Louisiana State University LSU Digital Commons LSU Master's Theses Graduate School 2008 Experimental and numerical investigation of fluid flow and heat transfer in microchannels Wynn Allen Phillips Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses Part of the Mechanical Engineering Commons Recommended Citation Phillips, Wynn Allen, "Experimental and numerical investigation of fluid flow and heat transfer in microchannels" (2008). LSU Master's Theses. 3821. https://digitalcommons.lsu.edu/gradschool_theses/3821 This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. EXPERIMENTAL AND NUMERICAL INVESTIGATION OF FLUID FLOW AND HEAT TRANSFER IN MICROCHANNELS A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering in The Department of Mechanical Engineering by Wynn Allen Phillips, Jr. B.S., Louisiana State University, 2007 August 2008 ACKNOWLEDGEMENTS Acknowledgement and thanks are given to Dr. Shengmin Guo, Dr. Wen Jin Meng, Dr. Dorel Moldovan, Dr. Srinath Ekkad, Fanghua Mei, and Pritish Parida for their guidance and support in this project. I have learned a great deal from them all. Very special thanks go to my wife, Lauren, for her constant support. I would also like to thank all of my family and friends who helped me get to where I am today. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS ............................................................................................................ ii LIST OF FIGURES ........................................................................................................................ v NOMENCLATURE ..................................................................................................................... vii ABSTRACT .................................................................................................................................... x CHAPTER 1: INTRODUCTION ....................................................................................................1 1.1 Microchannel Heat Exchangers ............................................................................................ 1 1.2 Literature Review .................................................................................................................. 2 1.2.1 Friction Factor and Turbulent Transition ....................................................................... 2 1.2.2 Nusselt Number and Heat Transfer ................................................................................ 5 1.3 Setup for the Present Study of Microchannel Fluid Flow and Heat Transfer ....................... 7 CHAPTER 2: BACKGROUND AND THEORY FOR INTERNAL CONVECTIVE HEAT TRANSFER ................................................................................................10 2.1 Tube Flow Energy Balance ................................................................................................. 10 2.2 Constant Surface Heat Flux ................................................................................................. 12 2.3 Constant Surface Temperature ............................................................................................ 13 2.4 Nusselt Numbers for Fully Developed Laminar Flow ........................................................ 14 2.5 Entrance Lengths ................................................................................................................. 16 2.6 Nusselt Number for Laminar Thermally Developing Flow ................................................ 19 2.7 Nusselt Number for Laminar Simultaneously Developing Flow ........................................ 21 2.8 Nusselt Number for Fully Developed Turbulent Flow ....................................................... 21 2.9 Knudsen Number ................................................................................................................. 23 CHAPTER 3: SECONDARY INVESTIGATIONS IN MICROCHANNEL FLUID FLOW AND HEAT TRANSFER ......................................................................................26 3.1 Designed Geometries .......................................................................................................... 26 3.1.1 Setup of Analysis .......................................................................................................... 26 3.1.2 Governing Equations and Meshing .............................................................................. 27 3.1.3 Solving for Friction Factor and Nusselt Number ......................................................... 30 3.2 Critical Analysis of Experiments from Literature ............................................................... 33 3.2.1 Setup of Analysis .......................................................................................................... 33 3.2.2 Problem Definition, Governing Equations, and Meshing ............................................ 34 3.2.3 Solution and Analysis ................................................................................................... 36 CHAPTER 4: EXPERIMENTAL SETUP ....................................................................................42 4.1 Experimental Theory ........................................................................................................... 42 4.2 MHE Construction .............................................................................................................. 43 4.3 Experimental Apparatus ...................................................................................................... 44 iii 4.3.1 Pressurizing System ...................................................................................................... 46 4.3.2 Heat Exchanger System ................................................................................................ 49 4.3.3 Data Acquisition System .............................................................................................. 53 4.4 Experimental Procedure and Uncertainty ........................................................................... 55 CHAPTER 5: EXPERIMENTAL DATA REDUCTION, RESULTS, AND ANALYSIS ...........58 5.1 Friction Factor ..................................................................................................................... 58 5.1.1 Friction Factor Data Reduction .................................................................................... 58 5.1.2 Friction Factor Results and Analysis ............................................................................ 63 5.2 Heat Transfer ....................................................................................................................... 66 5.2.1 Heat Transfer Data Reduction ...................................................................................... 66 5.2.2 Heat Transfer Results and Discussion .......................................................................... 67 CHAPTER 6: COMPUTATIONAL FLUID DYNAMICS ANALYSIS ......................................76 6.1 Modeling Setup and Governing Equations ......................................................................... 76 6.2 Basic Overview of the k-ω Turbulence Model ................................................................... 78 6.3 The Plenum Model .............................................................................................................. 81 6.4 The Microchannel Model .................................................................................................... 85 6.4.1 Microchannel Model Mesh ........................................................................................... 85 6.4.2 Grid Independence ........................................................................................................ 87 6.5 CFD Results and Analysis................................................................................................... 88 CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS .................................................93 REFERENCES ............................................................................................................................. 95 VITA ............................................................................................................................................. 99 iv LIST OF FIGURES Figure 2.1: Tube flow control volume ...........................................................................................11 Figure 2.2: Air Knudsen number variation with temperature. .......................................................24 Figure 2.3: Air Knudsen number variation with pressure..............................................................25 Figure 3.1: 5x geometry model. .....................................................................................................27 Figure 3.2: Grid independence for the 10x case, Re=2500. ..........................................................29 Figure 3.3: 5x geometry mesh: (a) side view; (b) raised view of a section. ..................................29 Figure 3.4: Friction factors for designed geometries .....................................................................32