transfer efficiency. The second trend is visible at the highest mass flux of G=1000 kg/m2s. With the increase in mass flux, the maximum point of the bell shaped curve decreases and at the highest tested mass fluxes it is not present anymore. Here, the heat transfer coefficients increase slowly with increase of heat flux, similar to heat transfer coefficients obtained for Surface #12. Figure 6-11. Boiling curves for FFMHS Surface #C 0 100 200 300 400 500 600 700 800 900 1000 0 10 20 30 40 50 60 q" ba se [W /cm 2] ?Tsat[?C] 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 184 (a) (b) Figure 6-12. Heat transfer coefficient based on base area versus base heat flux and (b) heat transfer coefficient based on wetted area versus outlet quality for FFMHS Surface #C 100000 150000 200000 250000 300000 350000 0 200 400 600 800 1000 hb as e[ W /m 2K ] q"base[W/cm2] 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 10000 15000 20000 25000 30000 35000 40000 45000 50000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 hw all [W /m 2K ] xout 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 185 The pressure drop values are shown in Figure 6-13. Similar to previous geometries, pressure drop curves exhibit a linear trend at high outlet qualities, and the pressure drop increases with an increase in mass flux and outlet quality. Due to smaller hydraulic diameter, pressure drops for Surface #C is significantly higher compared to other microgrooved surfaces at similar outlet qualities and mass fluxes. One important observation is that the highest heat transfer coefficients that technology currently provides, registered at low mass fluxes between G=300 kg/m2 and G=500 kg/m2s can be obtained with moderate pressure drops of less than 15 kPa. Figure 6-13. Pressure drop values versus outlet quality for FFMHS Surface #C 6.5. Comparison of Experimental Data with Convective Saturated Boiling Correlations The experimental data presented in the previous section revealed different trends of heat transfer coefficient for different heat fluxes, mass fluxes and 0 10 20 30 40 50 60 70 0 0.1 0.2 0.3 0.4 0.5 0.6 ????P [k Pa ] xout 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 186 microgrooved surface geometries. For small hydraulic diameter microchannels (Surface #C) at low to medium mass fluxes the heat transfer coefficients start to rise rapidly with increase in heat flux and outlet quality. Once the maximum heat transfer coefficients are reached, they start to drop sharply as the heat flux increases. The difference in heat transfer degradation is significant. The maximum wall heat transfer coefficients present at outlet qualities between 15 20%< outx . At higher mass fluxes, the increase in mass flux decreases the dramatic variation in heat transfer coefficients by lowering down the maximum point and creating a increasing trend at high heat fluxes. If the hydraulic diameter of the microgrooved surface is increased about four times (Surface #12), a different heat transfer trend is present. For most of the experimentally tested data, the heat transfer characteristics are similar, with slightly increasing trend with increase in heat flux and slightly dependent on mass flux. No maximum peaks and no sharp increase/decreases are present in this case. Heat transfer coefficients are generally lower compared with the maximum points observed for microgrooved Surface #C but higher than the minimum values at the end of the decreasing trend of Surface #C. For an intermediate microgrooved Surface #17, having microchannels with hydraulic diameters twice as large as Surface #C and twice as small as Surface #12, both heat transfer trends are visible. At low mass and heat fluxes the curves have a bell shape with visible maximums and sharp increase and decrease in heat transfer coefficient, while with increase in mass and heat fluxes the trend shifts to an almost monotonically slight increase in heat transfer coefficients. This trend suggests that the heat transfer characteristics for different 187 microgrooved surfaces, mass fluxes and heat fluxes may be controlled by different heat transfer mechanisms. The first step in analyzing the possible heat transfer trend and heat transfer characteristic of FFMHS was to compare the current experimental data with heat transfer correlations. Since no appropriate correlations were available to predict the two-phase heat transfer in FFMHS, five different correlations developed for saturated flow boiling were tested for this purpose. The selected correlations were developed by (J. C. Chen, 1966), (Kandlikar, 1990), (Tran, Wambsganss, & France, 1996), (Lazarek & Black, 1982) and (Warrier, Dhir, & Momoda, 2002) and they will be discussed in next section. All of these correlations were proposed to predict saturated flow boiling heat transfer and they are developed to be used with refrigerants. The objective of this part of the study was to compare the heat transfer trend of current experimental data with correlations developed for straight channels and to analyze the resulting trends. Since the convective flow in a FFMHS can be coupled with several complex phenomena such as flow turns, secondary flows and impingement effects, an exact prediction of two-phase heat transfer may not be possible. In order to be able to use the selected heat transfer correlations in this case, an assumption needs to be made. Here, the flow in the FFMHS shown in Figure 6-14 (a) was assumed to be as in a straight microchannel similar to the schematic shown in Figure 6-14 (b). With this assumption, the selected correlations can be easily applied without any complexity. However, the validity and error generation of this assumption need to be evaluated. 188 Figure 6-14. Flow schematic in (a) an FFMHS (b) a straight microchannel The convective boiling heat transfer correlations were developed based on the heat transfer mechanisms that authors believed to be dominant in their experimental data. For example, Chen correlation uses the concept of addition of heat transfer coefficient of macroscopic convection and the microscopic nucleate boiling. The Kandlikar correlation predicts local heat transfer coefficients on the basis that the heat transfer is dominated by either nucleate boiling or convective boiling. The Tran, Lazatek and Black and Warrier correlations were developed for nucleate boiling- dominant heat transfer. In the nucleate boiling-dominant heat transfer regime, the convection effects are less pronounced, and most of the heat is removed by the bubble growth and ebullition process. On the other hand, in the convective boiling-dominant regime the bubble nucleation is suppressed and heat is removed mainly by liquid convection and thin film evaporation. Therefore, by assuming a well distributed flow in FFMHS, the convective effects of flow turning, secondary flows and impingement can be less effective in the nucleate boiling-dominant regime. The convective heat transfer regime is usually modeled by including the liquid single-phase heat transfer coefficient and multiplying it with a correction factor (J. C. Chen, 1966), (Kandlikar, (a) (b) 189 1990). For capturing the effects of single phase convective part, the heat transfer in both FFMHS and straight microchannel design were tested and compared. The effective heat transfer ratio between an FFMHS and a straight microchannel defined as FFMHS MC h h was plotted against channel mass flux in Figure 6-15 for all three microgrooved surfaces. As seen in the figure, switching from an FFMHS to a straight microchannel flow with same dimensions can either enhance or reduce the heat transfer coefficient depending on microchannel geometry and flow condition. However, even at extreme conditions, the additional convective effects incorporated by the FFMHS did not exceed ?40% difference. Or in other words, both flow configurations can give similar convective heat transfer performances at high mass fluxes for Surface #C, at medium mass fluxes for Surface #17, and at low mass fluxes for Surface #12. Therefore, it may be concluded that a similar difference in the same order can be expected from the heat transfer correlations that incorporate single-phase convective heat transfer coefficients. For the correlations that predict local heat transfer coefficient zh , vapor quality distribution needs to be known. For this purpose, the microchannel was divided into ten equal division channels, and by assuming equal heat flux on fins and microchannel bottom, the quality in each division channel was averaged between inlet and outlet. The average heat transfer coefficient then was calculated by integrating the local heat transfer coefficients based on local quality as: 0 =? outx zh h dx (6-25) 190 Figure 6-15. Heat transfer coefficient comparison for single-phase convective heat transfer for selected microgrooved surfaces 6.5.1. Chen correlation The Chen correlation (J. C. Chen, 1966) is formulated based on additive heat transfer coefficients of macroscopic component resulting from convective heat transfer and the microscopic component, which takes place during the bubble nucleation and growth process. It was developed to predict saturated flow boiling in conventional channels with no liquid deficiency, and the applicable quality and heat flux ranges were defined as 1% 71%< ? ? ? ? ?? tt tt tt X F X X (6-28) where Martinelli parameter is based on turbulent-turbulent flow: 0.5 0.10.91 ? ? ? ? ? ? ? ??? ?= ? ? ? ?? ?? ? ? ? ? ?v ltt l v xX x (6-29) The microscopic heat transfer component is calculated as: 0.79 0.45 0.49 0.24 0.75 0.5 0.29 0.24 0.240.00122 ? ? ? ? ? ?= ? ? ? ?? ?l Pl lnb sat sat l lv v k Ch T P S h (6-30) where ? = ?sat w satT T T and ( )? = ?sat sat wP P T P . The coefficient S is the nucleate boiling suppression factor and is correlated as: ( )( ) 11.176 1.251 2.56 10 Re ??? ?= + ?? ?? ?fS F (6-31) 6.5.2. Kandlikar correlation Kandlikar correlation (Kandlikar, 1990) was originally developed for saturated convective boiling in conventional channels for water, refrigerants and cryogenic fluids. The correlation was validated successfully for a range of experimental data obtained from different publications. The correlation predicted the heat transfer coefficient well for a range of data for mass fluxes between 192 50 4586< C the heat transfer coefficients have a monotonic decreasing trend. This region represents the increasing trend of heat transfer coefficients with increase in heat flux at low heat fluxes, which in turn results in high C values. At lower C values, the evaporative forces start to become comparable to inertia forces and the heat transfer coefficients follow a decreasing trend due to backflow and dryout mechanisms mentioned before. This transition criterion can be a useful parameter in design stages of FFMHS. Fourth, for each visualization test where the flow instabilities were not present, it was observed that the inlet channel region was in liquid phase for low to medium heat fluxes, and the initiation of nucleate boiling was suppressed up to high heat fluxes. This is expected since the liquid that enters the microchannel is few degrees subcooled and the highest wall superheat is far away from this region. However a closer look to the nucleation incipience in this region can give additional 246 useful information regarding the liquid superheat that can be expected for microchannels with different hydraulic diameters. Figure 7-19. Variation of experimental heat transfer coefficients with stability criteria for Surface #12 Figure 7-20. Variation of experimental heat transfer coefficients with stability criteria for Surface #17 0 5000 10000 15000 20000 25000 30000 35000 40000 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 hw all [W /m 2K ] C 300 [kg/m2s] 400 [kg/m2s] 600 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 0 5000 10000 15000 20000 25000 30000 35000 40000 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 hw all [W /m 2K ] C 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] 1200 [kg/m2s] 1400 [kg/m2s] 247 Figure 7-21. Variation of experimental heat transfer coefficients with stability criteria for Surface #C Figure 7-22. Schematic of flow model in the inlet region for (a) Half FFMHS unit cell (a) Flow between parallel plates with constant wall heat flux For example, consider the inlet region shown in Figure 7-22 (a). Assuming that the fluid inertia is high, the liquid will enter from the top and it will flow towards the 0 10000 20000 30000 40000 50000 60000 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 hw all [W /m 2K ] C 200 [kg/m2s] 300 [kg/m2s] 400 [kg/m2s] 500 [kg/m2s] 600 [kg/m2s] 700 [kg/m2s] 800 [kg/m2s] 1000 [kg/m2s] side view front view Symmetry planes Inlet region Hch (a) (b) wl/2 q?=const z wl Hch 248 bottom of the channel where it will create an impingement zone. To further simplify the case, this region was assumed as flow between two parallel plates as shown in Figure 7-22 (b), with same channel width (wch) and channel length/height (Hch). In this case the flow will not create an impingement zone, instead it will be directed out from the bottom of the channel. Constant heat flux was applied to parallel plate walls. For this analysis, Surface #12 and Surface #C were selected since they represent the extreme geometries in terms of hydraulic diameter. For the flow configuration shown in Figure 7-22 (b), the local heat transfer coefficient along the inlet region for Surface #C and Surface #12 are calculated and shown in Figure 7-23 (a) and (b) respectively. For both cases, the flow is thermally developing, and due to lower hydraulic diameter, the local heat transfer coefficients of Surface #C are higher than those calculated for Surface #12. In fact, for fully developed flow, the local heat transfer coefficients are reversely proportional to hydraulic diameter; therefore they are almost three times higher for Surface #C comparing to Surface #12. Figure 7-23. Local heat transfer coefficients versus non dimensional entrance length for (a) Surface #C, (b) Surface #12 0.0 0.2 0.4 0.6 0.8 1.0 0 10,000 20,000 30,000 40,000 z/H ch hz[W/m2K] Thermally Developing Fully Developed 0.0 0.2 0.4 0.6 0.8 1.0 0 10,000 20,000 30,000 40,000 z/H ch hz[W/m2K] Thermally Developing Fully Developed (b) (a) Surface #C Fluid:R245fa G=200 kg/m2s Surface #12 Fluid:R245fa G=200 kg/m2s 249 The wall superheat required for onset of nucleate boiling can be calculated based on principles given in Section 2.4.3, using Equation (2-23) and local heat transfer coefficients given above. For a constant heat flux, the bulk temperature can be calculated as a function of distance from the inlet z. , 2 ? ??? = + bulk z i ch i p q zT T w V c (7-4) Using Equation (7-4), the wall superheat and liquid superheat are evaluated as: , , , ? ???? = + ? ? ?? ?sat wall z bulk z sat z qT T T h (7-5) , , ,? =? ?sat liq z bulk z satT T T (7-6) The variation of Equations (2-23), (7-5) and (7-6) with non dimensional distance from the entrance are shown in Figure 7-24 (a) and (b) for Surface #C and Surface #12 respectively. The blue curve represents the minimum wall superheat required to initiate nucleation, by assuming saturated liquid inlet and that all size of crevices are available on the heated surface. The red curve represents the actual wall superheat and the green line denotes the liquid superheat. The Onset of Nucleate Boiling (ONB) will occur when the wall superheat (red curve) exceeds the theoretical minimum required wall superheat of ONB (blue curve). Defining the ONB location will also determine the amount of liquid superheat at the same location. For example, for Surface #C, the ONB will occur at / 0.28=chz H down the inlet which also corresponds for a wall superheat of 4.5 ?C. At this point, the liquid is also superheated to a value of 2.0 ?C, due to suppression of nucleation upstream the ONB point. For larger hydraulic diameter microgrooved surfaces with same heat flux, mass 250 flux and saturation temperature, the initiation of boiling is much earlier. For example, for Surface #12 the ONB was calculated to occur at / 0.15=chz H and the corresponding wall and liquid superheats were 3.6 ?C and 0.3 ?C respectively. With this, it was demonstrated that for similar flow and heat input conditions, the hydraulic diameter has a significant impact on liquid and wall superheat values present in the system prior to nucleation. For smaller channels, the local heat transfer coefficient is much higher and the amount of thermal mass carried by the fluid is much less at constant heat flux, mass flux and saturation temperatures. Therefore the ONB will occur further downstream of the channel, which in turn will lead to building large amounts of liquid and wall superheat. As the hydraulic diameter is increased, this effect becomes less pronounced. This effect, combined with smaller bubble confinement at higher hydraulic diameters, explains the decreasing effect of rapid bubble expansion phenomena when going from small hydraulic diameter of Surface #C to higher hydraulic diameters of Surface #12. Figure 7-24. Onset of Nucleate Boiling (ONB) and wall and liquid superheats calculated for (a) Surface #C, (b) Surface #12 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 6 7 8 9 10 z/H ch ?T [K] Dtsat,ONB Dtsat,wall Dtsat,liquid 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 6 7 8 9 10 z/H ch ?T [K] Dtsat,ONB Dtsat,wall Dtsat,liquid (a) (b) Surface #C Fluid:R245fa G=200 kg/m2s Tsat = 307 K q?= 5 W/cm2 Surface #12 Fluid:R245fa G=200 kg/m2s Tsat = 307 K q?= 5 W/cm2 ONB ONB 251 CHAPTER 8: CONCLUSIONS AND FUTURE WORK RECOMMENDATIONS 8.1. Conclusions Summary The present research is the first of its kind to develop a better understanding of single-phase and phase-change heat transfer in FFMHS through flow visualization, numerical and experimental modeling of the phenomena, and multi-objective optimization of the heat sink and its comparison with two widely known cooling technologies, namely jet impingement and traditional micro channels. From an overview of the work conducted in the present study, a number of conclusions can be drawn which can be summarized based on the single-phase and phase-change studies in the present work. For single-phase heat transfer, a numerical study was performed to investigate the thermal performance and to optimize the geometry and flow of FFMHS. The main findings of this part of the study are as follows: ? The geometry and Reynolds number have a significant effect on both flow regimes and heat transfer characteristics. At low Reynolds numbers, the flow is viscous-dominated, which results in velocity stratification by creating a bypass zone between the inlet and outlet feed channels at the top of the microchannel. This effect in turn creates inefficient dead zones with low fluid circulation and low heat transfer. ? When the Reynolds number is increased, usually by increasing the hydraulic diameter or mass flux, the flow becomes inertia-dominated and the velocity 252 stratification reverses with a higher fluid core close to the bottom of the microchannel and with fluid recirculation zones close to the top part. The increase in fluid velocity also initiates secondary flows manifested in the form of vortex pairs in the microchannel cross-section. The vortices and flow impingement in turn reduce the convective thermal resistance and create local heat transfer maximums. ? The geometrical parameters that most strongly affect the heat transfer and pressure drop were microchannel height, microchannel width and inlet/outlet feed channel dimensions. ? An optimized FFMHS can operate much more efficiently in the parametrical range investigated in this study compared to TMHS and JIHS. For constant pumping power and a 1 x 1 cm2 base cooling area, FFMHS can achieve 72% more heat transfer compared to TMHS and 306% compared to JIHS. For a 1 x 1 cm2 base cooling area and constant heat transfer performance, the pumping power required by FFMHS is only 8.5% of the pumping power required by TMHS and 0.4% of the pumping power required by a JIHS. ? When going to larger cooling areas, the performance difference of FFMHS compared with TMHS is even more significant. The manifolding system that forms the short parallel microchannel structure in FFMHS allows cooling of large areas without the penalty of heat transfer degradation due to a rise in fluid temperature and increase in pressure drop and flow length. 253 ? With the observed superior performance, FFMHS technology has the potential to replace TMHS technology that is currently widely used for cooling of high heat fluxes. To investigate the thermal performance of FFMHS in two-phase heat transfer mode a two-step experimental approach was considered. In the first step, a parametric study was performed to study the effects of microgrooved surface geometry, heat flux and mass flux. The heat transfer characteristics resulting from this study were later explained by a visualization study performed in the second step. The main findings of this part can be summarized as follows: ? FFMHS have demonstrated that with an HFC fluid, the present heat sink configuration can cool a heat flux of " 1.23=baseq kW/cm2 with a superheat of 56.2? =satT ?C and pressure drop of 60.3? =P kPa. ? At high hydraulic diameter, high mass flux and high heat flux, the heat transfer coefficients have a slowly increasing trend with an increase in heat flux and outlet quality. The flow is dominated by inertial forces, and the flow regimes and transitions are expected to be similar to conventional microchannels. The heat transfer coefficients in this regime follow the Chen correlation, which was developed to predict saturated flow boiling in conventional channels. ? At low hydraulic diameters, low mass flux and low qualities the heat transfer coefficient curves have a bell-like shape with a sharp increase at low vapor qualities until they reach the maximum peak point. Here the flow is dominated by the viscous forces, and a single bubble expansion phenomenon is observed. 254 The thin liquid film under the elongated bubble can create an annular-like high heat transfer regime at low qualities. However, at high heat fluxes the bubble expansion becomes more chaotic, having a negative impact on heat transfer by blocking liquid inlet and creating vapor backflows. ? The CHF of FFMHS increases with mass flux, while the outlet qualities have a decreasing trend. The vapor backflow in the inlet manifold correlates with CHF, and this mechanism results from the vapor blankets that block the inlet liquid that wets the heated surface. At high mass fluxes the vapor is generated at the bottom of the channel, while at low mass fluxes the vapor is generated along the channel with bubbles close to the inlet, sending vapor into the inlet feed channel and creating vapor backflows. 8.2. Future Work Recommendations This is the first comprehensive study of the innovative force-fed micro channel heat sinks for high heat flux cooling. As documented in this study, the technique has demonstrated significant advantages over other technologies conventionally used for high heat flux cooling. Very high heat transfer coefficients, yet low pressure drops, make the technique attractive to other areas of heat transfer applications such as thermal energy conversion and waste heat utilization. Energy conversion and management are at the core of modern technology research; however, the applications of force-fed heat transfer in these areas will have many specific applications beyond the high heat flux cooling. For example, HVAC or ocean thermal energy conversion (OTEC) systems operate at very low temperature difference intervals. Heat has to be transferred at a minimum temperature difference 255 to make those processes efficient. In this case, future work should focus on low heat fluxes and minimum temperature differences that were not explored in this study. The future work recommendations are divided into two sections based on heat transfer mode: single-phase and two-phase. For single-phase heat transfer the following future work research is recommended: ? The current optimization was performed based on five parameters. Four of these parameters were geometrical and one was the flow parameter. The geometrical parameters were selected based on a parametric study that indicated the most important four out of eight possible parameters. Future research should extend the number of parameters, based on the computational limitations and capabilities. The next important parameters, which were not included in this study but are suggested for the future work, are fin aspect ratio and manifold thickness. Using these recommendations, the optimal performance of FFMHS could be further increased. ? The current optimization was based on copper microgrooved surfaces and water as the working fluid. The study could be extended to other material- working fluid couples, such as refrigerants and silicon-based microgrooved surfaces, which are commonly used in current power electronics cooling systems. The resulting database would provide a technical tool that will allow selection of optimum working FFMHS geometries at different inputs and materials. ? Another possible benefit of this work is the potential to perform an economical feasibility analysis and to optimize FFMHS based on cost evaluations. Cost 256 could be included as the third function in the multi-objective optimization procedure. The optimization results then could identify the most economically feasible heat sink design based on thermal performance characteristics and/or other criteria. ? The technology performance comparison study investigated in this work was performed on FFMHS and two well-established high heat flux cooling technologies, TMHS and JIHS. The comparison study could be further extended by including several other cooling technologies such as spray cooling, inline and staggered pin fins and offset strip pin fins. The future research recommendations for two phase heat transfer of FFMHS are summarized as follows: ? The parametrical study needs to be extended for a larger selection of microgrooved surface geometries and working fluids. This will lead to formation of a larger database of heat transfer coefficients and pressure drop data. The heat transfer performance trends observed in this study should be compared to the trends observed at difference geometrical FFMHS configurations, and the consistency or deviation of this trend needs to be addressed. The large database will also form the base to allow building correlations that can predict heat transfer coefficients and pressure drops. ? The current test section was not designed to test CHF due to the low thermal mass of the heater assembly. A secondary test chamber with hearers attached to a larger copper heat distributor would solve this problem. This test section 257 would increase the fabrication complexities but would allow testing CHF. The test setup control could be enhanced by addition of a fast response control circuit that could cut the power of the heater in a very short time after the temperature jump is sensed. ? The test section used in visualization tests in this study was a scaled-up model of the actual microgrooved surfaces. It was mainly designed to generate pictures and video images that can capture the effect of hydraulic diameter, mass flux and heat flux on two-phase flow regimes. The results obtained for parametric FFMHS experimental tests were explained by the assumption that similar phenomena occur at small scale too. Although these results were satisfactory, it is recommended that they be validated with a test section that can capture the flow regimes at the micro-scale. This test section needs to be carefully designed to be able to control and monitor significantly lower heat and mass fluxes. The heat gains and heat losses through lighting equipment, conduction heat losses, and radiation heat losses through the surface of the test section also need special attention. ? The two phase test section designed and fabricated in this study was developed to accurately simulate two phase phenomena in FFMHS and to understand the flow regimes and heat transfer mechanisms in these heat sinks in laboratory conditions. However, this flow configuration with long straight feed channels is not very practical for heat sink designs. A more practical and compact design that utilizes the same force fed concept can be developed using a zigzag manifold design, as shown in Figure 8-1. This low profile heat sink design is 258 more compact and easier to manufacture. The fluid enters the heat sink from one side, flows into the feed channels, it is distributed into the microchannels and is directed out of the heat sink from the opposite side. The manifold is compressed between the microgrooved surface and the flat plate located on the top of the heat sink. The feed channels and the dimensions of the zigzag header are designed based on the flow configuration. For two phase flow, the inlet feed channels are smaller comparing to the outlet feed channels to accommodate the large vapor flow. Fabrication and demonstration of such a heat sink will lead to a more compact and yet efficient low profile heat sink. Figure 8-1. Low profile FFMHS with zigzag manifold design Inlet Inlet Inlet Outlet Outlet Heat Flux Manifold Microgrooved surface 259 CHAPTER 9: APPENDICES 9.1. Appendix A The technical drawings and dimensions of the parts used in the experimental test chamber and visualization test section are given in this appendix. All dimensions are in mm unless otherwise specified. 260 9.1.1. Test chamber assembly 23 2.2 76.2 19 3.4 261 9.1.2. Test Chamber Flow Distribution Header F F 30 24.5 9.52 A A D D C 10 0 53 10 0 SECTION A-A 7.4 8 0.3 0.45 1.1 0.2 0.45 DETAIL C SCALE 6 : 1 E SECTION D-D 0.7 8 0.6 5 4.3 0.3 0.1 0.4 DETAIL E SCALE 6 : 1 25 10 G H SECTION F-F DETAIL G SCALE 6 : 1 DETAIL H SCALE 6 : 1 262 9.1.3. Test Chamber Top Flange 14.9 A A B B 25 .7 76.2 11.2 5.2 5 3.3 0 .8 4.1 4 6.46 4.5 19.2 SECTION A-A 11.2 8 32.6 SECTION B-B 263 9.1.4. Test Chamber Bottom Flange 14.9 8 x 4 B B C C 76.2 13 .1 5.2 5 3.3 64 .5 SECTION B-B 65.2 SECTION C-C 264 9.1.5. Test Chamber Heater Assembly 0.9 6.8 B B 40 30 6 20 11 9.5 9.5 1.5 12 0.8 3 1.2 1 SECTION B-B SCALE 2 : 1 265 9.1.6. Test Chamber Microgrooved Surface 7.8 0.6 5 1.9 53.2 5 0.65 1.95 3.25 R0. 15x 3 7.8 266 9.1.7. Visualization Test Section Assembly 267 9.1.8. Visualization Test Section Base 268 9.1.9. Visualization Test Section Heat Conductor 269 9.1.10. Visualization Test Section Teflon Layer 2 270 9.1.11. Visualization Test Section Teflon Layer 1 271 9.2. Appendix B The computational domain shown in Figure 9-1 is one quarter of the actual heater assembly. Therefore symmetry boundary condition was applied at specified faces. Three different components considered in this study are the composite base, PTFE layer and the alumina substrate. The thermal conductivity values for each of these substrates were selected as 1 W/mK, 0.5 W/mK and 18 W/mK respectively. The thin film resistor was modeled as a 2D layer on the top surface of alumina substrate. The contact resistance between each layer was neglected by assuming perfect contact condition. The final meshed geometry consists of 43919 tetrahedral cells and is shown in Figure 9-2. Figure 9-1. Boundary conditions and computational domain symmetry Thin film resistor Alumina substarate PTFE layer Composite base 272 Figure 9-2. The meshed geometry used in numerical model The thermal resistance from the surface to the fluid is a function of convective heat transfer coefficient. After exiting the manifold, the gravitation forces pull the fluid down and fluid flows downward wetting the side surfaces of the heater and the heater assembly. The convective heat transfer coefficient was evaluated based on evaporative falling film heat transfer mode. For evaporation over a uniformly distributed falling liquid film in a vertical tube, the average heat transfer coefficient was estimated using the correlation given by (Seban, 1978): (9-1) where represents the mass flow rate per unit depth, perpendicular to flow direction. Applying convective boundary condition with specified heat transfer coefficient for surfaces in contact with fluid, the numerical model was solved for a range of mass flow rates. The values of total thermal resistance habR , defined between film temperature and ambient fluid temperature, versus heat sink mass flow rate is given in Figure 9-3. Thermal resistance values are slightly lower at low mass flow rates due to the thinning of the film thickness and enhancing convective heat transfer. 273 Figure 9-3. Total thermal resistance versus mass flow rate for the bottom part of the heater assembly The thermal resistance values given in Figure 9-3 can be fit into a power law equation as a function of mass flow rate: (9-2) where is the total mass flow rate of the heat sink with the units of grams per minute. The regression equation can predict the numerical results with a mean absolute error less than 0.20%. 0 5 10 15 20 25 30 35 0 250 500 750 1000 1250 1500 Rha b[ K/ W] m [gr/min] 274 9.3. Appendix C 9.3.1. TMHS Model Used in Optimization The microchannel geometry used in the mathematical model is shown in Figure 9-4. It consists of a base material on the bottom, the single microchannel, two side fins with half thickness and the adiabatic cover on the top. Figure 9-4. Mathematical model of TMHS Due to high the axial conduction of the copper, the base surface was assumed to be at constant temperature. For a given inlet and base temperature the outlet temperature can be calculated as: (9-3) t fin/2 wch L ch Hch tbase x y 275 Where is the mass flow rate in the microchannel, pc is the specific heat of water and tR is the total thermal resistance from base surface to the water. tR includes the conduction through the base wall and the force convection resistance from the microchannel wet surface: ( ) 0 1base t tCu fin ch ch tR hAk t w L ?= ++ (9-4) where 2t ch ch ch chA H L w L= + is the total wet area and h is the average convection coefficient. 0? is the overall surface efficiency defined as: ( ) ( )0 21 1 1 12f chf f t ch ch A H A H w? ? ?= ? ? = ? ?+ (9-5) Here, the fin efficiency ?f for straight rectangular fins needs to be calculated. For a given mass flow rate the fluid velocity chV and Reynolds number are calculated as: (9-6) Re ch hV D? ?= (9-7) where hD is the hydraulic diameter defined as: ( ) 4 2 ch ch h ch ch H wD H w= + (9-8) For thermally developing flow, the overall heat transfer coefficient can be calculated as a function of dimensionless thermal entry length: 276 * Re Pr ch h Lx D= (9-9) The average Nusselt number for laminar thermally developing flow at constant temperature boundary condition can be calculated from (Lian-Tuu & Chu, 2002): ( ) ( ) 1/ 3* * 1 * * 2 3 ,0.005 0.01 / , 0.01m T g x xNu g g x x ?? < ?? (9-10) where 2 3 1 2.038 2.206 2.738 1.181g ? ? ?= ? + ? (9-11) 2 3 2 7.554 17.287 23.533 10.79g ? ? ?= ? + ? (9-12) and 2 3 3 0.0229 0.0546 0.0417 0.0141g ? ? ?= + ? ? (9-13) Here ? is the aspect ratio which takes a value between zero and one and is defined as: ch ch w H? = (9-14) From here the average heat transfer coefficient is calculated from definition of Nusselt number: ( )m T h Nu kh D= (9-15) where k represents the thermal conductivity of water. Using the heat transfer coefficient, the average fin efficiency can be calculated as: ( ) 1/ 21/ 2 2 2? ?+? ? ? ?= =? ? ? ? ? ?? ? ? ? fin chf Cu fc Cu fin ch h t LhPm k A k t L (9-16) 277 and ( )tanh ch f ch mH mH? = (9-17) where Cuk is the thermal conductivity of the copper. With known inlet and outlet fluid temperatures the total heat transfer is then evaluated as: (9-18) and the heat transfer coefficient based on footprint area and defined between base surface temperature and inlet fluid temperature is: (9-19) For a square TMHS with heat sink dimensions of ( chL x chL ) the total pumping power can be calculated as: = +p chpump ch fin W LP w t (9-20) where pW is the pumping power for a single microchannel and is defined as the product of volumetric flow rate and total pressure difference ? tP between inlet and outlet manifolds. (9-21) Volumetric flow rate is calculated as: (9-22) 278 and the total pressure drop is the sum of channel frictional pressure drop, inlet and outlet local entrance pressure losses caused by sudden contraction and expansion. t f c eP P P P? =? +? +? (9-23) The friction pressure drop is calculated using the average friction coefficient for laminar hydrodynamically developing flow: 2 4 2ch chf app h L VP f D ?? = (9-24) where the friction coefficient is defined as (Copeland, 1995a): ( ) ( )0.57 1/ 22 2Re 3.2 Reapp fdf x f?+? ?= +? ?? ? (9-25) Here x+ is nondimentional hydrodynamic entrance length and is calculated as: Re ch h Lx D + = (9-26) For fully developed flow the ( )Re fdf term is a function of aspect ratio only and is calculated as: ( ) 2 3Re 23.922 30.201 32.897 12.439fdf ? ? ?= ? + ? (9-27) The inlet local pressure loss is calculated as sudden contraction between two channels with different dimensions: 2 2 ch c c VP K ?? = (9-28) and the contraction coefficient is: 21 1c c K C? ?= ?? ? ? ? (9-29) where cC is the jet contraction coefficient calculated as (Webb, 2006): 279 20.6501 0.2093 0.3863 cC ? ?= ? + (9-30) where area ratio ? is defined between 0.2 0.9?? ? . The outlet pressure loss due to flow expansion is modeled as sudden flow expansion and is calculated as: 2 2 ch e e VP K ?? = (9-31) and the expansion coefficient is: ( )21eK ?= ? (9-32) 9.3.2. TMHS Optimization Results The numerical values obtained from the optimization study of TMHS and JIHS are listed below. Table 9-1. Optimum results obtained for the 1 x 1 cm2 TMHS Normalized variables Optimized geometry and flow variables Objective Functions x1 x2 x3 x4 Hch tfin wch Re h Ppump - - - - [mm] [mm] [mm] - [W/m2K] [W] 0.8236 0.4450 0.8939 0.0148 4.153 0.439 0.341 44 32059 1.02E-04 0.8355 0.4147 0.9961 0.0171 4.211 0.422 0.312 49 37000 1.77E-04 0.7581 0.3699 0.8896 0.0209 3.839 0.406 0.277 58 41601 3.44E-04 0.7385 0.2894 0.8958 0.0201 3.745 0.395 0.228 56 47085 5.93E-04 0.7054 0.3430 0.8369 0.0358 3.586 0.390 0.252 92 51544 1.17E-03 0.5214 0.3150 0.8276 0.0298 2.703 0.296 0.180 78 59591 2.25E-03 0.5343 0.3224 0.8862 0.0379 2.765 0.293 0.181 97 65472 3.50E-03 0.4900 0.2889 0.8486 0.0411 2.552 0.276 0.159 104 72506 5.99E-03 0.4641 0.2598 0.9718 0.0374 2.428 0.246 0.132 96 81045 9.23E-03 0.5002 0.2125 0.9865 0.0424 2.601 0.262 0.125 107 88884 1.43E-02 0.4246 0.2313 0.8740 0.0597 2.238 0.239 0.120 147 98461 2.93E-02 0.2578 0.2940 0.9561 0.0491 1.437 0.147 0.086 122 109597 5.43E-02 0.3043 0.2098 0.9359 0.0569 1.661 0.172 0.081 140 121693 8.70E-02 0.3529 0.1436 0.9938 0.0574 1.894 0.190 0.073 141 131690 1.26E-01 280 0.2709 0.1623 0.9027 0.0684 1.500 0.158 0.065 167 145324 2.43E-01 0.3580 0.1208 0.8896 0.0978 1.918 0.203 0.072 234 153746 3.58E-01 0.2614 0.2059 0.8897 0.0997 1.455 0.154 0.072 238 154380 3.61E-01 0.2432 0.2193 0.9378 0.1324 1.367 0.141 0.068 313 173033 7.47E-01 0.2260 0.1621 0.9002 0.1185 1.285 0.135 0.056 281 187932 1.12E+00 0.1346 0.2210 0.8302 0.1168 0.846 0.092 0.045 278 201680 1.89E+00 0.1486 0.1856 0.8930 0.1418 0.913 0.096 0.043 335 225302 3.44E+00 0.0856 0.2154 0.9137 0.1271 0.611 0.064 0.031 301 249949 7.28E+00 0.1075 0.1645 0.9591 0.1694 0.716 0.073 0.030 398 282025 1.40E+01 0.1318 0.1244 0.9052 0.2177 0.833 0.087 0.032 509 292797 2.04E+01 0.0762 0.2003 0.9807 0.2141 0.566 0.057 0.026 500 319225 3.35E+01 0.0554 0.1752 0.9345 0.2105 0.466 0.048 0.021 492 347748 6.61E+01 0.0777 0.1690 0.9304 0.3905 0.573 0.059 0.025 904 370843 1.33E+02 0.0595 0.1247 0.9071 0.3743 0.485 0.051 0.018 867 416197 2.99E+02 0.0366 0.1218 0.9388 0.3341 0.376 0.039 0.014 775 452389 5.57E+02 0.0161 0.1883 0.8667 0.3920 0.277 0.030 0.013 908 468249 8.28E+02 0.0257 0.1039 0.8867 0.3993 0.323 0.034 0.011 924 495415 1.38E+03 0.0147 0.1547 0.8813 0.5061 0.270 0.029 0.012 1169 516888 2.13E+03 0.0203 0.0758 0.9113 0.4608 0.297 0.031 0.009 1065 543168 3.55E+03 0.0088 0.1028 0.9946 0.6006 0.242 0.024 0.008 1385 595246 9.31E+03 Table 9-2. Optimum results obtained for the 2 x 2 cm2 TMHS Normalized variables Optimized geometry and flow variables Objective Functions x1 x2 x3 x4 Hch tfin wch Re h Ppump - - - - [mm] [mm] [mm] - [W/m2K] [W] 0.7812 0.7915 0.7208 0.0185 3.950 0.459 0.564 52 15605 1.08E-04 0.9648 0.6377 0.8057 0.0215 4.831 0.535 0.551 59 18577 1.61E-04 0.8573 0.5796 0.7100 0.0240 4.315 0.505 0.481 65 20549 2.83E-04 0.9565 0.4272 0.9638 0.0196 4.791 0.488 0.369 55 25507 5.15E-04 0.8328 0.4654 0.8417 0.0340 4.198 0.456 0.367 88 30106 1.28E-03 0.9476 0.3035 0.9317 0.0286 4.749 0.492 0.292 75 34915 2.04E-03 0.9468 0.3224 0.9401 0.0420 4.744 0.489 0.303 106 39586 3.69E-03 0.8735 0.2287 0.8364 0.0419 4.393 0.478 0.238 106 45124 7.47E-03 0.8251 0.2766 0.9050 0.0687 4.160 0.437 0.244 167 53174 1.79E-02 0.6799 0.3420 0.9490 0.0866 3.464 0.355 0.229 208 59032 3.36E-02 0.8025 0.2132 0.9602 0.0910 4.052 0.413 0.197 218 67894 6.15E-02 0.5389 0.2191 0.8890 0.0763 2.787 0.295 0.143 185 76023 1.08E-01 281 0.3623 0.2913 0.7609 0.0963 1.939 0.220 0.127 230 82827 2.17E-01 0.4746 0.1952 0.9237 0.1060 2.478 0.258 0.117 253 96888 3.83E-01 0.5492 0.2333 0.9340 0.1781 2.836 0.293 0.148 418 97073 5.45E-01 0.2733 0.2967 0.8989 0.1184 1.512 0.159 0.093 281 109712 8.70E-01 0.3860 0.1595 0.9362 0.1143 2.053 0.212 0.086 272 117935 1.11E+00 0.2963 0.2883 0.9608 0.1827 1.622 0.165 0.095 428 127966 2.02E+00 0.1843 0.2635 0.9176 0.1295 1.085 0.113 0.061 307 140228 3.67E+00 0.2617 0.1714 0.9330 0.1864 1.456 0.151 0.064 437 162922 7.18E+00 0.2180 0.1263 0.9132 0.1582 1.246 0.130 0.047 372 176476 1.26E+01 0.2224 0.2542 0.9736 0.3236 1.268 0.128 0.068 751 182351 1.77E+01 0.1726 0.1947 0.8732 0.2677 1.029 0.110 0.050 623 203183 2.96E+01 0.1347 0.2054 0.8083 0.2875 0.846 0.094 0.044 668 217291 4.83E+01 0.1660 0.1165 0.9203 0.2814 0.997 0.104 0.036 654 243659 8.75E+01 0.1607 0.1213 0.9329 0.3723 0.971 0.100 0.036 863 265802 1.62E+02 0.1056 0.1419 0.9127 0.3744 0.707 0.074 0.028 867 295116 3.19E+02 0.1075 0.1108 0.8910 0.4980 0.716 0.076 0.026 1150 328739 7.44E+02 0.1038 0.1109 0.9151 0.5931 0.698 0.073 0.025 1368 348674 1.20E+03 0.0696 0.1595 0.9454 0.6331 0.534 0.055 0.022 1460 373638 1.89E+03 0.0712 0.0843 0.9525 0.5433 0.542 0.055 0.017 1254 400412 3.18E+03 0.0640 0.0937 0.9607 0.6079 0.507 0.052 0.017 1402 416367 4.36E+03 0.0595 0.1298 0.9930 0.9592 0.486 0.049 0.018 2206 443964 8.82E+03 282 9.3.3. JIHS Optimum Results Table 9-3. Optimum results obtained for JIHS Normalized variables Optimized geometry and flow variables Objective Functions x1 x2 x3 x4 x5 Hch wl tman wv Repp h P?pump - - - - - [mm] [mm] [mm] [mm] - [W/m2K] [W/m2] 0.8772 0.9699 0.3264 0.9488 0.0004 0.182 0.364 0.231 0.357 1 3386 2.52E-03 0.8145 0.8597 0.1785 0.9508 0.0007 0.172 0.326 0.171 0.358 2 4412 4.23E-03 0.6366 0.8445 0.0765 0.7554 0.0013 0.145 0.321 0.131 0.289 2 5681 1.14E-02 0.2701 0.9264 0.0614 0.7245 0.0013 0.091 0.349 0.125 0.279 2 6523 2.12E-02 0.5047 0.8788 0.1999 0.7647 0.0025 0.126 0.333 0.180 0.293 4 7684 2.95E-02 0.4734 0.9198 0.0636 0.7518 0.0035 0.121 0.347 0.125 0.288 4 8700 4.67E-02 0.4520 0.8314 0.0963 0.7441 0.0041 0.118 0.316 0.139 0.285 5 9745 7.20E-02 0.4730 0.8405 0.1099 0.7437 0.0047 0.121 0.319 0.144 0.285 6 10208 8.93E-02 0.2723 0.8149 0.0964 0.7291 0.0056 0.091 0.310 0.139 0.280 7 12311 1.99E-01 0.0959 0.6183 0.1270 0.6805 0.0103 0.064 0.241 0.151 0.263 11 18175 1.31E+00 0.0546 0.6478 0.0176 0.6905 0.0125 0.058 0.252 0.107 0.267 14 20822 2.06E+00 0.0380 0.5204 0.0129 0.6630 0.0172 0.056 0.207 0.105 0.257 18 24356 4.25E+00 0.0491 0.6160 0.0331 0.7245 0.0290 0.057 0.241 0.113 0.279 30 27169 1.16E+01 0.0516 0.4188 0.0107 0.6746 0.0297 0.058 0.172 0.104 0.261 31 29536 1.39E+01 0.0403 0.4877 0.0071 0.6331 0.0433 0.056 0.196 0.103 0.247 44 35609 3.10E+01 0.0371 0.4136 0.0139 0.6428 0.0521 0.056 0.170 0.106 0.250 53 38924 5.08E+01 0.0513 0.4019 0.0060 0.6302 0.0653 0.058 0.166 0.102 0.246 66 42022 8.02E+01 0.0378 0.3059 0.0572 0.6143 0.0749 0.056 0.132 0.123 0.240 76 45523 1.65E+02 0.0297 0.3454 0.0014 0.6536 0.0966 0.054 0.146 0.101 0.254 97 51213 2.56E+02 0.0379 0.3036 0.0155 0.5970 0.1080 0.056 0.131 0.106 0.234 109 54017 4.04E+02 0.0496 0.4515 0.0070 0.6425 0.1766 0.057 0.183 0.103 0.250 177 68992 8.28E+02 283 0.0467 0.5471 0.0235 0.5764 0.2373 0.057 0.217 0.109 0.227 238 73745 1.45E+03 0.0900 0.3413 0.0657 0.5738 0.2634 0.063 0.144 0.126 0.226 264 75288 2.25E+03 0.0413 0.3212 0.0766 0.5734 0.2666 0.056 0.137 0.131 0.226 267 79857 2.94E+03 0.1002 0.3990 0.0788 0.4990 0.3536 0.065 0.165 0.132 0.200 354 91418 4.03E+03 0.0636 0.2365 0.1535 0.4864 0.3537 0.060 0.108 0.161 0.195 354 108291 6.71E+03 0.1149 0.2810 0.1263 0.5531 0.4898 0.067 0.123 0.151 0.219 490 112765 1.20E+04 0.1753 0.2300 0.1042 0.4213 0.5044 0.076 0.105 0.142 0.172 505 126117 1.61E+04 0.0655 0.1489 0.1202 0.5009 0.4896 0.060 0.077 0.148 0.200 490 130817 2.45E+04 0.1510 0.1124 0.1283 0.4294 0.6468 0.073 0.064 0.151 0.175 647 159376 6.20E+04 0.0564 0.1393 0.1372 0.5117 0.8206 0.058 0.074 0.155 0.204 821 167361 9.14E+04 0.1428 0.0791 0.1677 0.4060 0.9137 0.071 0.053 0.167 0.167 914 214502 2.24E+05 0.1518 0.0203 0.1185 0.3494 0.9146 0.073 0.032 0.147 0.147 915 237451 4.80E+05 284 9.4. Appendix D As observed in visualization study discussed in Chapter 7, the pulsating flow and the two-phase flow instabilities in FFMHS result in subsequent decrease in heat transfer coefficients. Therefore, a simple flow stability criterion has been developed for two phase flow in FFMHS. The criterion is based on the balance between the inertia forces of the incoming liquid and the evaporative forces of vapor generated in the microchannel. The flow is assumed to be non-pulsating when the liquid inertia forces can suppress the evaporative forces. When the evaporative forces are dominant, the incoming flow will be pushed back creating flow pulsation and very large dryouts, therefore decreasing the heat transfer coefficients and heat transfer efficiency of the heat sink. For two phase flow in the single unit cell shown in Figure 3-1 one can define the liquid velocity in straight section of the microchannel as: (9-33) where is the mass flow rate in the unit cell, ?l is the liquid density and chH and chw are the microchannel height and width, respectively. The vapor velocity for the same microchannel cross-section area can be defined as: ( ) 2 2 ? ? ??? + + +? ? ? ?= l v base ch fin man v v lv ch ch w wq w t t v Ch H w (9-34) where ??baseq is the heat flux applied at the base of the microgrooved surface, fint is the fin thickness, lw is the inlet feed channel width, vw is the outlet feed channel width, 285 mant is the manifold thickness, ?v is the vapor density, lvh is the latent heat and C is a parameter that accounts for the vapor escaping from the outlet feed channel. 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