A Heat Transfer Textbook Third Edition by John H. Lienhard IV and John H. Lienhard V Professor John H. Lienhard IV Department of Mechanical Engineering University of Houston Houston TX 77204-4792 U.S.A. Professor John H. Lienhard V Department of Mechanical Engineering Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge MA 02139-4307 U.S.A. Copyright ©2000 by John H.Lienhard IV and John H.Lienhard V All rights reserved Please note that this material is copyrighted under U.S. Copyright Law. The authors grant you the right to download and print it for your personal use or for non-profit instructional use.Any other use, including copying, distributing or modifying the work for commercial purposes, is subject to the restrictions of U.S. Copyright Law. International copyright is subject to the Berne International Copyright Convention. The authors have used their best efforts to ensure the accuracy of the methods, equations, and data described in this book, but they do not guarantee them for any particular purpose.The authors and publisher offer no warranties or representations, nor do they accept any liabilities with respect to the use of this information.Please report any errata to authors. Lienhard, John H., 1930– A heat transfer textbook / John H.Lienhard IV and John H.Lienhar d V — 3rd ed.— Cambridge, MA : J.H. Lienhard V, c2000 Includes bibliographic references 1.Heat—Transmission 2.Mass Transfer I.Lienhard, John H.,V, 1961– II.Title TJ260.L445 2000 Published by J.H. Lienhard V Cambridge, Massachusetts, U.S.A. This book was typeset in Lucida Bright and Lucida New Math fonts (designed by Bigelow & Holmes) using LATEX under the Y&Y TEX System. For updates and information, visit: http://web.mit.edu/lienhard/www/ahtt.html This copy is: Version 0.20 dated June 27, 2001 Preface iii Contents I The General Problem of Heat Exchange 1 1 Introduction 3 1.1 Heat transfer .................................... 3 1.2 Relation of heat transfer to thermodynamics .......... 6 1.3 Modes of heat transfer ............................ 10 1.4 A look ahead .................................... 35 1.5 Problems ....................................... 35 Problems ....................................... 37 References ..................................... 45 2 Heat conduction concepts, thermal resistance, and the overall heat transfer coefficient 49 2.1 The heat diffusion equation ........................ 49 2.2 Solutions of the heat diffusion equation .............. 58 2.3 Thermal resistance and the electrical analogy .......... 62 2.4 Overall heat transfer coefficient, U .................. 74 2.5 Summary ....................................... 82 Problems ....................................... 83 References ..................................... 91 3 Heat exchanger design 93 3.1 Function and configuration of heat exchangers ........ 93 3.2 Evaluation of the mean temperature difference in a heat exchanger ...................................... 97 3.3 Heat exchanger effectiveness ....................... 114 3.4 Heat exchanger design ............................ 120 Problems ....................................... 123 References ..................................... 129 v vi Contents II Analysis of Heat Conduction 131 4 Analysis of heat conduction and some steady one-dimensional problems 133 4.1 The well-posed problem ........................... 133 4.2 The general solution .............................. 135 4.3 Dimensional analysis ............................. 142 4.4 An illustration of dimensional analysis in a complex steady conduction problem .............................. 151 4.5 Fin design ...................................... 155 Problems ....................................... 173 References ..................................... 180 5 Transient and multidimensional heat conduction 181 5.1 Introduction .................................... 181 5.2 Lumped-capacity solutions ........................ 182 5.3 Transient conduction in a one-dimensional slab ........ 191 5.4 Temperature-response charts ...................... 196 5.5 One-term solutions ............................... 206 5.6 Transient heat conduction to a semi-infinite region ..... 208 5.7 Steady multidimensional heat conduction ............. 223 5.8 Transient multidimensional heat conduction .......... 235 Problems ....................................... 240 References ..................................... 250 III Convective Heat Transfer 253 6 Laminar and turbulent boundary layers 255 6.1 Some introductory ideas .......................... 255 6.2 Laminar incompressible boundary layer on a flat surface 262 6.3 The energy equation .............................. 278 6.4 The Prandtl number and the boundary layer thicknesses . 282 6.5 Heat transfer coefficient for laminar, incompressible flow over a flat surface ................................ 286 6.6 The Reynolds analogy ............................. 297 6.7 Turbulent boundary layers ......................... 299 Problems ....................................... 310 References ..................................... 315 Contents vii 7 Forced convection in a variety of configurations 317 7.1 Introduction .................................... 317 7.2 Heat transfer to and from laminar flows in pipes ....... 318 7.3 Turbulent pipe flow .............................. 330 7.4 Heat transfer surface viewed as a heat exchanger ....... 340 7.5 Heat transfer coefficients for noncircular ducts ........ 342 7.6 Heat transfer during cross flow over cylinders ......... 342 7.7 Other configurations ............................. 352 Problems ....................................... 354 References ..................................... 359 8 Natural convection in single-phase fluids and during film condensation 363 8.1 Scope .......................................... 363 8.2 The nature of the problems of film condensation and of natural convection ............................... 364 8.3 Laminar natural convection on a vertical isothermal surface 367 8.4 Natural convection in other situations ............... 382 8.5 Film condensation ............................... 394 Problems ....................................... 409 References ..................................... 416 9 Heat transfer in boiling and other phase-change configurations 421 9.1 Nukiyama’s experiment and the pool boiling curve ..... 421 9.2 Nucleate boiling ................................. 428 9.3 Peak pool boiling heat flux ......................... 436 9.4 Film boiling ..................................... 450 9.5 Minimum heat flux ............................... 452 9.6 Transition boiling and system influences ............. 453 9.7 Forced convection boiling in tubes .................. 460 9.8 Two-phase flow in horizontal tubes .................. 466 9.9 Forced convective condensation heat transfer ......... 469 9.10 Dropwise condensation ........................... 470 9.11 The heat pipe ................................... 473 Problems ....................................... 475 References ..................................... 478 viii Contents IV Thermal Radiation Heat Transfer 485 10 Radiative heat transfer 487 10.1 The problem of radiative exchange .................. 487 10.2 Kirchhoff’s law .................................. 495 10.3 Simple radiant heat exchange between two surfaces .... 497 10.4 Heat transfer among gray bodies .................... 512 10.5 Gaseous radiation ................................ 522 10.6 Solar energy .................................... 530 Problems ....................................... 535 References ..................................... 542 V Mass Transfer 545 11 An Introduction to Mass Transfer 547 11.1 Introduction .................................... 547 11.2 Mixture compositions and species fluxes ............. 550 11.3 Diffusion fluxes and Fick’s Law ..................... 558 11.4 Transport properties of mixtures ................... 562 11.5 The equation of species conservation ................ 576 11.6 Steady mass transfer through a stagnant layer ......... 586 11.7 Mass transfer coefficients .......................... 593 11.8 Simultaneous heat and mass transfer ................ 606 Problems ....................................... 616 References ..................................... 628 VI Appendices 631 A Some thermophysical properties of selected materials 633 References ..................................... 636 B Units and conversion factors 663 References ..................................... 664 C Nomenclature 667 Citation Index 673 Subject Index 679 Part I The General Problem of Heat Exchange 1 1. Introduction The radiation of the sun in which the planet is incessantly plunged, pene- trates the air, the earth, and the waters; its elements are divided, change direction in every way, and, penetrating the mass of the globe, would raise its temperature more and more, if the heat acquired were not exactly balanced by that which escapes in rays from all points of the surface and expands through the sky. The Analytical Theory of Heat, J. Fourier 1.1 Heat transfer People have always understood that something flows from hot objects to cold ones.We call that flow heat. In the eighteenth and early nineteenth centuries, scientists imagined that all bodies contained an invisible fluid which they called caloric. Caloric was assigned a variety of properties, some of which proved to be inconsistent with nature (e.g., it had weight and it could not be created nor destroyed).But its most important feature was that it flowed from hot bodies into cold ones.It was a very useful way to