Advanced Heat Transfer Advanced Heat Transfer Third Edition Greg F. Naterer Third Edition published 2022 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN © 2022 Greg F. Naterer Second Edition published by CRC Press 2018 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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ISBN: 978-1-032-07247-0 (hbk) ISBN: 978-1-032-07251-7 (pbk) ISBN: 978-1-003-20612-5 (ebk) DOI: 10.1201/9781003206125 Typeset in Times by SPi Technologies India Pvt Ltd (Straive) Visit the Support Materials: https://www.routledge.com/9781032072470 Dedication In memory of my son Jordan who inspires me by his everlasting zeal of exploring and climbing to greater heights. Contents Preface ..............................................................................................................................................xv Author ............................................................................................................................................xvii Lists of Abbreviations ...................................................................................................................xviii Chapter 1 Introduction ..................................................................................................................1 1.1 Fundamental Concepts and Definitions .............................................................2 1.2 Conservation of Energy .....................................................................................4 1.3 Thermophysical Properties ................................................................................5 1.3.1 Thermodynamic Properties ...................................................................5 1.3.2 Transport Properties ..............................................................................7 1.4 Heat Conduction ................................................................................................9 1.5 Convection .......................................................................................................11 1.6 Thermal Radiation ...........................................................................................12 1.7 Phase Change Heat Transfer ............................................................................14 1.8 Mass Transfer ..................................................................................................15 References ..................................................................................................................17 Problems .....................................................................................................................17 Chapter 2 Heat Conduction .........................................................................................................21 2.1 Introduction .....................................................................................................21 2.2 One-Dimensional Heat Conduction ................................................................22 2.2.1 Heat Conduction Equation ..................................................................22 2.2.2 Steady Conduction in a Plane Layer ...................................................24 2.3 Thermal Resistance and Shape Factor .............................................................25 2.4 Fins and Extended Surfaces .............................................................................31 2.5 Multidimensional Conduction .........................................................................35 2.5.1 Cartesian Coordinates .........................................................................35 2.5.2 Orthogonal Curvilinear Coordinates ...................................................36 2.5.3 Cylindrical and Spherical Coordinates ...............................................39 2.6 Method of Separation of Variables ..................................................................41 2.7 Nonhomogeneous Systems ..............................................................................44 2.8 Conformal Mapping ........................................................................................46 2.9 Transient Heat Conduction ..............................................................................53 2.9.1 Lumped Capacitance Method .............................................................53 2.9.2 Semi-Infinite Solid ..............................................................................55 2.9.3 Finite Regions .....................................................................................58 2.10 Time-Dependent Boundary Conditions ...........................................................59 2.11 Conduction in Porous Media ...........................................................................61 2.12 Heat Transfer in Living Tissue ........................................................................62 2.13 Microscale Conduction ....................................................................................65 References ..................................................................................................................67 Problems .....................................................................................................................67 vii viii Contents Chapter 3 Convection ..................................................................................................................73 3.1 Introduction .....................................................................................................73 3.2 Governing Equations .......................................................................................74 3.2.1 Conservation of Mass (Continuity Equation) .....................................74 3.2.2 Conservation of Momentum (Navier–Stokes Equations) ...................75 3.2.3 Total Energy (First Law of Thermodynamics) ...................................79 3.2.4 Mechanical Energy Equation ..............................................................80 3.2.5 Internal Energy Equation ....................................................................82 3.3 Nondimensional Form of Equations ................................................................83 3.3.1 Dimensionless Variables .....................................................................83 3.3.2 Buckingham–Pi Theorem ...................................................................86 3.4 Convection Boundary Layer ............................................................................88 3.4.1 Boundary Layer Equations .................................................................88 3.4.2 Heat and Momentum Analogies .........................................................92 3.5 Evaporative Cooling ........................................................................................93 3.6 Flat Plate Boundary Layer ...............................................................................94 3.6.1 Scaling Analysis ..................................................................................95 3.6.2 Integral Solution .................................................................................96 3.6.3 Similarity Solution ..............................................................................98 3.7 Flow Past a Wedge .........................................................................................103 3.8 Cylinder in Cross Flow ..................................................................................105 3.9 Other External Flow Configurations ..............................................................107 3.9.1 Sphere ...............................................................................................107 3.9.2 Tube Bundles ....................................................................................108 3.10 Internal Flow ..................................................................................................109 3.10.1 Poiseuille Flow in Tubes ...................................................................109 3.10.2 Non-Circular Ducts ...........................................................................116 3.11 Free Convection .............................................................................................118 3.11.1 Vertical Flat Plate ..............................................................................118 3.11.2 Body Gravity Function Method ........................................................123 3.11.3 Spherical Geometries ........................................................................127 3.12 Introduction to Turbulence ............................................................................128 3.12.1 Turbulence Spectrum ........................................................................128 3.12.2 Reynolds Averaged Navier–Stokes Equations ..................................130 3.12.3 Eddy Viscosity ..................................................................................132 3.12.4 Mixing Length ..................................................................................132 3.12.5 Near-Wall Flow .................................................................................133 3.12.6 One and Two-Equation Closure Models ...........................................134 3.13 Entropy and the Second Law .........................................................................136 3.13.1 Formulation of Entropy Production ..................................................136 3.13.2 Apparent Entropy Production Difference .........................................139 3.13.3 Dimensionless Entropy Production Number ....................................142 References ................................................................................................................143 Problems ...................................................................................................................144 Chapter 4 Thermal Radiation ....................................................................................................151 4.1 Introduction ...................................................................................................151 4.2 Fundamentals of Radiation ............................................................................152 Contents ix 4.2.1 Electromagnetic Spectrum ................................................................152 4.2.2 Radiation Intensity ............................................................................153 4.2.3 Blackbody Radiation ........................................................................156 4.3 Radiative Surface Properties ..........................................................................158 4.4 Radiation Exchange between Surfaces ..........................................................162 4.5 Thermal Radiation in Enclosures ..................................................................165 4.5.1 Radiation Exchange at a Surface ......................................................165 4.5.2 Radiation Exchange between Surfaces .............................................166 4.5.3 Two-Surface Enclosures ...................................................................168 4.6 Radiation in Participating Media ...................................................................171 4.6.1 Attenuation by Absorption and Scattering ........................................171 4.6.2 Scattering from Other Directions ......................................................173 4.6.3 Enhancement of Intensity by Emission ............................................174 4.7 Equations of Energy Transfer for Participating Media ..................................176 4.7.1 General Equation of Transfer ............................................................176 4.7.2 Radiative Flux Vector ........................................................................177 4.7.3 Conservation of Energy ....................................................................179 4.8 Approximate Solutions of the Equation of Transfer ......................................180 4.8.1 Transparent Gas Approximation .......................................................180 4.8.2 Emission Approximation ..................................................................180 4.8.3 Rosseland Approximation .................................................................181 4.9 Coupled Radiation and Convection ...............................................................183 4.10 Solar Radiation ..............................................................................................185 4.10.1 Components of Solar Radiation ........................................................185 4.10.2 Solar Angles ......................................................................................189 4.10.3 Incident Solar Radiation ...................................................................192 4.11 Solar Collectors .............................................................................................195 4.11.1 Collector Efficiency and Heat Losses ...............................................195 4.11.2 Temperature Distribution ..................................................................198 4.11.3 Heat Removal Factor ........................................................................199 References ................................................................................................................202 Problems ...................................................................................................................203 Chapter 5 Gas–Liquid Two-Phase Flows ..................................................................................207 5.1 Introduction ...................................................................................................207 5.2 Pool Boiling ...................................................................................................208 5.2.1 Physical Processes ............................................................................208 5.2.2 Nucleate Pool Boiling .......................................................................209 5.2.3 Film Pool Boiling .............................................................................211 5.3 Forced Convection Boiling in External Flow ................................................212 5.3.1 Over a Flat Plate ...............................................................................213 5.3.2 Outside a Horizontal Tube ................................................................213 5.3.3 Other Surface Configurations ...........................................................213 5.4 Two-Phase Flow in Vertical Tubes.................................................................214 5.4.1 Vertical Flow Regimes ......................................................................214 5.4.2 Formation of Bubbles .......................................................................215 5.4.3 Models of Annular Flow and Heat Transfer .....................................218 5.5 Internal Horizontal Two-Phase Flows ...........................................................221