Thermal Design. Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat Exchangers, and Solar Cells. HoSung Lee JOHN WILEY & SONS, INC.

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5 Thermal Design Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat Exchangers, and Solar Cells HoSung Lee JOHN WILEY & SONS, INC.

6 This book is printed on acid-free paper. Copyright c 2010 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) , fax (978) , or on the Web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) , fax (201) , or online at Limit of Liability/Disclaimer of Warranty: While the publisher and the author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor the author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information about our other products and services, please contact our Customer Care Department within the United States at (800) , outside the United States at (317) or fax (317) Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our Web site at Library of Congress Cataloging-in-Publication Data: Lee, Ho Sung. Thermal design : heat sinks, thermoelectrics, heat pipes, compact heat exchangers, and solar cells / Ho Sung Lee. p. cm. Includes index. ISBN (hardback); (ebk); (ebk); (ebk); (ebk); (ebk); (ebk) 1. Heat engineering Materials. 2. Heat-transfer media. 3. Thermodynamics. 4. Thermoelectric apparatus and appliances. I. Title. TJ255.5.L dc ISBN: Printed in the United States of America

7 Preface xv 1 Introduction Introduction Humans and Energy Thermodynamics Energy, Heat, and Work The First Law of Thermodynamics Heat Engines, Refrigerators, and Heat Pumps The Second Law of Thermodynamics Carnot Cycle Heat Transfer Introduction Conduction Convection Parallel Flow on an Isothermal Plate A Cylinder in Cross Flow Flow in Ducts Free Convection Radiation Thermal Radiation View Factor Radiation Exchange between Diffuse-Gray Surfaces 31 References 32 2 Heat Sinks Longitudinal Fin of Rectangular Profile Heat Transfer from Fin Fin Effectiveness Fin Efficiency Corrected Profile Length Optimizations Constant Profile Area A p Constant Heat Transfer from a Fin Constant Fin Volume or Mass Multiple Fin Array I Free (Natural) Convection Cooling Small Spacing Channel 45 v

8 vi Large Spacing Channel Optimum Fin Spacing Forced Convection Cooling Small Spacing Channel Large Spacing Channel Multiple Fin Array II Natural (Free) Convection Cooling Thermal Resistance and Overall Surface Efficiency Fin Design with Thermal Radiation Single Longitudinal Fin with Radiation 81 References 94 Problems 94 3 Thermoelectrics Introduction Thermoelectric Effect Seebeck Effect Peltier Effect Thomson Effect Thomson (or Kelvin) Relationships Thermoelement Couple (Thermocouple) The Figure of Merit Similar and Dissimilar Materials Similar Materials Dissimilar Materials Thermoelectric Generator (TEG) Similar and Dissimilar Materials Similar Materials Dissimilar Materials Conversion Efficiency and Current Maximum Conversion Efficiency Maximum Power Efficiency Maximum Performance Parameters Multicouple Modules Thermoelectric Coolers (TEC) Similar and Dissimilar Materials Similar Materials Dissimilar Materials The Coefficient of Performance Optimum Current for the Maximum Cooling Rate Maximum Performance Parameters Optimum Current for the Maximum COP Generalized Charts 131

9 vii Optimum Geometry for the Maximum Cooling in Similar Materials Thermoelectric Modules Commercial TEC Multistage Modules Commercial Multistage Peltier Modules Design Options Applications Thermoelectric Generators Thermoelectric Coolers Design Example Design Concept Design of Internal and External Heat Sinks Design of Thermoelectric Cooler (TEC) Finding the Exact Solution for T c and T h Performance Curves for Thermoelectric Air Cooler Thermoelectric Module Design Thermal and Electrical Contact Resistances for TEG Thermal and Electrical Contact Resistances for TEC Design Example of TEC Module Design Concept Summary of Design of a TEC Module 173 References 174 Problems Heat Pipes Operation of Heat Pipe Surface Tension Heat Transfer Limitations Capillary Limitation Maximum Capillary Pressure Difference Vapor Pressure Drop Liquid Pressure Drop Normal Hydrostatic Pressure Drop Axial Hydrostatic Pressure Drop Approximation for Capillary Pressure Difference Sonic Limitation Entrainment Limitation Boiling Limitation Viscous Limitation Heat Pipe Thermal Resistance Contact Resistance Variable Conductance Heat Pipes (VCHP) Gas-Loaded Heat Pipes 203

10 viii Clayepyron-Clausius Equation Applications Loop Heat Pipes Micro Heat Pipes Steady-State Models Conventional Model Cotter s Model Working Fluid Figure of Merit Compatibility Wick Structures Design Example Selection of Material and Working Fluid Working Fluid Properties Estimation of Vapor Space Radius Estimation of Operating Limits Capillary Limits Sonic Limits Entrainment Limits Boiling Limits Wall Thickness Wick Selection Maximum Arterial Depth Design of Arterial Wick Capillary Limitation Liquid Pressure Drop in the Arteries Liquid Pressure Drop in the Circumferential Wick Vapor Pressure Drop in the Vapor Space Performance Map Check the Temperature Drop 235 References 236 Problems Compact Heat Exchangers Introduction Fundamentals of Heat Exchangers Counterflow and Parallel Flows Overall Heat Transfer Coefficient Log Mean Temperature Difference (LMTD) Flow Properties Nusselt Numbers 250

11 ix Effectiveness NTU (ε-ntu) Method Parallel Flow Counterflow Crossflow Heat Exchanger Pressure Drop Fouling Resistances (Fouling Factors) Overall Surface (Fin) Efficiency Reasonable Velocities of Various Fluids in Pipe Flow Double-Pipe Heat Exchangers Shell-and-Tube Heat Exchangers Baffles Multiple Passes Dimensions of Shell-and-Tube Heat Exchanger Shell-side Tube Layout Plate Heat Exchangers (PHE) Flow Pass Arrangements Geometric Properties Friction Factor Nusselt Number Pressure Drops Pressure Drops in Compact Heat Exchangers Fundamentals of Core Pressure Drop Core Entrance and Exit Pressure Drops Contraction and Expansion Loss Coefficients Circular-Tube Core Square-Tube Core Flat-Tube Core Triangular-Tube Core Finned-Tube Heat Exchangers Geometrical Characteristics Flow Properties Thermal Properties Correlations for Circular Finned-Tube Geometry Pressure Drop Correlations for Louvered Plate-Fin Flat-Tube Geometry Plate-Fin Heat Exchangers Geometric Characteristics Correlations for Offset Strip Fin (OSF) Geometry Louver-Fin-Type Flat-Tube Plate-Fin Heat Exchangers Geometric Characteristics Correlations for Louver Fin Geometry 355 References 372 Problems 373

12 x 6 Solar Cells Introduction Operation of Solar Cells Solar Cells and Technology Solar Irradiance Air Mass Nature of Light Quantum Mechanics Atomic Structure Bohr s Model Line Spectra De Broglie Wave Heisenberg Uncertainty Principle Schrödinger Equation A Particle in a 1-D Box Quantum Numbers Electron Configurations Van der Waals Forces Covalent Bonding Energy Band Pseudo-Potential Well Density of States Number of States Effective Mass Equilibrium Intrinsic Carrier Concentration Fermi Function Nondegenerate Semiconductor Equilibrium Electron and Hole Concentrations Intrinsic Semiconductors Intrinsic Carrier Concentration, n i Intrinsic Fermi Energy Alternative Expression for n 0 and p Extrinsic Semiconductors in Thermal Equilibrium Doping, Donors, and Acceptors Extrinsic Carrier Concentration in Equilibrium Built-in Voltage Principle of Detailed Balance Majority and Minority Carriers in Equilibrium Generation and Recombination Direct and Indirect Band Gap Semiconductors Absorption Coefficient Photogeneration 424

13 xi 6.7 Recombination Recombination Mechanisms Band Energy Diagram under Nonequilibrium Conditions Back Surface Field (BSF) Low-Level Injection Low-Level Injection Band-to-Band Recombination Trap-Assisted (SRH) Recombination Simplified Expression of the SRH Recombination Rate Auger Recombination Total Recombination Rate Carrier Transport Drift Carrier Mobility Diffusion Total Current Densities Einstein Relationship Semiconductor Equations Minority-Carrier Diffusion Equations P n Junction Calculation of Depletion Width Energy Band Diagram with a Reference Point Quasi-Fermi Energy Levels Minority Carrier Transport Boundary Conditions Minority Carrier Lifetimes Minority Carrier Diffusion Lengths Minority Carrier Diffusion Equation for Holes Minority Carrier Diffusion Equation for Electrons Characteristics of Solar Cells Current Density Current-Voltage Characteristics Figures of Merit Effect of Minority Electron Lifetime on Efficiency Effect of Minority Hole Lifetime on Efficiency Effect of Back Surface Recombination Velocity on Efficiency Effect of Base Width on Efficiency Effect of Emitter Width W N on Efficiency Effect of Acceptor Concentration on Efficiency Effect of Donor Concentration on Efficiency Band Gap Energy with Temperature Effect of Temperature on Efficiency 477

14 xii 6.11 Additional Topics Parasitic Resistance Effects (Ohmic Losses) Quantum Efficiency Ideal Solar Cell Efficiency Modeling Modeling for a Silicon Solar Cell Comparison of the Solar Cell Model with a Commercial Product Design of a Solar Cell Solar Cell Geometry with Surface Recombination Velocities Donor and Acceptor Concentrations Minority Carrier Diffusion Lifetimes Grid Spacing Anti-Reflection, Light Trapping and Passivation 512 References 512 Problems 513 Appendix A Thermophysical Properties 518 Appendix B Thermoelectrics 561 B.1 Thermoelectric Effects 561 Seebeck Effect 561 Peltier Effect 562 Thomson Effect 562 B.2 Thomson (or Kelvin) Relationships 562 B.3 Heat Balance Equation 566 B.4 Figure of Merit and Optimum Geometry 568 References 573 Appendix C Pipe Dimensions 574 Appendix D Curve Fitting of Working Fluids 576 Curve Fit for Working Fluids Chosen 576 D.1 Curve Fitting for Working Fluid Properties Chosen 576 D.1.1 MathCad Format 576 Appendix E Tutorial I for 2-D 580 Problem Description for Tutorial I 580 E.1 Tutorial I: Using Gambit and Fluent for Thermal Behavior of an Electrical Wire 581 E.1.1 Creating Geometry in Gambit 581 E.2 Calculations for Heat Generation 588

15 xiii Appendix F Tutorial II for 3-D 590 Problem Description for Tutorial II 590 F.1 Tutorial II Double-Pipe Heat Exchanger: Using SolidWorks, Gambit, and Fluent 591 F.1.1 Double-Pipe Heat Exchanger 591 F.1.2 Construct Model in SolidWorks 591 F.1.3 Meshing the Double Pipe Heat Exchanger in Gambit 595 F.1.4 Analysis of Heat Exchanger in Fluent 600 Appendix G Computational Work of Heat Pipe 605 G.1 A Heat Pipe and Heat Sink 605 Appendix H Computational Work of a Heat Sink 607 H.1 Electronic Package Cooling 607 Appendix I Tutorial for MathCAD 608 I.1 Tutorial Problem for MathCAD 608 Index 613

BASICS OF ANALYTICAL CHEMISTRY AND CHEMICAL EQUILIBRIA

BASICS OF ANALYTICAL CHEMISTRY AND CHEMICAL EQUILIBRIA BASICS OF ANALYTICAL CHEMISTRY AND CHEMICAL EQUILIBRIA BRIAN M. TISSUE Virginia Tech Department of Chemistry Blacksburg, VA Cover Design: Wiley Cover