A HEAT TRANSFER TEXTBOOK THIRD EDITION John H. Lienhard IV / John H. Lienhard V A Heat Transfer Textbook Lienhard & Lienhard Phlogiston Press ISBN 0-9713835-0-2 PSB 01-04-0249 A HEAT TRANSFER TEXTBOOK THIRD EDITION John H. Lienhard IV / John H. Lienhard V A Heat Transfer Textbook Lienhard & Lienhard A Heat Transfer Textbook A Heat Transfer Textbook Third Edition by John H. Lienhard IV and John H. Lienhard V Phlogiston Press Cambridge Massachusetts Professor John H. Lienhard IV Department of Mechanical Engineering University of Houston 4800 Calhoun Road 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 ©2003 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 the authors. Lienhard, John H., 1930– A heat transfer textbook / John H. Lienhard IV and John H. Lienhard V — 3rd ed. — Cambridge, MA : Phlogiston Press, c2003 Includes bibliographic references and index. 1. Heat—Transmission 2. Mass Transfer I. Lienhard, John H., V, 1961– II. Title TJ260.L445 2003 Published by Phlogiston Press Cambridge, Massachusetts, U.S.A. This book was typeset in Lucida Bright and Lucida New Math fonts (designed by Bigelow & Holmes) using L A T E X under the Y&Y T E X System. For updates and information, visit: http://web.mit.edu/lienhard/www/ahtt.html This copy is: Version 1.12 dated January 19, 2003 Preface This book is meant for students in their introductory heat transfer course — students who have learned calculus (through ordinary differential equa- tions) and basic thermodynamics. We include the needed background in fluid mechanics, although students will be better off if they have had an introductory course in fluids. An integrated introductory course in thermofluid engineering should also be a sufficient background for the material here. Our major objectives in rewriting the 1987 edition have been to bring the material up to date and make it as clear as possible. We have substan- tially revised the coverage of thermal radiation, unsteady conduction, and mass transfer. We have replaced most of the old physical property data with the latest reference data. New correlations have been intro- duced for forced and natural convection and for convective boiling. The treatment of thermal resistance has been reorganized. Dozens of new problems have been added. And we have revised the treatment of turbu- lent heat transfer to include the use of the law of the wall. In a number of places we have rearranged material to make it flow better, and we have made many hundreds of small changes and corrections so that the text will be more comfortable and reliable. Lastly, we have eliminated Roger Eichhorn’s fine chapter on numerical analysis, since that topic is now most often covered in specialized courses on computation. This book reflects certain viewpoints that instructors and students alike should understand. The first is that ideas once learned should not be forgotten. We have thus taken care to use material from the earlier parts of the book in the parts that follow them. Two exceptions to this are Chapter 10 on thermal radiation, which may safely be taught at any point following Chapter 2, and Chapter 11 on mass transfer, which draws only on material through Chapter 8. v vi We believe that students must develop confidence in their own ability to invent means for solving problems. The examples in the text therefore do not provide complete patterns for solving the end-of-chapter prob- lems. Students who study and absorb the text should have no unusual trouble in working the problems. The problems vary in the demand that they lay on the student, and we hope that each instructor will select those that best challenge their own students. The first three chapters form a minicourse in heat transfer, which is applied in all subsequent chapters. Students who have had a previous integrated course thermofluids may be familiar with this material, but to most students it will be new. This minicourse includes the study of heat exchangers, which can be understood with only the concept of the overall heat transfer coefficient and the first law of thermodynamics. We have consistently found that students new to the subject are greatly encouraged when they encounter a solid application of the material, such as heat exchangers, early in the course. The details of heat exchanger de- sign obviously require an understanding of more advanced concepts — fins, entry lengths, and so forth. Such issues are best introduced after the fundamental purposes of heat exchangers are understood, and we develop their application to heat exchangers in later chapters. This book contains more material than most teachers can cover in three semester-hours or four quarter-hours of instruction. Typical one- semester coverage might include Chapters 1 through 8 (perhaps skipping some of the more specialized material in Chapters 5, 7, and 8), a bit of Chapter 9, and the first four sections of Chapter 10. We are grateful to the Dell Computer Corporation’s STAR Program, the Keck Foundation, and the M.D. Anderson Foundation for their partial support of this project. JHL IV, Houston, Texas JHL V, Cambridge, Massachusetts August 2002 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 46 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 78 2.5 Summary 86 Problems 86 References 96 3 Heat exchanger design 99 3.1 Function and configuration of heat exchangers 99 3.2 Evaluation of the mean temperature difference in a heat exchanger 103 3.3 Heat exchanger effectiveness 120 3.4 Heat exchanger design 126 Problems 129 References 136 vii viii Contents II Analysis of Heat Conduction 139 4 Analysis of heat conduction and some steady one-dimensional problems 141 4.1 The well-posed problem 141 4.2 The general solution 143 4.3 Dimensional analysis 150 4.4 An illustration of dimensional analysis in a complex steady conduction problem 159 4.5 Fin design 163 Problems 183 References 190 5 Transient and multidimensional heat conduction 193 5.1 Introduction 193 5.2 Lumped-capacity solutions 194 5.3 Transient conduction in a one-dimensional slab 203 5.4 Temperature-response charts 208 5.5 One-term solutions 218 5.6 Transient heat conduction to a semi-infinite region 220 5.7 Steady multidimensional heat conduction 235 5.8 Transient multidimensional heat conduction 247 Problems 252 References 265 III Convective Heat Transfer 267 6 Laminar and turbulent boundary layers 269 6.1 Some introductory ideas 269 6.2 Laminar incompressible boundary layer on a flat surface 276 6.3 The energy equation 292 6.4 The Prandtl number and the boundary layer thicknesses 296 6.5 Heat transfer coefficient for laminar, incompressible flow over a flat surface 300 6.6 The Reynolds analogy 311 6.7 Turbulent boundary layers 313 6.8 Heat transfer in turbulent boundary layers 322 Problems 330 References 338 [...]... controversy until 18 22 4 The heat flux, q, is a heat rate per unit area and can be expressed as Q /A, where A is an appropriate area Figure 1. 3 An analogy for the three modes of heat transfer 11 Introduction 12 1. 3 Figure 1. 4 Baron Jean Baptiste Joseph Fourier (17 68 18 30) (Courtesy of Appl Mech Rev., vol 26, Feb 19 73.) The heat flux is a vector quantity Equation (1. 8) tells us that if temperature decreases with... lived a remarkable double life He served as a high government official in Napoleonic France and he was also an applied mathematician of great importance He was with Napoleon in Egypt between 17 98 and 18 01, and he was subsequently prefect of the administrative area (or “Department”) of Isère in France until Napoleon’s first fall in 18 14 During the latter period he worked on the theory of heat flow and in 18 07... penetrates 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... 513 References 517 Contents x IV Thermal Radiation Heat Transfer 10 Radiative heat transfer 10 .1 The problem of radiative exchange 10 .2 Kirchhoff’s law 10 .3 Radiant heat exchange between two finite black bodies 10 .4 Heat transfer among gray bodies 10 .5 Gaseous radiation ... fluxes and Fick’s law 608 11 .4 Transport properties of mixtures 614 11 .5 The equation of species conservation 627 11 .6 Mass transfer at low rates 635 11 .7 Steady mass transfer with counterdiffusion 648 11 .8 Mass transfer coefficients at high rates of mass transfer 654 11 .9 Simultaneous heat and mass transfer ... increases where Q is the heat transfer rate and Wk is the work transfer rate They may be expressed in joules per second (J/s) or watts (W) The derivative dU/dt is the rate of change of internal thermal energy, U, with time, t This interaction is sketched schematically in Fig 1. 1a The analysis of heat transfer processes can generally be done without reference to any work processes, although heat transfer. .. several lesser ones The major ones are the condensation of refrigerant at room temperature to reject heat, the absorption of heat from within the refrigerator by evaporating the refrigerant, and the balancing heat leakage from the room to the inside • Let’s drink our iced tea quickly because heat transfer from the room to the water and from the water to the ice will first dilute, and then warm, our tea... 50◦ C If the area of the slab is 0.4 m2 and it is 0.03 m thick, compute the heat flux, q, and the heat transfer rate, Q Solution For the moment, we presume that dT /dx is a constant equal to (Tback − Tfront )/(xback − xfront ); we verify this in Chapter 2 Modes of heat transfer 1. 3 13 Figure 1. 5 Heat conduction through gas separating two solid walls Thus, eqn (1. 8) becomes q = −35 50 − 11 0 0.03 = +70,... reservoirs as shown in Fig 1. 2 As long as T1 > T2 , heat will flow spontaneously and irreversibly from 1 to 2 In accordance with our understanding of the Second Law of Thermodynamics, we expect the entropy of the universe to increase as a consequence of this process If T2 → T1 , the process will approach being quasistatic and reversible But the rate of heat transfer will also approach 2 T = absolute temperature,... thermodynamics They include Fourier’s law, Newton’s law of cooling, and the Stefan-Boltzmann law We introduce these laws later in the chapter The important thing to remember is that a description of heat transfer requires that additional principles be combined with the First Law of Thermodynamics Reversible heat transfer as the temperature gradient vanishes Consider a wall connecting two thermal reservoirs . HEAT TRANSFER TEXTBOOK THIRD EDITION John H. Lienhard IV / John H. Lienhard V A Heat Transfer Textbook Lienhard & Lienhard A Heat Transfer Textbook A Heat Transfer Textbook Third Edition by John. A HEAT TRANSFER TEXTBOOK THIRD EDITION John H. Lienhard IV / John H. Lienhard V A Heat Transfer Textbook Lienhard & Lienhard Phlogiston Press ISBN 0-9 713 83 5-0 -2 PSB 0 1- 0 4-0 249 A HEAT. 614 11 .5 The equation of species conservation 627 11 .6 Mass transfer at low rates 635 11 .7 Steady mass transfer with counterdiffusion 648 11 .8 Mass transfer coefficients at high rates of mass transfer