THERMAL COMPUTATIONS FOR ELECTRONICS THERMAL COMPUTATIONS FOR ELECTRONICS Conductive, Radiative, and Convective Air Cooling Gordon N. Ellison Second edition published 2020 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN © 2020 Taylor & Francis Group, LLC First edition published by CRC Press 2010 CRC Press is an imprint of Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. 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Title: Thermal computations for electronics : conductive, radiative, and convective air cooling / Gordon Ellison. Description: Second edition. | Boca Raton, FL : CRC Press/Taylor & Francis Group, 2020. | Includes bibliographical references and index. Identifiers: LCCN 2019060142 (print) | LCCN 2019060143 (ebook) | ISBN 9780367465315 (hardback) | ISBN 9781003029328 (ebook) Subjects: LCSH: Electronic apparatus and appliances--Thermal properties--Mathematical models. | Electronic apparatus and appliances--Cooling--Mathematics. Classification: LCC TK7870.25 .E43 2020 (print) | LCC TK7870.25 (ebook) | DDC 621.381/044--dc23 LC record available at https://lccn.loc.gov/2019060142 LC ebook record available at https://lccn.loc.gov/2019060143 ISBN: 9780367465315 (hbk) ISBN: 9781003029328 (ebk) Visit the eResources: https://www.crcpress.com/9780367465315 Dedication I dedicate this book to my wife, Sharon, who has stood by me with patient encouragement as I labored uncountable weekends and evenings from my student years to the present in an effort to be the best that I could be. Those people who know me well understand the important role played by my family both in the United States and Norway (counties of Sogn og Fjordane and Innlandet) and I dedicate this book to them also. With regard to the latter country, genealogist Bjørn Løkken of Trondheim, Norway, deserves special recognition for his contribution of countless hours devoted to the discovery of the life and exploits of my grandfather, Peder Eliassen. v Contents Preface to the Second Edition xiii Preface to the First Edition xv About the Author xix Chapter 1 Introduction 1 1.1 Primary mechanisms of heat flow 1 1.2 Conduction 1 1.3 Application example: Silicon chip resistance calculation 4 1.4 Convection 5 1.5 Application example: Chassis panel cooled by natural convection 6 1.6 Radiation 6 1.7 Application example: Chassis panel cooled only by radiation 7 1.8 Illustrative example: Simple thermal network model for a heat sinked 8 power transistor on a circuit board 1.9 Illustrative example: Thermal network circuit for a printed circuit board 9 1.10 Compact component models 10 1.11 Illustrative example: Pressure and thermal circuits for a forced 11 air cooled enclosure 1.12 Illustrative example: A single chip package on a printed circuit board - 14 the problem 1.13 Illustrative example: A single chip package on a printed circuit board - 14 Fourier series analytical solution 1.14 Illustrative example: A single chip package on a printed circuit board - 15 thermal network solution 1.15 Illustrative example: A single chip package on a printed circuit board - 16 finite element method solution 1.16 Illustrative example: A single chip package on a printed circuit board - 17 three solution methods compared Exercises 18 Chapter 2 Thermodynamics of airflow 21 2.1 The first law of thermodynamics 21 2.2 Heat capacity at constant volume 23 2.3 Heat capacity at constant pressure 23 2.4 Steady gas flow as an open, steady, single stream 24 2.5 Air temperature rise: Temperature dependence 25 2.6 Air temperature rise: T identified using differential forms of∆T,∆Q 26 2.7 Air temperature rise: T identified as average bulk temperature 27 Exercises 28 Chapter 3 Airflow I: Forced flow in systems 29 3.1 Preliminaries 29 3.2 Bernoulli’s equation 30 3.3 Bernoulli’s equation with losses 31 3.4 Fan testing 32 3.5 Estimate of fan test error accrued by measurement of downstream static pressure 33 3.6 Derivation of the “one velocity” head formula 34 3.7 Fan and system matching 35 3.8 Adding fans in series and parallel 38 vii viii Contents 3.9 Airflow resistance: Common elements 40 3.10 Airflow resistance: True circuit boards 42 3.11 Modeled circuit board elements 44 3.12 Combining airflow resistances 46 3.13 Application example: Forced air cooled enclosure 47 Exercises 53 Chapter 4 Airflow II: Forced flow in ducts, extrusions, and pin fin arrays 59 4.1 The airflow problem for channels with a rectangular cross-section 59 4.2 Entrance and exit effects for laminar and turbulent flow 60 4.3 Friction coefficient for channel flow 61 4.4 Application example: Two-sided extruded heat sink 62 4.5 A pin fin correlation 66 4.6 Application example: Pin fin problem from Khan et al. 67 4.7 Flow bypass effects according to Lee 69 4.8 Application example: Interfin air velocity calculation for a heat sink in a circuit 71 board channel using the flow bypass method of Lee with the Muzychka and Yovanovich friction factor correlation 4.9 Application example: Interfin air velocity calculation for a heat sink in a circuit 73 board channel using the flow bypass method of Lee with the Handbook of Heat Transfer friction factor correlation 4.10 Flow bypass effects according to Jonsson and Moshfegh 75 4.11 Application example: Pin fin problem from Khan et al., using the Jonsson and 76 Moshfegh correlation, non-bypass Exercises 77 Chapter 5 Airflow III: Buoyancy driven draft 79 5.1 Derivation of buoyancy driven head 79 5.2 Matching buoyancy head to system 81 5.3 Application example: Buoyancy-draft cooled enclosure 82 5.4 System models with buoyant airflow 83 Exercises 84 Chapter 6 Forced convective heat transfer I: Components 87 6.1 Forced convection from a surface 87 6.2 Dimensionless numbers: Nusselt, Reynolds, and Prandtl 88 6.3 More on the Reynolds number 92 6.4 Classical flat plate forced convection correlation: Uniform surface 93 temperature, laminar flow 6.5 Empirical correction to classical flat plate forced convection 95 correlation, laminar flow 6.6 Application example: Winged aluminum heat sink 96 6.7 Classical flat plate forced convection correlation: Uniform heat rate 97 per unit area, laminar flow 6.8 Classical flat plate (laminar) forced convection correlation extended 98 to small Reynolds numbers: Uniform surface temperature 6.9 Circuit boards: Adiabatic heat transfer coefficients and adiabatic temperatures 100 6.10 Adiabatic heat transfer coefficient and temperature according to Faghri et al. 102 6.11 Adiabatic heat transfer coefficient and temperature for low-profile components 103 according to Wirtz 6.12 Application example: Circuit board with 0.82 in. 0.24 In. 0.123 in. convecting 105 modules Contents ix Exercises 107 Chapter 7 Forced convective heat transfer II: Ducts, extrusions, and pin fin arrays 111 7.1 Boundary layer considerations 111 7.2 A convection/conduction model for ducts and heat sinks 112 7.3 Conversion of an isothermal heat transfer coefficient from referenced- 115 to-inlet air to referenced-to-local air 7.4 Nusselt number for fully developed laminar duct flow corrected for 116 entry length effects 7.5 A newer Nusselt number for laminar flow in rectangular (cross-section) 119 ducts with entry length effects 7.6 Nusselt number for turbulent duct flow 119 7.7 Application example: Two-sided extruded heat sink 120 7.8 Flow bypass effects according to Jonsson and Moshfegh 123 7.9 Application example: Heat sink in a circuit board channel using the flow 126 bypass method of Lee 7.10 In-line and staggered pin fin heat sinks 130 7.11 Application example: Thermal resistance of a pin fin heat sink using the 132 7.12 Lee’s flow bypass adapted to non-zero bypass resistance problem, compared 133 empirical method of Jonsson & Moshfegh Exercises 140 Chapter 8 Natural convection heat transfer I: Plates 143 8.1 Dimensionless numbers: Nusselt and Grashof 143 8.2 Classical flat plate correlations 146 8.3 Small device flat plate correlations 150 8.4 Application example: Vertical convecting plate 153 8.5 Application example: Vertical convecting and radiating plate 154 8.6 Vertical parallel plate correlations applicable to circuit board channels 155 8.7 Application example: Vertical card assembly 159 8.8 Recommended use of vertical channel models in sealed and vented 163 enclosures 8.9 Conversion of isothermal wall channel heat transfer coefficients from 164 referenced-to-inlet air to referenced-to-local air 8.10 Application example: Enclosure with circuit boards - enclosure 165 temperatures only 8.11 Application example: Enclosure with circuit boards - circuit board 170 temperatures only 8.12 Application example: Enclosure with circuit boards, comparison of 175 Sections 8.10 and 8.11 approximate results with CFD 8.13 Illustrative example: Metal-walled enclosure, ten PCBs 175 8.14 Illustrative example: Metal-walled enclosure with heat dissipation provided by 176 several wire-wound resistors Exercises 177 Chapter 9 Natural convection heat transfer II: Heat sinks 183 9.1 Heat sink geometry and some nomenclature 183 9.2 A rectangular U-channel correlation from Van de Pol and Tierney 183 9.3 Design plots representing the Van de Pol and Tierney correlation 184 9.4 A few useful formulae 191