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DTPQDT02019019646.pdf

ANALYSIS OF HEAT TRANSFER ENHANCEMENT THROUGH MULTI-HARMONIC WAVY MICROCHANNELS A Thesis Presented to The Faculty of the Department of Mechanical Engineering California State University, Los Angeles In Partial Ful llment of the Requirements for the Degree Master of Science in Mechanical Engineering By Justin Moon May 2019     ProQuest Number     All rights reserved  INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted.  In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion.      ProQuest  Published by ProQuest LLC . Copyright of the Dissertation is held by the Author.   All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition ProQuest LLC.   ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 13864346 13864346 2019 a169 2019 Justin Moon ALL RIGHTS RESERVED ii The thesis of Justin Moon is approved. Arturo Pacheco-Vega, Committee Chair Je Santner Yen Jim Kuo Nancy Warter-Perez, Department Chair California State University, Los Angeles May 2019 iii ABSTRACT Analysis of Heat Transfer Enhancement Through Multi-harmonic Wavy Microchannels By Justin Moon In this study, a three-dimensional nite element model of steady-state ow and heat transfer in micro-channels are simulated to investigate the e ects of conjugate heat transfer. The baseline geometry consists of a copper block with water as the working uid as the micro-sized heat exchanger system. The governing equations of both an incompressible non-isothermal laminar ow and conjugate heat transfer are built and solved. The focus is on the in uence of channel surface-topography for the proposed multi-harmonic geometry, through a parametric analysis via nite element methods. The analysis is then extended by considering a variety of conductive materials for the solid block that encloses the channel, and their impact on the heat transfer enhancement in these devices. The same governing equations are used, for repre- sentative single- and harmonic-wavy-channel models, with copper, aluminum, silicon, and steel-317 as solid-block materials and di erent operating conditions, by the nite element technique. By using the ratio of the Nusselt number for wavy to straight channels, a parametric analysis { for a set of cold-water ow-rates Re 50, 100 and 150 { shows that the addition of harmonic surfaces enhances the transfer of energy and that such ratio achieves the highest value with wave harmonic numbers of n 2. iv Regardless of the material, as wave amplitude and Reynolds number increase, so does the e ectiveness of the device, and that the selection of speci c material highly impacts the di usion of heat in the solid, but it is negligible on the Nusselt number for the uid. Finally, results of the performance factor PF, de ned as the ratio of the Nus- selt number to the pressure drop, indicate that the device is ine ective in the heat transfer enhancement relative to the required pumping power for small values of Reynolds number Re, but the device becomes very e ective for larger Re-values. v ACKNOWLEDGMENTS I must rst begin with properly acknowledging role of my advisor, Dr. Arturo Javier Pacheco-Vega, for his integral role in my professional development as a graduate student. It would be impossible to count all the ways that Dr. Pacheco-Vega has helped me in my academic career. Initially, I was surprised and taken aback after witnessing rsthand his uncompromising duty to and genuine care for his students, but I came to understand that he is a modern day Don Quixote innocently committed with a pure heart to making all students, under his wing, much better researchers. I cannot succinctly put into words how grateful I am for his valuable time and mentor- ship, but if I could come up with the best that I got, I would like to say Thank you for challenging me, like no one before had. My continuing education would not have been possible without the nan- cial support and funding security o ered by California State University Los Ange- les CSULA. I am extremely grateful to The Center for Energy and Sustainability CEaS for the scholarship and to the O ce of Graduate Studies Travel Awards for the favorable circumstances to be involved at out-of-state conferences. For the daily fun adventures aimed at researching methods of research pro- crastination and for always providing a helping hand despite their busy schedules and deadlines, I thank my alumni lab-mates Hector Gomez, Kin-Man Li, and Joshua Bal- tazar. I would like to thank my fellow lab-mates, Armen Yarian and Danny Clemons, for their support during my research and thesis writing process. To the next gener- ation of Dr. Pacheco’s students, Johanna Sanchez and Antonio Jose Arceo, I hope that you can fully live up to the legacy and make Dr. Pacheco’s Lab great vi I would like to acknowledge the Department of Mechanical Engineering at the California State University, Los Angeles and the College of Engineering, Com- puter Science and Technology for providing the opportunity to further my education. Thanks to the various sta of the Engineering college, including Andrea and Chris, who kept me a oat. I thank Dr. Yen Jim Kuo and Dr. Santner, members of my thesis committee, for your time. I would also like to mention the splendid opportunities of being a teaching assistant for Dr. Chivey Wu, Dr. Yen Jim Kuo, and Dr. Angel David Martinez. My thanks and appreciations also go to Dr. Warter-Perez, Chair of the Mechanical Engineering Department, whose great idea paved a way for me to become a hit on YouTube making homework solution videos during my time here. Finally, I would like to acknowledge friends and family, who have supported me during my time here. I would like thank my parents David and Jackie Moon for the endless support through-out my education and time of need. I would also like to thank my brother, Kevin, for the many moments of support and reproach, whose opinions I value highly. My endless gratitude goes to my paternal grandmother, Soon-seok, who spent the Summers during my childhood tutoring me Math. I am extremely grateful for my family for their continuous guidance and support through the years. vii TABLE OF CONTENTS Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2. Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1. Wavy Topology . . . . . . . . . . . . . . . . . . . . . 4 1.2.2. Fluid Material . . . . . . . . . . . . . . . . . . . . . 11 1.3. Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4. Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . 15 2. Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1. Fourier Sine Series . . . . . . . . . . . . . . . . . . . 19 2.1.2. Multi-harmonic Wave Addition . . . . . . . . . . . . 24 2.2. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3. Governing Equations . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1. Conservation of Mass . . . . . . . . . . . . . . . . . . 28 2.3.2. Conservation of Momentum . . . . . . . . . . . . . . 29 viii 2.3.3. Conservation of Energy . . . . . . . . . . . . . . . . 30 2.3.4. Parameters . . . . . . . . . . . . . . . . . . . . . . . 31 2.4. Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 31 3. Numerical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1. History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2. Finite Element Method . . . . . . . . . . . . . . . . . . . . . . 34 3.3. COMSOL Multiphysics . . . . . . . . . . . . . . . . . . . . . . 35 3.4. Convergence Test . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5. Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . 38 4. Results of Parametric Studies . . . . . . . . . . . . . . . . . . . . . . 43 4.1. Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.1. Straight Channels . . . . . . . . . . . . . . . . . . . 44 4.1.2. Wavy Channels . . . . . . . . . . . . . . . . . . . . . 49 4.2. Multiharmonic Model . . . . . . . . . . . . . . . . . . . . . . . 59 4.3. Thermal Performance . . . . . . . . . . . . . . . . . . . . . . . 63 4.3.1. Nusselt Number . . . . . . . . . . . . . . . . . . . . 63 4.3.2. Performance Factor . . . . . . . . . . . . . . . . . . . 66 5. Impact of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.1. Parametric Analysis . . . . . . . . . . . . . . . . . . . . . . . 69 5.2. Thermal Performance . . . . . . . . . . . . . . . . . . . . . . . 79 5.2.1. Nusselt Number . . . . . . . . . . . . . . . . . . . . 79 5.2.2. Performance Factor . . . . . . . . . . . . . . . . . . . 82 6. Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . 91 ix 6.1. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.2. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Appendices A. Modeling in COMSOL Multiphysics . . . . . . . . . . . . . . . . . . . 102 A.1. Micro-Wavy Multiharmonic Channel . . . . . . . . . . . . . . 102 B. Solid-Fluid Interface Wall Area . . . . . . . . . . . . . . . . . . . . . 153 C. Matlab Scripts Pre-Processing . . . . . . . . . . . . . . . . . . . . . 159 C.1. Straight Channel Model Run . . . . . . . . . . . . . . . . . . . 159 C.2. Wavy Channel Model Run . . . . . . . . . . . . . . . . . . . . 161 C.3. Harmonic Channel Model Run . . . . . . . . . . . . . . . . . . 163 D. Matlab Scripts Post-Processing . . . . . . . . . . . . . . . . . . . . . 166 D.1. Channel Temperature . . . . . . . . . . . . . . . . . . . . . . . 166 D.2. Fluid Bulk Temperature . . . . . . . . . . . . . . . . . . . . . 169 D.3. Fluid Pressure and Velocity . . . . . . . . . . . . . . . . . . . 172 D.4. Solid Wall Temperature . . . . . . . . . . . . . . . . . . . . . 175 E. Multi-harmonic Channel Fluid Plots . . . . . . . . . . . . . . . . . . 178 E.1. Streamwise Pressure . . . . . . . . . . . . . . . . . . . . . . . 178 E.2. Streamwise Temperature . . . . . . . . . . . . . . . . . . . . . 188 F. Two-Dimensional Model for Shape Optimization . . . . . . . . . . . . 198 F.1. Two-Dimensional Model . . . . . . . . . . . . . . . . . . . . . 198 x LIST OF TABLES Table 2.1. Baseline micro-channel parameter attribution . . . . . . . . . . . . . 24 2.2. Wavy micro-channel parameter attribution . . . . . . . . . . . . . . . 25 2.3. Multi-harmonic micro-channel parameter attribution . . . . . . . . . 25 2.4. Physical assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5. Fluid parameter selection . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6. Solid parameter selection . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.7. Boundary conditions applied to the FEA model . . . . . . . . . . . . 32 3.1. Percentage di erence in P values for Re 50 . . . . . . . . . . . . 41 3.2. Percentage di erence in P values for Re 100 . . . . . . . . . . . . 41 3.3. Percentage di erence in P values for Re 150 . . . . . . . . . . . . 41 4.1. Fluid properties used in simulations . . . . . . . . . . . . . . . . . . . 44 4.2. Solid properties used in simulations . . . . . . . . . . . . . . . . . . . 44 4.3. Percentage di erence in pressure drop for straight channels A 0 . . 46 5.1. Properties of the solid-block material used in simulations. . . . . . . . 69 5.2. Performance factor in wavy channels values for Re 50 . . . . . . . . 83 5.3. Performance factor in wavy channels values for Re 100 . . . . . . . 83 5.4. Performance factor in wavy channels values for Re 150 . . . . . . . 83 5.5. Performance factor Al positive harmonic channels values . . . . . . . 85 5.6. Performance factor Al negative harmonic channels values . . . . . . . 86 5.7. Performance factor Si positive harmonic channels values . . . . . . . 87 xi 5.8. Performance factor Si negative harmonic channels values . . . . . . . 88 5.9. Performance factor 317 positive harmonic channels values . . . . . . . 89 5.10. Performance factor 317 negative harmonic channels values . . . . . . 90 xii LIST OF FIGURES Figure 1.1. Schematic of a minichannel [10]. . . . . . . . . . . . . . . . . . . . . . 6 1.2. Schematic of a single-layer wavy microchannel [17]. . . . . . . . . . . 8 1.3. Schematic of a double-layer wavy microchannel [17]. . . . . . . . . . . 9 1.4. Schematic of a TWC heat sink [18]. . . . . . . . . . . . . . . . . . . . 10 1.5. Schematic of a LWC heat sink [18]. . . . . . . . . . . . . . . . . . . . 10 2.1. Baseline geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2. Square wave decomposition [29]. . . . . . . . . . . . . . . . . . . . . . 22 2.3. Fourier sine series decomposition [30]. . . . . . . . . . . . . . . . . . . 23 2.4. Side view schematic of the multi-harmonic micro-channel. . . . . . . . 26 3.1. Example of a physical domain. . . . . . . . . . . . . . . . . . . . . . . 36 3.2. Grid independence test. . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3. Pressure drop validation. . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4. Pressure drop percentage di erence . . . . . . . . . . . . . . . . . . . 39 3.5. Wavy channel pressure drop . . . . . . . . . . . . . . . . . . . . . . . 42 4.1. Straight channel pressure values. . . . . . . . . . . . . . . . . . . . . 45 4.2. Straight channel temperature values. . . . . . . . . . . . . . . . . . . 47 4.3. Straight channel temperature contours. . . . . . . . . . . . . . . . . . 48 4.4. Low-Re wavy channels uid pressure and temperature. . . . . . . . . 50 4.5. Low-Re wavy channels streamwise uid temperature. . . . . . . . . . 51 4.6. Low-Re wavy channels wall temperature. . . . . . . . . . . . . . . . 51 xiii 4.7. Low Re wavy channels temperature contours. . . . . . . . . . . . . . 52 4.8. Mid-Re wavy channels uid pressure and temperature. . . . . . . . . 53 4.9. Mid-Re wavy channels streamwise uid temperature. . . . . . . . . . 54 4.10. Mid-Re wavy channels wall temperature. . .

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