`
`SECOND EDITION
`
`HEAT
`TRANSFER
`
`
`
`
`a4
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`MASIMO 2159
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`MASIMO 2159
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`

`HEAT
`TRANSFER
`
`
`
`Second Edition
`
`|
`
`A. KF. MILLS
`University of California at Los Angeles
`Los Angeles, California 90024-5197
`
`ws
`
`Prentice Hall, Upper Saddle River, New Jersey 07458
`
`MASIMO 2159
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`

`
`
`Library of Congress Cataloging-in-Publication Data
`
`Mills, A. F.
`Basic Heat and Mass Transfer 2/E by A.F. Mills
`“aensaetisosraphial
`ISBN 0-13-947624-5
`ncludes bibliographical references and
`CIP data available.
`
`ref
`
`tina
`
`index.
`
`.
`General Library System
`University of Wisconsin - Madison
`:
`;
`:
`.
`.
`728 State Street
`Madison, WI 53706-149
`U.S.A.
`
`*
`
`Acquisitions Editor: Bill Stenquist
`Editorial/Production Supervision: Sharyn Vitrano
`Editor-in-Chief: Marcia Horton
`Managing Editor: Eileen Clark
`Cover Director: Jayne Conte
`Director of Production and Manufacturing: David W. Riccardi *
`Manufacturing Buyer: Pat Brown
`Editorial Assistant: Meg Weist
`
`=>
`
`©1999 by Prentice-Hall, Inc.
`Simon & Schuster/A Viacom Company
`Upper Saddle River, New Jersey 07458
`
`The author and publisher of this book have used their best efforts in preparing this book. These efforts
`include the development, research, andtest of the theories and programsto determine their effectiveness. The
`author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or
`the documentation contained in this book. The author and publisher shall not be liable in any event for
`incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use
`of these programs.
`
`All rights reserved. No part of this book may be reproduced in any form or by any means, without
`permission in writing from the publisher.
`
`Printed in the United States of America
`
`100987654321
`
`ISBN 0-13-947624-5
`
`Prentice-Hall International (U.K.) Limited, London
`Prentice-Hall of Australia Pty. Limited, Sydney
`Prentice-Hall Canada Inc., Toronto
`Prentice-Hall Hispanoamericana, S.A., Mexico
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`Prentice-Hall of Japan, Inc., Tokyo
`Simon & Schuster Asia Pte. Ltd., Singapore
`Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
`
`not warm enough to completely melt this permafrost before the next winter,
`
`About the Cover; The columns supporting portions ofthe trans-Alaska oil pipeline system are
`gravity-flow ammonia heatpipes (see Chapter 7). In winter, the ground underneath the columns 1s
`warmer than the environment. Ammonia liquid evaporates inside the base of a column and condenses
`at the top, with the enthalpy of vaporization dissipated to the environment by convection and
`radiation fromthe cooling fins. The heat extracted from the ground causes a large volume of ice to
`form underneath the columns and provides a solid foundationfor the pipeline. The Arctic summeris
`
`MASIMO 2159
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`

`

`Le), wd
`TJ
`AO
`MS2...
`1999
`
`To Brigid
`For your patience and understanding.
`
`
`
`MASIMO 2159
`
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`
`

`

`
`
`
`
`PREFACE
`
`
`
`
`Heat Transfer has been written for undergraduates in mechanical, aerospace, nuclear,
`and chemical engineering programs. Apart from the usual lower-division mathemat-
`ics and science courses,
`the preparation required of the student is introductory
`courses in fluid mechanics and thermodynamics, and preferably the usual junior-
`level engineering mathematics course. The ordering of the material and the pace at
`whichit is presented have been carefully chosen so that the beginning student can
`proceed from the most elementary concepts to those that are moredifficult. As a re-
`sult, the book should prove to be quite versatile. It can be used as the text for an
`introductory course during the junior or senior year, although the coverageis suffi-
`ciently comprehensive for use as a reference work in laboratory and design courses,
`and by the practicing engineer.
`Throughout the text, the emphasis is on engineering calculations, and each topic
`is developed to a point that will provide students with the tools needed to practice
`the art of design. The worked examplesnot only illustrate the use of relevant equa-
`tions but also teach modeling as both an art and science. A supporting feature of
`Heat Transferis the fully integrated software available from the Prentice-Hall web-
`site at www.prenhall.com. The software is intended to serve primarily as a tool for
`the student, both at college and after graduation in engineering practice. The pro-
`gramsare designed to reduce the effort required to obtain reliable numericalresults
`and thereby increasethe efficiency and effectiveness of the engineer. I have found
`the impact of the software on the educational process to be encouraging.It is now
`possible to assign more meaningful and interesting problems, because the students
`need not get bogged downin lengthy calculations. Parametric studies, which are the
`essence of engineering design, are relatively easily performed. Of course, computer
`programs are not a substitute for a proper understanding. The instructor is free to
`choose the extent to which the software is used by students because of the unique
`exact correspondence between the software and the text material. My practice has
`been to initially require students to perform various hand calculations, using the
`
`MASIMO 2159
`Apple v. Masimo
`IPR2022-01299
`
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`IPR2022-01299
`
`

`

`vi
`
`PREFACE
`
`computer to give immediate feedback. For example, they do not have to wait a week
`or two until homework is returned to find that a calculated convective heat transfer
`coefficient was incorrect because a property table was misread.
`The extent to which engineering design should be introduced in a heat transfer
`course is a controversial subject. It is my experience that students can be best intro-
`duced to design methodology through an increased focus on equipment suchas heat
`exchangers: Heat Transfer presents more extensive coverage of exchanger design
`than do comparable texts. In the context of such equipment one can conveniently in-
`troduce topics such as synthesis, parametric studies, trade-offs, optimization, eco-
`nomics, and material constraints. The computer program HEX2assists the student to
`explore the consequences of changing the many parameters involved in a design
`process. If an appropriate selection of this material is taught, I am confident that Ac-
`creditation Board for Engineering and Technology guidelines for design content will
`be met. More important, I believe that engineering undergraduates are well served by
`being exposed to this material, even if it means studying somewhatless heat trans-
`fer science.
`Morethan 300 new exercises have been addedfor this edition. They fall into two
`categories: (1) relatively straightforward exercises designed to help students under-
`stand fundamental concepts, and (2) exercises that introduce new heat transfer tech-
`nology and that have a practical flavor. The latter play a very important role in mo-
`tivating students; considerable care has been taken to ensure that they are realistic in
`terms of parameter values and focus onsignificant aspects of real engineering prob-
`lems. The practical exercises are first steps in the engineering design process and
`many have substantial design content. Since environmental considerations have re-
`quired the phasing out of CFC refrigerants, R-12 and R-113 property data, worked
`examples and exercises, have been replaced with corresponding material for R-22
`and R-134a.
`Heat Transfer contains the following chapters and appendixes:
`
`1 2 3 4 5
`
`. Elementary Heat Transfer
`
`Steady One-Dimensional Heat Conduction
`
`Multidimensional and Unsteady Conduction
`
`. Convection Fundamentals and Correlations
`
`. Convection Analysis
`
`6. Thermal Radiation
`
`7. Condensation, Evaporation, and Boiling
`
`8. Heat Exchangers
`
`A. Property Data
`
`B. Units, Conversion Factors, and Mathematics
`
`C. Charts
`
`MASIMO 2159
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`

`

`PREFACE
`
`vii
`
`Inafirst course, the focus is always on the key topics of conduction, convec-
`tion, radiation, and heat exchangers. Particular care has been taken to order the
`material on these topics from simpler to more difficult concepts. In Chapter 2
`one-dimensional conduction andfins are treated before deriving the general partial
`differential heat conduction equation in Chapter 3. In Chapter 4 the studentis taught
`how to use convection correlations before encountering the partial differential equa-
`tions governing momentum and energy conservation in Chapter 5. In Chapter6 ra-
`diation properties are introduced onatotal energy basis and the shape factoris in-
`troduced as a geometrical concept to allow engineering problem solving before
`having to deal with the directional and spectral aspects of radiation. Also, wherever
`possible, advanced topics are located at the ends of chapters, and thuscan beeasily
`omitted in a first course.
`Chapter 1 is a brief but self-contained introduction to heat transfer. Students are
`given an overview of the subject and some material needed in subsequent chapters.
`Interesting and relevant engineering problems can then be introducedat the earliest
`opportunity,
`thereby motivating student interest. All
`the exercises can be solved
`without accessing the property data in Appendix A.
`Chapters 2 and 3 present a relatively conventional treatment of heat conduction,
`though the outdated and approximate Heissler and Gréber charts are replaced by
`exact charts and the computer program COND2. Thetreatmentof finite-difference
`numerical methods for conduction has been kept concise and is based on finite-
`volume energy balances. Students are encouraged to solve the difference equations
`by writing their own computer programs, or by using standard mathematics software
`such as Mathcad or MATLAB.
`In keeping with.the overall philosophy of the book, the objective of Chapter 4 is
`to develop the students’ ability to calculate convective heat transfer coefficients. The
`physics of convectionis explainedin a brief introduction, and the heattransfer coef-
`ficient is defined. Dimensional analysis using the Buckingham pi theorem is used to
`introduce the required dimensional groups andto allow a discussion of the impor-
`tance of laboratory experiments. A large numberofcorrelation formulas follow; in-
`structors can discuss selected geometrical configurations as class time allows, and
`students can use the associated computer program CONVtoreliably calculate heat
`transfer coefficients and skin friction coefficients or pressure drop for a wide range
`of configurations. Being able to do parametric studies with a wide variety of corre-
`lations enhancesthe students’ understanding more than can be accomplished by hand
`calculations. Design alternatives can also be explored using CONV.
`Analysis of convection is deferred to Chapter 5: simple laminar flows are consid-
`ered, and high-speed flowsare treated first in Section 5.2, since an understanding of
`the recovery temperature concept enhances the students’ problem-solving capabili-
`ties. Each of the topics in Sections 5.3 through 5.8 are essentially self-contained, and
`the instructor can select as few or as manyas required.
`Chapter 6 focuses on thermal radiation. Radiation properties are initially defined
`on a total energy basis, and the shape factor is introduced as a simple geometrical
`concept. This approach allows students to immediately begin solving engineering ra-
`diation exchange problems. Only subsequently need they tackle the moredifficult di-
`
`
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`

`
`
`Vili
`
`PREFACE
`
`rectional and spectral aspects of radiation. For gas radiation, the ubiquitous Hottel
`charts have been replaced by the more acciirate methods developed by Edwards; the
`accompanying computer program RAD3 makestheir use particularly simple.
`The treatment of condensation and evaporation heat transfer in Chapter 7 has
`novel features, while the treatment of pool boiling is quite conventional. Forced con-
`vection boiling and condensation is taken far enough tofacilitate calculation of both
`pressure drop and heat transfer. Heatpipes are dealt with in somedetail, enabling stu-
`dents to calculate the wicking limit and to analyze the performance of simple gas-
`controlled heatpipes.
`Chapter 8 expands the presentation of the thermal analysis of heat exchangers
`beyond the customary and includes regenerators and the effect of axial conduction
`on thermal performance. The treatment of heat exchanger design includes the calcu-
`lation of exchanger pressure drop, thermal-hydraulic design, heat transfer surface
`selection for compact heat exchangers, and economic analysis leading to the calcu-
`lation of the benefit-cost differential associated with heat recovery operations. The
`computer program HEX2 serves to introduce students to computer-aided design of
`heat exchangers.
`The author and publisher appreciate the efforts of all those who provided input
`that helped develop and improve the text. We remain dedicated to furtherrefining the
`text in future editions, and encourage you to contact us with any suggestions or com-
`ments you might have.
`
`A. F. Mills
`amills @ucla.edu
`
`Bill Stenquist
`Executive Editor
`william_stenquist@ prenhall.com
`
`MASIMO 2159
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`

`
`
`
`
`ACKNOWLEDGMENTS
`
`
`
`
`Reviewers commissioned for the previous edition, published by Richard D. Irwin,
`Inc., provided helpful feedback. The author wouldlike to thank the following for
`their contributionsto the first edition.
`
`David Antoniuk, TRW Systems, Inc.
`Theodore Bergman, University of Texas at Austin
`Robert K Boehm, University of Nevada—Las Vegas
`John M. Boyd, Worcester Polytechnic Institute
`Harry Buchberg, University of California—Los Angeles
`Vernon E. Denny, Science Applications International Corporation
`Creighton A. Depew, University of Washington
`A. M. Dhanak, Michigan State University
`ThomasE.Diller, Virginia Polytechnic Institute & State University
`D. K. Edwards, University of California—Irvine
`L. W. Florschuetz, Arizona State University
`J. C. Han, Texas A&M University
`B. K. Hodge, Mississippi State University
`Sukhyun Kim, Kukmin University, Korea
`V. V. Klimenko, Nuclear Safety Institute, USSR
`Allan Kirkpatrick, Colorado State University
`Adrienne Lavine, University of California—Los Angeles
`Gordan D. Mallinson, University of Auckland, New Zealand
`Atila Mertol, LSI Logic Corporation
`
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`

`
`
`ACKNOWLEDGMENTS
`
`Ronald S. Mullisen, California Polytechnic State University—San Luis Obispo
`M. Ohadi, University of Maryland
`Calvin C. Oliver, University of Florida—Gainesville
`Patrick H. Oosthuizen, Queen’s University, Kingston, Ontario
`Peter Othmer, California State University — Fullerton
`Gerald Pomraning, University of California—Los Angeles
`John P. Renie, Indiana University/Purdue University at Fort Wayne
`Frank W. Schmidt, Pennsylvania State University
`Terry Simon, University of Minnesota
`E. M. Sparrow, University of Minnesota
`J. Edward Sunderland, University of Massachusetts
`John A. Tichy, Rensselaer Polytechnic Institute
`Brian Vick, Virginia Polytechnic & State University
`Andrew Wortman, California State Air Resources Board
`Walter W. Yuen, University of California—Santa Barbara
`
`A
`
`Someof the material in Heat Transfer, in the form of examples and exercises, has
`been adapted from an earlier text by my former colleagues at UCLA, D. K. Edwards
`and V. E. Denny (Transfer Processes \/e, Holt, Rinehart & Winston, 1973; 2/e Hemi-
`sphere-McGraw-Hill, 1979). I have also drawn on material in radiation heat trans-
`fer from a more recent text by D. K. Edwards (Radiation Heat Transfer Notes,
`Hemisphere, 1981). I gratefully acknowledge the contributions of these gentle-
`men, both to this book and to my professional career. The computer software
`was expertly written by Baek Youn. I would also like to thank former students
`S. W. Hiebert, H. Choi, R. Tsai, B. Cowan, E. Myhre, B. H. Chang, D. C. Weatherly,
`A. Gopinath,J. I. Rodriguez, B. P. Dooher, and M. A. Friedman.
`In preparing the second edition, I have had useful input from a number of peo-
`ple, including Professor F. Forster, University of Washington; Professor N. Sham-
`sundar, University of Houston; Professor S. Kim, Kukmin University; and Profes-
`sor A. Lavine, UCLA. Students who have helped include P. Hwang, M.Tari, B. Tan,
`J. Sigler, M. Fabri, and A. Na-Nakornpanom.
`Myspecial thanks to the secretarial staff at UCLA and the University of Auck-
`land: Phyllis Gilbert, Joy Wallace, and Julie Austin provided enthusiastic and expert
`typing of the manuscript. Mrs. Gilbert also provided expert typing of the solutions
`manual.
`
`MASIMO 2159
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`

`
`
`NOTES TO
`THE INSTRUCTOR
`AND STUDENT
`
`
`
`
`
`
`
`These notes have been prepared to assist the instructor and student and should be
`read before the text is used. Topics covered include conventions for artwork and
`mathematics, the format for example problems, organization of the exercises, com-
`ments on the thermophysical property data in Appendix A, and a guide for use of
`the accompanying computer software.
`
`
`
`ARTWORK
`
`= C
`
`onventions used in the figures are as follows.
`
`—_—P
`
`Conduction or convection heat flow
`
`——)P
`
`Radiation heat flow
`
`——_—
`
`Fluid flow
`
`MATHEMATICAL SYMBOLS
`
`Symbols that may needclarification are as follows.
`
`=
`=
`[x
`
`Nearly equal
`Of the same order of magnitude
`All quantities in the term to theleft of the bar are evaluated at x
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`

`
`
`xii
`
`NOTES TO THE INSTRUCTOR AND STUDENT
`
`EXAMPLES
`asss...
`
`Use of standard format for presenting the solutions of engineering problems is a
`good practice. The format used for the examples in Heat Transfer, which is but one
`possible approach,is as follows.
`
`Problem statement
`
`Solution
`
`Given:
`
`Required:
`
`Assumptions:1.
`2. etc.
`
`Sketch (when appropriate)
`
`Analysis (diagrams when appropriate)
`
`Properties evaluation
`Calculations
`
`Results (tables or graphs when appropriate)
`
`Comments
`
`1.
`
`2.
`
`ete.
`
`It is always assumedthat the problem statement precedes the solution (as in the
`text) or that it is readily available (as in the Solutions Manual). Thus, the Given
`and Required statements are concise and focus on the essential features of the
`problem. Under Assumptions, the main assumptions required to solve the problem
`are listed; when appropriate, they are discussed further in the body of the solution.
`A sketch of the physical system is included when the geometry requires clarifica-
`tion; also, expected temperature profiles are given when appropriate. (Schematics
`that simply repeat the information in the problem statements are used sparingly. I
`know that many instructors always require a schematic. My viewis that students need
`to develop an appreciation of whenafigure or graph is necessary, because artworkis
`usually an expensive componentof engineering reports. For example, I seelittle use
`for a schematic that shows a 10 m length of straight 2 cm—O.D. tube.) The analysis
`may consist simply of listing some formulas from the text, or it may require setting
`up a differential equation and its solution. Strictly speaking, a property should not
`be evaluated until its need is identified by the analysis. However, in routine calcula-
`tions, such as evaluation of convective heat transfer coefficients, it is often convenient
`
`
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`

`NOTES TO THE INSTRUCTOR AND STUDENT
`
`xiii
`
`to list all the property values taken from an Appendix A table in one place. The
`calculations then follow with results listed, tabulated, or graphed as appropriate.
`Under Comments, the significance of the results can be discussed, the validity of
`assumptions further evaluated, or the broader implications of the problem noted.
`In presenting calculations for the examples in Heat Transfer, I have rounded off
`results at each stage of the calculation. If additional figures are retained for the
`complete calculations, discrepancies in the last figure will be observed. Since many
`of the example calculations are quite lengthy, I believe my policy will facilitate
`checking a particular calculation step of concern. As is common practice, I have
`generally given results to more significant figures than is justified, so that these
`results can be conveniently used in further calculations. It is safe to say that no
`engineering heat transfer calculation will be accurate to within 1%, and that most
`experienced engineers will be pleased with results accurate to within 10% or 20%.
`Thus, preoccupation with a third or fourth significant figure is misplaced (unless
`required to prevent error magnification in operations such as subtraction).
`
`EXERCISES
`MM
`
`The diskette logo next to an exercise statement indicates that it should be solved using
`the Heat Transfer software, and that the sample solution provided to the instructor
`has been prepared accordingly. There are many additional exercises that can be
`solved using the software but that do not have the logo designation. These exercises
`are intended to give the student practice in hand calculations, and thus the sample
`solutions were also prepared manually.
`The exercises have been ordered to correspond with the order in which the material
`is presented in the text, rather than in some increasing degree of difficulty. Since
`the range of difficulty of the exercises is considerable,
`the instructor is urged to
`give students guidance in selecting exercises for self-study. Answers to all exercises
`are listed in the Solutions Manual provided to instructors. Odd- and even-numbered
`exercises are listed separately; the instructor may chooseto give eitherlist to students
`to assist self-study.
`
`PROPERTY DATA’
`
`A considerable quantity of property data has been assembled in Appendix A. Key
`sources are given as references or are listed in the bibliography. Since Heat Trans-
`fer is a textbook, my primary objective in preparing Appendix A wasto provide
`the student with a wide range of data in an easily used form. Wheneverpossible,
`I have used the most accurate data that I could obtain, but accuracy was not al-
`ways the primary concern. For example,
`the need to have consistent data over a
`wide range of temperature often dictated the choice of source. All the tables are in
`SI units, with temperature in kelvins. The computer program UNITS can be used
`for conversions to other systems of units. Appendix A should serve most needs of the
`
`MASIMO 2159
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`

`
`
`xiv
`
`NOTES TO THE INSTRUCTOR AND STUDENT
`
`student, as well as of the practicing engineer, for doing routine calculations. If a
`heat transfer research project requires accurate and reliable thermophysical property
`data, the prudent researcher should carefully check relevant primary data sources.
`
`SOFTWARE
`ee
`The Heat Transfer software has a menu that describes the content of each program.
`The programsare also described at appropriate locations in the text. The input format
`and program use are demonstrated in example problemsin the text. Use of the text
`index is recommended for locating the program déscriptions and examples. There
`is a one-to-one correspondence between the text and the software. In principle, all
`numbers generated by the software can be calculated manually from formulas, graphs,
`and data given in the text. Small discrepancies may be seen when interpolation in
`graphsor property tables is required, since someof the data are stored in the software
`as polynomial curvefits.
`The software facilitates self-study by the student. Practice hand calculations can
`be immediately checked using the software. When programs such as CONV, PHASE,
`and BOILare used, properties evaluation and intermediate calculation steps can also
`be checked whenthe final results do not agree.
`Since there is a large thermophysical property database stored in the software
`package, the programscan also be conveniently used to evaluate these properties for
`other purposes. For example, in CONV both the wall and fluid temperatures can be
`set equal to the desired temperature to obtain property values required for convection
`calculations. We can even go one step further when evaluating a convective heat
`transfer coefficient from a new correlation not contained in CONV:if a corresponding
`item is chosen, the values of relevant dimensionless groups can also be obtained from
`CONV,further simplifying the calculations.
`
`MASIMO 2159
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`IPR2022-01299
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`

`

`
`
`
`
`CONTENTS
`
`
`
`
`
`CHAPTER
`=z
`
`1
`
`ELEMENTARY HEAT TRANSFER 1
`
`3
`
`8
`
`13
`
`24
`
`2
`Introduction
`1.1
`1.2 Heat Transfer and Its Relation to Thermodynamics
`1.3. Modesof Heat Transfer
`7
`1.3.1 Heat Conduction
`1.3.2 Thermal Radiation
`17
`1.3.3 Heat Convection
`1.4 Combined Modes of Heat Transfer
`1.4.1 Thermal Circpits
`24
`27
`1.4.2 Surface Energy Balances
`29
`1.5 Transient Thermal Response
`1.5,1 The Lumped Thermal Capacity Model
`1.5.2 Combined Convection and Radiation
`1.6 Heat Exchangers
`37 '
`1.6.1 Single- and Two-Stream Exchangers
`1.6.2 Analysis of aCondenser
`40
`1.6.3 Other Sirigle-Stream Exchangers
`1.7 Dimensions and Units
`45
`1.8 Closure
`47
`Exercises
`48
`
`29
`34
`,
`38
`
`45
`
`STEADY ONE-DIMENSIONAL HEAT CONDUCTION
`
`67
`
`68
`Introduction
`2.1
`2.2 Fourier’s Law of Heat Conduction
`2.2.1 Thermal Conductivity
`469
`2.2.2 Contact Resistance
`
`71
`
`68
`
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`
`
`
`
`xvi
`
`CONTENTS
`
`77
`
`82
`
`2.3 Conduction across Cylindrical and Spherical Shells
`2.3.1 Conduction across a Cylindrical Shell
`73
`2.3.2 Critical Thickness of Insulation on a Cylinder
`2.3.3 Conduction across a Spherical Shell
`80
`2.3.4 Conduction with Internal Heat Generation
`2.4 Fins
`86
`86
`2.4.1 The Pin Fin
`2.4.2 Fin Resistance and Surface Efficiency
`2.4.3 Other Fin Type Analyses
`95
`100
`2.4.4 Fins of Varying Cross-Sectional Area
`2.4.5 The Similarity Principle and Dimensional Analysis
`2.5 Closure
`111
`References
`112
`Exercises
`112
`
`94
`
`73
`
`108
`
`MULTIDIMENSIONAL AND UNSTEADY CONDUCTION 143
`
`145
`
`154
`161
`
`168
`
`144
`Introduction
`3.1
`144
`3.2 The Heat Conduction Equation
`145
`3.2.1 Fourier’s Law as a Vector Equation
`3.2.2 Derivation of the Heat Conduction Equation
`3.2.3. Boundary and Initial Conditions
`150
`3.24 Solution Methods
`153
`154
`3.3 Multidimensional Steady Conduction
`3.3.1 Steady Conduction in a Rectangular Plate
`3.3.2 Steady Conduction in a Rectangular Block
`3.3.3 Conduction Shape Factors
`164
`3.4 Unsteady Conduction
`167
`3.4.1 The Slab with Negligible Surface Resistance
`3.4.2 The Semi-Infinite Solid
`175
`187
`3.4.3 Convective Cooling of Slabs, Cylinders, and Spheres
`3.4.4 Product Solutions for Multidimensional Unsteady Conduction
`3.5 Moving-Boundary Problems
`203
`3.5.1 Solidification from a Melt
`203
`3.5.2 Steady-State Melting Ablation
`3.6 Numerical Solution Methods
`212
`3.6.1 A Finite-Difference Method for Two-Dimensional Steady
`Conduction
`213
`3.6.2 Finite-Difference Methods for One-Dimensional Unsteady
`Conduction
`221
`230
`3.6.3 Resistance-Capacitance (RC) Formulation
`3.6.4 A Finite-Difference Method for Moving-Boundary Problems
`3.7 Closure
`242
`References
`243
`Exercises
`244
`
`207
`
`198
`
`237
`
`MASIMO 2159
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2159
`Apple v. Masimo
`IPR2022-01299
`
`

`

`CONTENTS
`
`xvii
`
`CONVECTION FUNDAMENTALS AND CORRELATIONS=275
`
`4.1
`4.2
`
`4.3
`
`4.4
`
`4.5
`
`4.6
`
`4.7
`
`4.8
`4.9
`
`301
`
`276
`Introduction
`276
`Fundamentals
`4.2.1 The Convective Heat Transfer Coefficient
`4.2.2 Dimensional Analysis
`283
`295
`4.2.3 Correlation of Experimental Data
`4.2.4 Evaluation of Fluid Properties
`299
`Forced Convection
`301
`4.3.1 Forced Flow in Tubes and Ducts
`4.3.2 External Forced Flows
`312
`Natural Convection
`325
`325
`4.4.1 External Natural Flows
`333
`4.4.2 Internal Natural Flows
`4.4.3 Mixed Forced and Natural Flows
`Tube Banks and Packed Beds
`347
`4.5.1 Flow through Tube Banks
`348
`4.5.2 Flow through Packed Beds
`355
`Rotating Surfaces
`362
`4.6.1 Rotating Disks, Spheres, and Cylinders
`Rough Surfaces
`365
`366
`4.7.1 Effect of Surface Roughness
`The Computer Program CONV 375
`Closure
`375
`References
`384
`Exercises
`387
`
`340
`
`277
`
`362
`
`CONVECTION ANALYSIS
`
`413
`
`5.1
`5.2
`
`5.3
`
`5.4
`
`5.5
`
`420
`
`414
`Introduction
`415
`High-Speed Flows
`415
`5.2.1 A Couette Flow Model
`5.2.2 The Recovery Factor Concept
`Laminar Flow ina Tube
`422
`5.3.1 Momentum Transfer in Hydrodynamically Fully Developed
`Flow 423
`5.3.2 Fully Developed Heat Transfer for a Uniform Wall Heat Flux
`Laminar Boundary Layers
`432
`5.4.1 The Governing Equations for Forced Flow along a Flat Plate
`5.4.2 The Plug Flow Model
`435
`5.4.3 Integral Solution Method
`437
`5.4.4 Self-Similar Solutions
`446
`5.4.5 Natural Convection on an Isothermal Vertical Wall
`Turbulent Flows
`461
`5.5.1 The Prandtl Mixing Length and the Eddy Diffusivity Model
`
`455
`
`426
`
`433
`
`462
`
`MASIMO 2159
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2159
`Apple v. Masimo
`IPR2022-01299
`
`

`

`
`
`5.6
`
`5.7
`
`5.8
`
`5.9
`
`6.1
`6.2
`
`6.3
`
`6.4
`
`6.5
`
`6.6
`
`6.7
`
`xviii
`
`CONTENTS
`
`486
`
`465
`
`486
`
`493
`
`503
`
`5.5.2 Forced Flow along a Flat Plate
`5.5.3 Flow ina Tube
`478
`5.5.4 More Advanced Turbulence Models
`Similarity and Modeling
`486
`5.6.1 Dimensionless Equations and Boundary Conditions
`5.6.2 Modeling
`492
`The General Conservation Equations
`5.7.1 Conservation of Mass
`493
`5.7.2 Conservation of Momentum 495
`5.7.3 Conservation of Energy
`499
`5.7.4 Use of the Conservation Equations
`Scale Analysis
`504
`504
`5.8.1 Forced-Convection Laminar Boundary Layers
`5.8.2 Natural-Convection Laminar Boundary Layer on a Vertical Wall
`Closure
`515
`References
`516
`Exercises
`517
`
`510
`
`THERMAL RADIATION=531
`
`532
`Introduction
`532
`The Physics of Radiation
`6.2.1 The Electromagnetic Spectrum 533
`6.2.2 The Black Surface
`534
`6.2.3 Real Surfaces
`536
`538
`Radiation Exchange between Surfaces
`6.3.1 Radiation Exchange between Black Surfaces
`6.3.2 Shape Factors and Shape Factor Algebra
`540
`547
`6.3.3 Electrical Network Analogy for Black Surfaces
`6.3.4 Radiation Exchange between Two Diffuse Gray Surfaces
`6.3.5 Radiation Exchange between Many Diffuse Gray Surfaces
`6.3.6 Radiation Transfer through Passages
`565
`Solar Radiation
`568
`568
`6.4.1 Solar Irradiation
`570
`6.4.2 Atmospheric Radiation
`572
`6.4.3 Solar Absorptance and Transmittance
`Directional Characteristics of Surface Radiation
`6.5.1 Radiation Intensity and Lambert’s Law 578
`6.5.2 Shape Factor Determination
`581
`584
`6.5.3 Directional Properties of Real Surfaces
`Spectral Characteristics of Surface Radiation
`590
`6.6.1 Planck’s Law and Fractional Functions
`590
`6.6.2 Spectral Properties
`592
`Radiation Transfer through Gases
`6.7.1 The Equation of Transfer
`600
`6.7.2 Gas Radiation Properties
`601
`
`538
`
`577
`
`599
`
`550
`557
`
`MASIMO 2159
`
`Apple v. Masimo
`IPR2022-01299
`
`MASIMO 2159
`Apple v. Masimo
`IPR2022-01299
`
`

`

`
`
`CONTENTS
`
`xix
`
`609
`6.7.3 Effective Beam Lengths for an Isothermal Gas
`6.7.4 Radiation Exchange between an Isothermal Gas and a Black
`Enclosure
`614
`6.7.5 Radiation Exchange between an Isothermal Gray Gas and a Gray
`Enclosure
`615
`6.7.6 Radiation Exchange between an Isothermal Nongray Gas and a
`Single-Gray-Surface Enclosure
`619
`Closure
`622
`References
`623
`Exercises
`624
`
`6.8
`
`CONDENSATION, EVAPORATION, AND BOILING 651
`
`71
`72
`
`7.3
`
`7.4
`
`7.5
`
`7.6
`
`7.7
`
`7.8
`
`685
`
`668
`674
`
`681
`
`702
`
`716
`
`652
`Introduction
`652
`Film Condensation
`654
`7.2.1 Laminar Film Condensation on a Vertical Wall
`7.2.2 Wavy Laminar and Turbulent Film Condensation on a Vertical
`Wall
`662
`7.2.3 Laminar Film Condensation on Horizontal Tubes
`7.2.4 Effects of Vapor Velocity and Vapor Superheat
`Film Evaporation
`681
`7.3.1 Falling Film Evaporation on a Vertical Wall
`Pool Boiling
`685
`7.4.1 Regimes of Pool Boiling
`7.4.2 Boiling Inception
`688
`7.4.3 Nucleate Boiling
`691
`7.4.4 The Peak Heat Flux
`693
`7.4.5 Film Boiling
`696
`Forced-Convection Boiling and Condensation
`7.5.1 Two-Phase Flow Patterns
`702
`7.5.2 Pressure Drop
`708
`712
`7.5.3 Internal Forced-Convection Boiling
`7.5.4 Internal Forced-Convection Condensation
`Phase Change at Low Pressures
`719
`719
`7.6.1 Kinetic Theory of Phase Change
`7.6.2 Interfacial Heat Transfer Resistance
`723
`725
`7.6.3 Nusselt Analysis Including Interfacial Resistance
`7.6.4 Engineering Significance of the Interfacial Resistance
`Heatpipes
`730
`733
`7.7.1 Capillary Pumping
`7.7.2 Sonic, Entrainment, and Boiling Limitations
`7.7.3, Gas-Loaded Heatpi