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John H. Lienhard IV / John H. Lienhard V

A Heat

Transfer Textbook

Lienhard & Lienhard

Phlogiston PressISBN 0-9713835-0-2 PSB 01-04-0249

John H. Lienhard IV / John H. Lienhard V

A Heat

Transfer Textbook

Lienhard & Lienhard

A Heat Transfer Textbook A Heat Transfer Textbook

A Heat Transfer Textbook Third Edition

John H. Lienhard IV and John H. Lienhard V


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 7 Massachusetts Avenue Cambridge MA 02139-4307U.S.A.

Copyright ©2001 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. Lienhard V — 3rd ed. — Cambridge, MA : Phlogiston Press, c2001

Includes bibliographic references and index. 1. Heat—Transmission 2. Mass Transfer

I. Lienhard, John H., V, 1961– I. Title TJ260.L445 2000

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 LATEX.

For updates and information, visit:

This copy is: Version 1.01 dated August 17, 2001


This book is meant for students in their introductory heat transfer course —studentswhohavelearnedcalculus(throughordinarydifferentialequations) 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 updating the 1987edition have been to bring the material up to date and make it as clear as possible. We have replaced most of the old physical property data with the latest reference data. New correlations for forced and natural convection have been included. We have significantly revised the unsteady conduction material. And we have revised the treatment of turbulent heat transfer to include the use of the law of the wall. In several places we have rearranged material to make it flow better, and we have made 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, sincethattopicisnowmostoftencoveredinspecializedcourses 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 3, and Chapter 1 on mass transfer, which draws only on material through Chapter 8.

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.

Wehaveconsistentlyfoundthatstudentsnewtothesubjectaregreatly encouraged when they encounter a solid application of the material, such as heat exchangers, early in the course. The details of heat exchanger design 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.

The present edition 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 most 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 2001


I The General Problem of Heat Exchange 1

1.1 Heat transfer3
1.2 Relation of heat transfer to thermodynamics6
1.3 Modes of heat transfer10
1.4 A look ahead34
1.5 Problems35

2 Heat conduction concepts, thermal resistance, and the overall heat transfer coefficient 49

2.1 The heat diffusion equation49
2.2 Solutions of the heat diffusion equation58
2.3 Thermal resistance and the electrical analogy62
2.4 Overall heat transfer coefficient, U74
2.5 Summary82
3.1 Function and configuration of heat exchangers93

3 Heat exchanger design 93

3.3 Heat exchanger effectiveness114
3.4 Heat exchanger design120

3.2 Evaluation of the mean temperature difference in a heat vii viii Contents

I Analysis of Heat Conduction 131

4 Analysis of heat conduction and some steady one-dimensional problems 133

4.1 The well-posed problem133
4.2 The general solution135
4.3 Dimensional analysis142
conduction problem151
4.5 Fin design155

4.4 Anillustrationofdimensionalanalysisinacomplexsteady

5.1 Introduction181
5.2 Lumped-capacity solutions182
5.3 Transient conduction in a one-dimensional slab191
5.4 Temperature-response charts196
5.5 One-term solutions206
5.6 Transient heat conduction to a semi-infinite region208
5.7Steady multidimensional heat conduction223
5.8 Transient multidimensional heat conduction235

5 Transient and multidimensional heat conduction 181

I Convective Heat Transfer 253

6.1 Some introductory ideas255
6.3 The energy equation278

6 Laminar and turbulent boundary layers 255 6.2 Laminar incompressible boundary layer on a flat surface 262 6.4 The Prandtl number and the boundary layer thicknesses . 282

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