[PDF] Fundamentals of Heat and Mass Transfer, 6e

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SIXTH EDITIONFundamentalsof Heat and MassTransferFRANK P. INCROPERACollege of EngineeringUniversity of Notre DameDAVID P. DEWITTSchool of Mechanical EngineeringPurdue UniversityTHEODORE L. BERGMANDepartment of Mechanical EngineeringUniversity of ConnecticutADRIENNE S. LAVINEMechanical and Aerospace Engineering DepartmentUniversity of California, Los AngelesJOHNWILEY& SONSffirs.qxd 3/6/06 11:11 AM Page iwww.konkur.in

ASSOCIATE PUBLISHERDaniel SayreACQUISITIONS EDITORJoseph HaytonSENIOR PRODUCTION EDITOR Valerie A. VargasMARKETING MANAGERPhyllis CerysSENIOR DESIGNERMadelyn LesureCOVER and TEXT DESIGNER Karin Gerdes KincheloeCOVER ILLUSTRATIONSCarol GrobeSENIOR ILLUSTRATION EDITOR Sandra RigbyEDITORIAL ASSISTANTMary Morgan-McGeeMEDIA EDITORStefanie LiebmanPRODUCTION SERVICESIngrao AssociatesThis book was set in 10/12 Times Roman by GGS Information Services and printed and bound by R.R. Donnelley. The cover was printed by Phoenix Color.This book is printed on acid-free paper.
Copyright © 2007 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions.To order books or for customer service, please call 1-800-CALL WILEY (225-5945).Library of Congress Cataloging-in-Publication DataIncropera, Frank P.Fundamentals of heat and mass transfer. / Frank P. Incropera . . . [et al.]. - 6th ed. / FrankP. Incropera . . . [et al].p. cm.Includes bibliographical references and index.ISBN-13: *978-0-471-45728-2 (cloth)ISBN-10: 0-471-45728-0 (cloth)1. Heat - Transmission. 2. Mass transfer. I. Title.QC320.145 2006621.402
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In MemoryDavid P. DeWittMarch 2, 1934ÐMay 17, 2005The year 2005 was marked by the loss of Dr. David P. DeWitt, a dear friend and col-league who contributed signiÞcantly to heat transfer technology and pedagogythroughout a distinguished 45-year career. Dave was educated as a mechanical engi-neer, receiving a BS degree from Duke University, an MS from MIT, and the PhDdegree from Purdue University. His graduate studies at Purdue nucleated a stronginterest in the Þelds of thermal physics and radiometry, in which he worked untilillness made it impossible to continue. Dave was instrumental in developing radio-metric measurement standards at PurdueÕs Thermophysical Properties ResearchCenter, eventually becoming its deputy director and president of Technometrics Inc.,an optical and thermal instrument design company. In 1973 he joined PurdueÕsSchool of Mechanical Engineering at the rank of professor, where he taught and con-ducted research until his retirement in 2000. From 2000 to 2004, he worked in theOptical Technology Division of the National Institute of Technology and Standards.Dave was an excellent and demanding teacher, a good researcher and a superbengineer. In our nearly thirty-year collaboration, he provided complementary skillsthat contributed signiÞcantly to the success of the books we have co-authored.However, it is much more on a personal than a professional level that I have myfondest memories of this very special colleague.As co-authors, Dave and I spent thousands of hours working together on allfacets of our books, typically in blocks of three to Þve hours. This time often in-volved spontaneous diversions from the task at hand, typically marked by humor orreßections on our personal lives.Dave and I each have three daughters of comparable ages, and we would oftenshare stories on the joys and challenges of nurturing them. ItÕs hard to think aboutDave without reßecting on the love and pride he had for his daughters (Karen, Amy,and Debbie). In 1990 Dave lost his Þrst wife Jody due to cancer, and I witnessedÞrst hand his personal character and strength as he supported her in battling this terrible disease. I also experienced the joy he felt in the relationship he developedwith his second wife Phyllis, whom he married in 1997.I will always remember Dave as a sensitive and kind person of good humor andgenerosity. Dear friend, we miss you greatly, but we are comforted by the knowl-edge that you are now free of pain and in a better place.Frank P. IncroperaNotre Dame, Indianaffirs.qxd 3/6/06 11:11 AM Page iiiwww.konkur.in

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Forward to PrefaceNot too long after Þnishing the previous editions of Fundamentals of Heat andMass TransferandIntroduction to Heat Transfer, Dave DeWitt and I felt the needto plan for that time when we would no longer be able to add appropriate value tofuture editions. There were two matters of special concern. First, we were advanc-ing in years, and the potential for disruption due to declining health or our own mor-tality could not be ignored. But, perhaps more pertinent to maintaining freshnessand vitality to the text books, we also recognized that we were becoming ever moredistant from leading-edge activities in the Þeld.In 2002, we concluded that we should proactively establish a succession planinvolving the participation of additional co-authors. In establishing desired attrib-utes of potential candidates, we placed high priority on the following: a record ofsuccess in teaching heat and mass transfer, active involvement with research in theÞeld, a history of service to the heat transfer community, and the ability to sustainan effective collaborative relationship. A large weighting factor was attached to thislast attribute, since it was believed to have contributed signiÞcantly to whateversuccess Dave DeWitt and I have enjoyed with the previous editions.After reßecting long and hard on the many excellent options, Dave and I in-vited Ted Bergman and Adrienne Lavine, professors of Mechanical Engineering atthe University of Connecticut and the University of California, Los Angeles, re-spectively, to join us as co-authors. We were grateful for their acceptance. Ted andAdrienne are listed as third and fourth authors for this edition, will move to Þrst andsecond authors on the next edition, and will thereafter appear as sole authors.Ted and Adrienne have worked extremely hard on the current edition, and youwill see numerous enhancements from their efforts, particularly in modern applica-tions related to subjects such as nano and biotechnology. It is therefore most appro-priate for Ted and Adrienne to share their thoughts in the following preface.Frank P. IncroperaNotre Dame, Indianaffirs.qxd 3/6/06 11:11 AM Page vwww.konkur.in

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PrefaceSince the last edition, fundamental changes have occurred, both nationally andglobally, in how engineering is practiced, with questions raised about the future ofthe profession. How will the practice of engineering evolve over the next decade?Will tomorrowÕs engineer be more valued if he is a specialist, or more handsomelyrewarded if she has knowledge of greater breadth but less depth? How will engi-neering educators respond to changing market forces? Will the traditional bound-aries that separate the engineering disciplines in the typical college or universityremain in place?We believe that, because technology provides the foundation for improving thestandard of living of all humankind, the future of engineering is bright. But, in lightof the tension between external demand for generalizationand intellectual satisfac-tion of specialization, how will the discipline of heat transfer remain relevant? Whatwill the value of this discipline be in the future? To what new problems will theknowledge of heat transfer be applied?In preparing this edition, we attempted to identify emerging issues in technol-ogy and science in which heat transfer is centralto the realization of new productsin areas such as information technology, biotechnology and pharmacology, alterna-tive energy, and nanotechnology. These new applications, along with traditional ap-plications in energy generation, energy utilization, and manufacturing, suggest thatthe discipline of heat transfer is healthy. Furthermore, when applied to problemsthat transcend traditional boundaries, heat transfer will be a vital and enabling disci-plineof the future.We have strived to remain true to the fundamental pedagogical approach ofprevious editions by retaining a rigorous and systematic methodology for problemsolving, by including examples and problems that reveal the richness and beauty ofthe discipline, and by providing students with opportunities to meet the learning objectives.fpref.qxd 3/6/06 11:11 AM Page viiwww.konkur.in

Approach and OrganizationFrom our perspective, the four learning objectives desired in any Þrst course in heattransfer, detailed in the previous edition, remain as follows:1. The student should internalize the meaning of the terminology and physical prin-ciples associated with the subject.2. The student should be able to delineate pertinent transport phenomena for anyprocess or system involving heat transfer.3. The student should be able to use requisite inputs for computing heat transferrates and/or material temperatures.4. The student should be able to develop representative models of real processesand systems and draw conclusions concerning process/system design or perfor-mance from attendant analysis.As in the previous edition, learning objectives for each chapter are clariÞed toenhance the means by which they are achieved, as well as means by which achieve-ment may be assessed. The summary of each chapter highlights key terminologyand concepts developed in the chapter, and poses questions to test and enhance stu-dent comprehension.For problems involving complex models and/or exploratory, what-if, and para-meter sensitivityconsiderations, it is recommended that they be addressed by using acomputational equation-solving package. To this end, the Interactive Heat Transfer(IHT) package developed by Intellipro, Inc. (New Brunswick, New Jersey) andavailable in the previous edition has been updated. The seasoned user will Þnd thetechnical content of IHT to be largely unchanged, but the computational capabilityand features have been improved signiÞcantly. SpeciÞcally, IHT is now capable ofsolving 300 or more simultaneous equations. The user interface has been updated toinclude a full-function workspace editor with complete control over formatting oftext, copy and paste functionality, an equation editor, a new graphing subsystem, andenhanced syntax checking. In addition, the software now has the capability to exportIHT-speciÞc functions (e.g. properties and correlations) as Microsoft Excel add-ins.A second software package, Finite Element Heat Transfer(FEHT), developed by F-Chart Software of Middleton, Wisconsin, provides enhanced capabilities for solv-ing two-dimensional conduction heat transfer problems.As in the previous edition, many homework problems that involve a computer-based solution appear as extensions to problems that can be solved by hand calcula-tion. This approach is time tested and allows students to validate their computerpredictions by checking the predictions with their hand solutions. They may thenproceed with parametric studies that explore related design and operating conditions.Such problems are identiÞed by enclosing the exploratory part in a red rectangle, as,for example (b) , (c), or (d). This feature also allows instructors who wish to limittheir assignments of computer-based problems to beneÞt from the richness of theseproblems. Solutions to problems for which the number itself is highlighted, as, forexample, 1.26 , should be entirely computer based.We are aware that some instructors who use the text have not utilized IHT intheir courses. We encourage our colleagues to dedicate, at a minimum, one-half hourof lecture or recitation time to demonstrate IHT as a tool for solving simultaneousequations, and for evaluating the thermophysical properties of various materials. WeviiiPrefacefpref.qxd 3/6/06 11:11 AM Page viiiwww.konkur.in

have found that, once students have seen its power and ease of use, they will eagerlyutilize IHTÕs additional features on their own. This will enable them to solve prob-lems faster, with fewer numerical errors, thereby freeing them to concentrate on themore substantive aspects of the problems.WhatÕs New in the 6th EditionProblem SetsThis edition contains a significant number of new, revised, andrenumbered end-of-chapter problems. Many of the new problems require relativelystraightforward analyses, and many involve applications in nontraditional areas ofscience and technology. The solutions manual has undergone extensive revision.Streamlined PresentationThe text has been streamlined by moving a smallamount of material to stand-alone supplemental sections that can be accessed elec-tronically from the companion website. The supplemental sections are called outwith marginal notes throughout the text. If instructors prefer to use material fromthe supplemental sections, it is readily available from the Wiley website (seebelow). Homework problem statements associated with the supplemental sectionsare also available electronically.Chapter-by-Chapter Content ChangesTo help motivate the reader, Chap-ter 1 includes an expanded discussion of the relevance of heat transfer. The rich-ness and pertinence of the topic are conveyed by discussion of energy conversiondevicesincluding fuel cells, applications in information technologyand biologicalas well as biomedical engineering. The presentation of the conservation of energyrequirementhas been revised.New material on micro- and nanoscale conductionhas been included in Chap-ter 2. Because in-depthtreatment of these effects would overwhelm most students,they are introduced and illustrated by describing the motion of energy carriersin-cluding phononsand electrons. Approximate expressions for the effective thermalconductivity of thin Þlmsare presented and are explained in terms of energy carrierbehavior at physical boundaries. The thermal conductivity of nanostructuredversusconventionalmaterials is presented and used to demonstrate practical applicationsof recent nanotechnology research. Microscale-related limitations of the heat diffu-sion equationare explained. The bioheat equationis introduced in Chapter 3, andits similarity to the heat equation for extended surfaces is pointed out in order to fa-cilitate its use and solution.The Chapter 4 discussion of conduction shape factors, applied to multidimen-sional steady-state conduction, is embellished with recent results involving the di-mensionless conduction heat rate. Although we have moved the graphical method tothe supplemental material, discussion of two-dimensional isothermand heat ßow linedistributionshas been enhanced in order to assist students to conceptualize the con-duction process. Use of the dimensionless conduction heat rate is extended to tran-sient situations in Chapter 5. A new, uniÞed approachto transient heat transfer ispresented; easy-to-use approximate solutionsassociated with a range of geometriesand time scales have been added. Recently, we have noted that few students use thegraphical representations of the one-dimensional, transient conduction solutions(Heisler charts); most prefer to solve the approximate or exact analytical expressions.Prefaceixfpref.qxd 3/6/06 11:11 AM Page ixwww.konkur.in

Hence, we have relegated the graphical representations to the supplemental material.Because of the ease and frequency with which computational methods are used bystudents today, analytical solutions involving multidimensional effects have alsobeen moved to the supplemental material. We have added a brief section on periodicheating and have demonstrated its relevance by presenting a modern method used tomeasure the thermophysical properties of nanostructured materials.Introduction to the fundamentals of convection, included in Chapter 6, has beensimpliÞed and streamlined. The description of turbulenceand transition to turbu-lencehas been updated. Proper accounting of the temperature-dependence of ther-mophysical propertiesis emphasized. Derivation of the convection transferequations is now relegated to the supplemental material.The treatment of external ßowin Chapter 7 is largely unchanged. Chapter 8 cor-relations for the entrance regionsof internal ßowhave been updated, while the dis-cussion of heat transfer enhancement has been expanded by adding correlations forflow in curved tubes. Microsale-related limitations of the convective correlationsforinternal flow are presented. Chapter 9 correlations for the effective thermal conduc-tivity associated with free convectionin enclosures have been revised in order tomore directly relate these correlations to the conduction results of Chapter 3.Presentation of boiling heat transferin Chapter 10 has been modified to im-prove student understanding of the boiling curve by relating aspects of boiling phe-nomena to forced convection and free convection concepts from previous chapters.Values of the constants used in the boiling correlations have been modified to re-flect the current literature. Reference to refrigerants that are no longer used has beeneliminated, and replacement refrigerant properties have been added. Heat transfercorrelations for internal two-phase ßoware presented. Microscale-related limita-tions of the correlationsfor internal two-phase flow are discussed. A much-simpli-fied method for solution of condensation problems is presented.The use of the log mean temperature difference (LMTD) method is retained for de-veloping correlations for concentric tube heat exchangers in Chapter 11, but, because ofthe flexibility of the effectiveness-NTUmethod, the LMTD-based analysis of heat ex-changers of other types has been relegated to the supplemental material. Again, the sup-plemental sections can be accessed at the companion website. Treatment of radiationheat transfer in Chapter 12 and 13 has undergone modest revision and streamlining.The coverage of mass transfer, Chapter 14, has been revised extensively. Thechapter has been reorganized so that instructors can either cover the entire contentor seamlesslyrestrict attention to mass transfer in stationary media. The latter approach is recommended if time is limited, and/or if interest is limited to masstransfer in liquids or solids. The new example problems of Chapter 14 reflect con-temporary applications. Discussion of the various boundary conditions used in masstransfer has been clarified and simplified.AcknowledgmentsWe are immensely indebted to Frank Incropera and Dave DeWitt who entrusted usto join them as co-authors. We are especially thankful to Frank for his patience,thoughtful advice, detailed critique of our work, and kind encouragement as thisedition was being developed.xPrefacefpref.qxd 3/6/06 11:11 AM Page xwww.konkur.in

PrefacexiAppreciation is extended to our colleagues at the University of Connecticut andUCLA who provided valuable input. Eric W. Lemmon of the National Institute ofStandards and Technology is acknowledged for his generosity in providing proper-ties of new refrigerants.We are forever grateful to our wonderful spouses and children, Tricia, Nate,Tico, Greg, Elias, and Jacob for their love, support, and endless patience. Finally,we both extend our appreciation to Tricia Bergman who, despite all her responsibil-ities, somehow found the time to expertly and patiently process the solutions for thenew end-of-chapter problems.Theodore L. Bergman (tberg@engr.uconn.edu)Storrs, ConnecticutAdrienne S. Lavine (lavine@seas.ucla.edu)Los Angeles, CaliforniaSupplemental and Website MaterialThe companion website for the text is www.wiley.com/college/incropera. By click-ing on the Ôstudent companion siteÕ link, studentsmay access the answers to thehomework problems and the Supplemental Sections of the text.Material available for instructors onlyincludes the instructor Solutions Man-ual, Powerpoint slides that can be used by instructors for lectures, and electronicversions of Þgures from the texts for those wishing to prepare their own materialsfor electronic classroom presentation. The instructor Solutions Manual is for use byinstructors who are requiring use of the text for their course. Copying or distribut-ing all or part of the Solutions Manual in any form without the PublisherÕs permis-sion is a violation of copyright law.Interactive Heat Transfer v3.0/FEHT with UserÕs Guideis available eitherwith the text or as a separate purchase. This software tool provides modeling andcomputational features useful in solving many problems in the text, and enableswhat-ifand exploratory analysisof many types of heat transfer problems. TheCD/booklet package is available as a stand-alone purchase from the Wiley website,www.wiley.com, or through your local bookstore. Faculty interested in using thistool in their course may order the software shrinkwrapped to the text at a signiÞcantdiscount. Contact your local Wiley representative for details.fpref.qxd 3/6/06 11:11 AM Page xiwww.konkur.in

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ContentsSymbolsxxiiiCHAPTER 1Introduction11.1What and How? 21.2Physical Origins and Rate Equations 31.2.1 Conduction31.2.2 Convection61.2.3 Radiation91.2.4 Relationship to Thermodynamics121.3The Conservation of Energy Requirement 131.3.1 Conservation of Energy for a Control Volume131.3.2 The Surface Energy Balance251.3.3 Application of the Conservation Laws: Methodology281.4Analysis of Heat Transfer Problems: Methodology29ftoc.qxd 3/6/06 11:11 AM Page xiiiwww.konkur.in

1.5Relevance of Heat Transfer 321.6Units and Dimensions 351.7Summary 38References 41Problems 41CHAPTER 2Introduction to Conduction572.1The Conduction Rate Equation 582.2The Thermal Properties of Matter 602.2.1 Thermal Conductivity602.2.2 Other Relevant Properties672.3The Heat Diffusion Equation 702.4Boundary and Initial Conditions 772.5Summary 81References 82Problems 82CHAPTER 3One-Dimensional, Steady-State Conduction953.1The Plane Wall 963.1.1 Temperature Distribution963.1.2 Thermal Resistance983.1.3 The Composite Wall993.1.4 Contact Resistance1013.2An Alternative Conduction Analysis1123.3Radial Systems1163.3.1 The Cylinder1163.3.2 The Sphere1223.4Summary of One-Dimensional Conduction Results1253.5Conduction with Thermal Energy Generation1263.5.1 The Plane Wall1273.5.2 Radial Systems1323.5.3 Application of Resistance Concepts1373.6Heat Transfer from Extended Surfaces1373.6.1 A General Conduction Analysis1393.6.2 Fins of Uniform Cross-Sectional Area1413.6.3 Fin Performance1473.6.4 Fins of Nonuniform Cross-Sectional Area1503.6.5 Overall Surface EfÞciency1533.7The Bioheat Equation1623.8Summary166References168Problems169xivContentsftoc.qxd 3/6/06 11:11 AM Page xivwww.konkur.in

CHAPTER 4Two-Dimensional, Steady-State Conduction2014.1Alternative Approaches 2024.2The Method of Separation of Variables 2034.3The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 2074.4Finite-Difference Equations 2124.4.1 The Nodal Network2134.4.2 Finite-Difference Form of the Heat Equation2144.4.3 The Energy Balance Method2154.5Solving the Finite-Difference Equations2224.5.1 The Matrix Inversion Method2224.5.2 GaussÐSeidel Iteration2234.5.3 Some Precautions2294.6Summary234References235Problems2354S.1The Graphical MethodW-14S.1.1 Methodology of Constructing a Flux PlotW-14S.1.2 Determination of the Heat Transfer RateW-24S.1.3 The Conduction Shape FactorW-3ReferencesW-6ProblemsW-6CHAPTER 5Transient Conduction2555.1The Lumped Capacitance Method 2565.2Validity of the Lumped Capacitance Method 2595.3General Lumped Capacitance Analysis 2635.4Spatial Effects 2705.5The Plane Wall with Convection 2725.5.1 Exact Solution2725.5.2 Approximate Solution2735.5.3 Total Energy Transfer2745.5.4 Additional Considerations2755.6Radial Systems with Convection2765.6.1 Exact Solutions2765.6.2 Approximate Solutions2775.6.3 Total Energy Transfer2775.6.4 Additional Considerations2785.7The Semi-InÞnite Solid2835.8Objects with Constant Surface Temperatures or Surface Heat Fluxes2905.8.1 Constant Temperature Boundary Conditions2905.8.2 Constant Heat Flux Boundary Conditions2925.8.3 Approximate Solutions2935.9Periodic Heating299Contentsxvftoc.qxd 3/6/06 11:11 AM Page xvwww.konkur.in

5.10Finite-Difference Methods 3025.10.1 Discretization of the Heat Equation: The Explicit Method3025.10.2 Discretization of the Heat Equation: The Implicit Method3105.11Summary317References319Problems3195S.1Graphical Representation of One-Dimensional, Transient Conduction in the Plane Wall, Long Cylinder, and SphereW-85S.2Analytical Solution of Multidimensional EffectsW-13ReferencesW-18ProblemsW-18CHAPTER 6Introduction to Convection3476.1The Convection Boundary Layers 3486.1.1 The Velocity Boundary Layer3486.1.2 The Thermal Boundary Layer3496.1.3 The Concentration Boundary Layer3506.1.4 SigniÞcance of the Boundary Layers3526.2Local and Average Convection CoefÞcients 3526.2.1 Heat Transfer3526.2.2 Mass Transfer3536.2.3 The Problem of Convection3556.3Laminar and Turbulent Flow3596.3.1 Laminar and Turbulent Velocity Boundary Layers3596.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers3616.4The Boundary Layer Equations3646.4.1 Boundary Layer Equations for Laminar Flow3656.5Boundary Layer Similarity: The Normalized Boundary Layer Equations 3676.5.1 Boundary Layer Similarity Parameters3686.5.2 Functional Form of the Solutions3686.6Physical SigniÞcance of the Dimensionless Parameters3746.7Boundary Layer Analogies3776.7.1 The Heat and Mass Transfer Analogy3776.7.2 Evaporative Cooling3816.7.3 The Reynolds Analogy3846.8The Convection CoefÞcients3856.9Summary385References386Problems3876S.1Derivation of the Convection Transfer EquationsW-216S.1.1 Conservation of MassW-216S.1.2 NewtonÕs Second Law of MotionW-226S.1.3 Conservation of EnergyW-266S.1.4 Conservation of SpeciesW-28ReferencesW-33ProblemsW-33xviContentsftoc.qxd 3/6/06 11:11 AM Page xviwww.konkur.in

CHAPTER 7External Flow4017.1The Empirical Method 4037.2The Flat Plate in Parallel Flow 4057.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution4057.2.2 Turbulent Flow over an Isothermal Plate4107.2.3 Mixed Boundary Layer Conditions4117.2.4 Unheated Starting Length4127.2.5 Flat Plates with Constant Heat Flux Conditions4137.2.6 Limitations on Use of Convection CoefÞcients4147.3Methodology for a Convection Calculation4147.4The Cylinder in Cross Flow4237.4.1 Flow Considerations4237.4.2 Convection Heat and Mass Transfer4257.5The Sphere4337.6Flow Across Banks of Tubes4367.7Impinging Jets4477.7.1 Hydrodynamic and Geometric Considerations4477.7.2 Convection Heat and Mass Transfer4497.8Packed Beds4527.9Summary454References456Problems457CHAPTER 8Internal Flow4858.1Hydrodynamic Considerations 4868.1.1 Flow Conditions4868.1.2 The Mean Velocity4878.1.3 Velocity ProÞle in the Fully Developed Region4888.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow4908.2Thermal Considerations 4918.2.1 The Mean Temperature4928.2.2 NewtonÕs Law of Cooling4938.2.3 Fully Developed Conditions4938.3The Energy Balance4978.3.1 General Considerations4978.3.2 Constant Surface Heat Flux4988.3.3 Constant Surface Temperature5018.4Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations5058.4.1 The Fully Developed Region5058.4.2 The Entry Region5128.5Convection Correlations: Turbulent Flow in Circular Tubes5148.6Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 5188.7Heat Transfer Enhancement521Contentsxviiftoc.qxd 3/6/06 11:11 AM Page xviiwww.konkur.in

8.8Microscale Internal Flow 5248.8.1 Flow Conditions in Microscale Internal Flow5248.8.2 Thermal Considerations in Microscale Internal Flow5258.9Convection Mass Transfer5288.10Summary531References533Problems534CHAPTER 9Free Convection5599.1Physical Considerations 5609.2The Governing Equations 5639.3Similarity Considerations 5649.4Laminar Free Convection on a Vertical Surface 5669.5The Effects of Turbulence 5689.6Empirical Correlations: External Free Convection Flows 5719.6.1 The Vertical Plate5719.6.2 Inclined and Horizontal Plates5749.6.3 The Long Horizontal Cylinder5799.6.4 Spheres5839.7Free Convection within Parallel Plate Channels 5849.7.1 Vertical Channels5859.7.2 Inclined Channels5879.8Empirical Correlations: Enclosures 5879.8.1 Rectangular Cavities5879.8.2 Concentric Cylinders5909.8.3 Concentric Spheres5919.9Combined Free and Forced Convection5939.10Convection Mass Transfer5949.11Summary595References596Problems597CHAPTER 10Boiling and Condensation61910.1Dimensionless Parameters in Boiling and Condensation 62010.2Boiling Modes 62110.3Pool Boiling 62210.3.1 The Boiling Curve62210.3.2 Modes of Pool Boiling62410.4Pool Boiling Correlations 62710.4.1 Nucleate Pool Boiling62710.4.2 Critical Heat Flux for Nucleate Pool Boiling62910.4.3 Minimum Heat Flux62910.4.4 Film Pool Boiling63010.4.5 Parametric Effects on Pool Boiling631xviiiContentsftoc.qxd 3/6/06 11:11 AM Page xviiiwww.konkur.in

10.5Forced Convection Boiling 63610.5.1 External Forced Convection Boiling63710.5.2 Two-Phase Flow63710.5.3 Two-Phase Flow in Microchannels64010.6Condensation: Physical Mechanisms 64110.7Laminar Film Condensation on a Vertical Plate 64310.8Turbulent Film Condensation 64610.9Film Condensation on Radial Systems 65110.10Film Condensation in Horizontal Tubes 65410.11Dropwise Condensation 65510.12Summary 655References 656Problems 657CHAPTER 11Heat Exchangers66911.1Heat Exchanger Types 67011.2The Overall Heat Transfer CoefÞcient 67311.3Heat Exchanger Analysis: Use of the Log Mean Temperature Difference 67511.3.1 The Parallel-Flow Heat Exchanger67611.3.2 The Counterßow Heat Exchanger67911.3.3 Special Operating Conditions67911.4Heat Exchanger Analysis: The EffectivenessÐNTU Method 68611.4.1 DeÞnitions68611.4.2 EffectivenessÐNTU Relations68811.5Heat Exchanger Design and Performance Calculations: Using the EffectivenessÐNTU Method69411.6Compact Heat Exchangers70011.7Summary705References706Problems70711S.1Log Mean Temperature Difference Method for Multipass and Cross-Flow Heat ExchangersW-37ReferencesW-41ProblemsW-41CHAPTER 12Radiation: Processes and Properties72312.1Fundamental Concepts 72412.2Radiation Intensity 72712.2.1 Mathematical DeÞnitions72712.2.2 Radiation Intensity and Its Relation to Emission72812.2.3 Relation to Irradiation73312.2.4 Relation to Radiosity73512.3Blackbody Radiation 73612.3.1 The Planck Distribution73712.3.2 WienÕs Displacement Law737Contentsxixftoc.qxd 3/6/06 11:11 AM Page xixwww.konkur.in

12.3.3 The Stefan-Boltzmann Law73812.3.4 Band Emission73912.4Emission from Real Surfaces 74412.5Absorption, Reflection, and Transmission by Real Surfaces 75212.5.1 Absorptivity75412.5.2 Reflectivity75512.5.3 Transmissivity75612.5.4 Special Considerations75712.6Kirchhoff's Law76212.7The Gray Surface76412.8Environmental Radiation77012.9Summary776References780Problems780CHAPTER 13Radiation Exchange Between Surfaces81113.1The View Factor 81213.1.1 The View Factor Integral81213.1.2 View Factor Relations81313.2Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure 82213.2.1 Net Radiation Exchange at a Surface82313.2.2 Radiation Exchange Between Surfaces82413.2.3 Blackbody Radiation Exchange83013.2.4 The Two-Surface Enclosure83113.2.5 Radiation Shields83213.2.6 The Reradiating Surface83513.3Multimode Heat Transfer83913.4Radiation Exchange with Participating Media84213.4.1 Volumetric Absorption84313.4.2 Gaseous Emission and Absorption84313.5Summary847References849Problems849CHAPTER 14Diffusion Mass Transfer87914.1Physical Origins and Rate Equations 88014.1.1 Physical Origins88014.1.2 Mixture Composition88114.1.3 Fick's Law of Diffusion88214.1.4 Mass Diffusivity88314.2Mass Transfer in Nonstationary Media88514.2.1 Absolute and Diffusive Species Fluxes88514.2.2 Evaporation in a Column88814.3The Stationary Medium Approximation893xxContentsftoc.qxd 3/6/06 11:11 AM Page xxwww.konkur.in

14.4Conservation of Species for a Stationary Medium 89414.4.1 Conservation of Species for a Control Volume89414.4.2 The Mass Diffusion Equation89414.4.3 Stationary Media with SpeciÞed Surface Concentrations89714.5Boundary Conditions and Discontinuous Concentrations at Interfaces 90014.5.1 Evaporation and Sublimation90114.5.2 Solubility of Gases in Liquids and Solids90214.5.3 Catalytic Surface Reactions90514.6Mass Diffusion with Homogeneous Chemical Reactions 90814.7Transient Diffusion 91114.8Summary 916References 917Problems 917APPENDIX AThermophysical Properties of Matter927APPENDIX BMathematical Relations and Functions959APPENDIX CThermal Conditions Associated with Uniform EnergyGeneration in One-Dimensional, Steady-State Systems965APPENDIX DThe Convection Transfer Equations973D.1Conservation of Mass 974D.2NewtonÕs Second Law of Motion 974D.3Conservation of Energy 975D.4Conservation of Species 976APPENDIX EBoundary Layer Equations for Turbulent Flow977APPENDIX FAn Integral Laminar Boundary Layer Solutionfor Parallel Flow over a Flat Plate981Index985Contentsxxiftoc.qxd 3/6/06 11:11 AM Page xxiwww.konkur.in

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SymbolsAAarea, m2Abarea of prime (unÞnned) surface, m2Accross-sectional area, m2Afffree-ßow area in compact heat exchangercore (minimum cross-sectional areaavailable for ßow through the core), m2Afrheat exchanger frontal area, m2ApÞn proÞle area, m2Arnozzle area ratioaacceleration, m/s2BiBiot numberBoBond numberCmolar concentration, kmol/m3; heatcapacity rate, W/KCDdrag coefÞcientCffriction coefÞcientCtthermal capacitance, J/KCoConÞnement numbercspeciÞc heat, J/kg
K; speed of light, m/scpspeciÞc heat at constant pressure, J/kg
KcvspeciÞc heat at constant volume, J/kg
KDdiameter, mDABbinary mass diffusivity, m2/sDbbubble diameter, mDhhydraulic diameter, mEthermal plus mechanical energy, J;electric potential, V; emissive power,W/m2Etottotal energy, JEcEckert numbergrate of energy generation, Winrate of energy transfer into a controlvolume, Woutrate of energy transfer out of controlvolume, WEúEúEústrate of increase of energy stored within acontrol volume, Wethermal internal energy per unit mass,J/kg; surface roughness, mFforce, N; heat exchanger correctionfactor; fraction of blackbody radiationin a wavelength band; view factorFoFourier numberFrFroude numberffriction factor; similarity variableGirradiation, W/m2; mass velocity, kg/s
m2GrGrashof numberGzGraetz numberggravitational acceleration, m/s2gcgravitational constant, 1 kg
m/N
s2or32.17 ft
lbm/lbf
s2Hnozzle height, m; HenryÕs constant, barshconvection heat transfer coefÞcient,W/m2
K; PlanckÕs constanthfglatent heat of vaporization, J/kghsflatent heat of fusion, J/kghmconvection mass transfer coefÞcient, m/shradradiation heat transfer coefÞcient, W/m2
KIelectric current, A; radiation intensity,W/m2
srielectric current density, A/m2; enthalpyper unit mass, J/kgJradiosity, W/m2JaJakob numberdiffusive molar ßux of species irelativeto the mixture molar average velocity,kmol/s
m2J*iEúftoc.qxd 3/6/06 11:11 AM Page xxiiiwww.konkur.in

jidiffusive mass ßux of species irelativeto the mixture mass average velocity,kg/s
m2jHColburn jfactor for heat transferjmColburn jfactor for mass transferkthermal conductivity, W/m
K;BoltzmannÕs constantk0zero-order, homogeneous reaction rateconstant, kmol/s
m3k1Þrst-order, homogeneous reaction rateconstant, s
1Þrst-order, homogeneous reaction rateconstant, m/sLcharacteristic length, mLeLewis numberMmass, kg; number of heat transfer lanesin a ßux plot; reciprocal of the Fourier number for Þnite-differencesolutionsirate of transfer of mass for species, i,kg/si,grate of increase of mass of species idueto chemical reactions, kg/sinrate at which mass enters a controlvolume, kg/soutrate at which mass leaves a controlvolume, kg/sstrate of increase of mass stored within acontrol volume, kg/s
imolecular weight of species i,kg/kmolmmass, kgmass ßow rate, kg/smimass fraction of species i, ?i/?Nnumber of temperature increments in aßux plot; total number of tubes in atube bank; number of surfaces in anenclosureNL,NTnumber of tubes in longitudinal andtransverse directionsNuNusselt numberNTUnumber of transfer unitsNimolar transfer rate of species irelative toÞxed coordinates, kmol/smolar ßux of species irelative to Þxedcoordinates, kmol/s
m2imolar rate of increase of speciesi perunit volume due to chemical reactions,kmol/s
m3surface reaction rate of species i,kmol/s
m2mass ßux of species irelative to Þxedcoordinates, kg/s
m2imass rate of increase of species iper unitvolume due to chemical reactions,kg/s
m3Pperimeter, m; general ßuid propertydesignationPL,PTdimensionless longitudinal andtransverse pitch of a tube banknún
iNú
iNúN
imúMúMúMúMúMúk
1PePeclet number (RePr)PrPrandtl numberppressure, N/m2Qenergy transfer, Jqheat transfer rate, Wrate of energy generation per unitvolume, W/m3qheat transfer rate per unit length, W/mq
heat ßux, W/m2q*dimensionless conduction heat rateRcylinder radius, muniversal gas constantRaRayleigh numberReReynolds numberReelectric resistance, Rffouling factor, m2
K/WRmmass transfer resistance, s/m3Rm,nresidual for the m, nnodal pointRtthermal resistance, K/WRt,cthermal contact resistance, K/WRt,fÞn thermal resistance, K/WRt,othermal resistance of Þn array, K/Wrocylinder or sphere radius, mr, ?, zcylindrical coordinatesr, , ?spherical coordinatesSsolubility, kmol/m3
atm; shape factorfor two-dimensional conduction, m;nozzle pitch, m; plate spacing, mScsolar constantSD, SL, STdiagonal, longitudinal, and transversepitch of a tube bank, mScSchmidt numberShSherwood numberStStanton numberTtemperature, Kttime, sUoverall heat transfer coefÞcient, W/m2
K; internal energy, Ju, v, wmass average ßuid velocitycomponents, m/su*, v*, w*molar average velocity components,m/sVvolume, m3; ßuid velocity, m/svspeciÞc volume, m3/kgWwidth of a slot nozzle, mrate at which work is performed, WWeWeber numberXvapor qualityX, Y, Zcomponents of the body force per unitvolume, N/m3x, y, zrectangular coordinates, mxccritical location for transition toturbulence, mxfd,cconcentration entry length, mxfd,hhydrodynamic entry length, mxfd,tthermal entry length, mximole fraction of species i, Ci/CWúqúxxivSymbolsftoc.qxd 3/6/06 11:11 AM Page xxivwww.konkur.in

Greek Lettersthermal diffusivity, m2/s; heatexchanger surface area per unitvolume, m2/m3; absorptivityvolumetric thermal expansioncoefficient, K
1mass flow rate per unit width in filmcondensation, kg/s
mhydrodynamic boundary layer thickness, mcconcentration boundary layer thickness, mpthermal penetration depth, mtthermal boundary layer thickness, memissivity; porosity of a packed bed;heat exchanger effectivenessffin effectivenesssimilarity variableffin efficiencyooverall efficiency of fin arrayzenith angle, rad; temperature difference,K absorption coefficient, m
1

wavelength, m

mfpmean free path length, nmviscosity, kg/s
mkinematic viscosity, m2/s; frequency ofradiation, s
1
mass density, kg/m3; reflectivity

Stefan-Boltzmann constant; electricalconductivity, 1/
m; normal viscousstress, N/m2; surface tension, N/m;ratio of heat exchanger minimumcross-sectional area to frontal areaviscous dissipation function, s
2azimuthal angle, radstream function, m2/sshear stress, N/m2; transmissivitysolid angle, sr; perfusion rate, s
1SubscriptsA, B species in a binary mixtureabs absorbedam arithmetic meanbbase of an extended surface; blackbodyccross-sectional; concentration; cold fluidcr critical insulation thicknesscond conductionconv convectionCF counterflowDdiameter; dragdif diffusioneexcess; emission; electronevap evaporationffluid properties; fin conditions; saturatedliquid conditionsfc forced convectionfd fully developed conditionsgsaturated vapor conditionsHheat transfer conditions hhydrodynamic; hot fluid; helicaligeneral species designation; innersurface of an annulus; initialcondition; tube inlet condition;incident radiationLbased on characteristic lengthlsaturated liquid conditionslat latent energylm log mean conditionMmomentum transfer conditionmmean value over a tube cross sectionmax maximum fluid velocitymfp mean free pathocenter or midplane condition; tube outletcondition; outerph phononRreradiating surfacer,ref reflected radiationrad radiationSsolar conditionsssurface conditions; solid propertiessat saturated conditionssens sensible energysky sky conditionsss steady statesur surroundingstthermaltr transmittedvsaturated vapor conditionsxlocal conditions on a surface

spectral
free stream conditionsSuperscriptsfluctuating quantity* molar average; dimensionless quantityOverbarsurface average conditions; time mean Symbolsxxvftoc.qxd 3/6/06 11:11 AM Page xxvwww.konkur.in

ftoc.qxd 3/6/06 11:11 AM Page xxviwww.konkur.in CHAPTERIntroduction 1c01.qxd 3/6/06 10:21 AM Page 1www.konkur.in

2Chapter 1
IntroductionFrom the study of thermodynamics, you have learned that energy can be trans-ferred by interactions of a system with its surroundings. These interactions arecalled work and heat. However, thermodynamics deals with the end states of theprocess during which an interaction occurs and provides no information concerningthe nature of the interaction or the time rate at which it occurs. The objective of thistext is to extend thermodynamic analysis through study of the modesof heat trans-fer and through development of relations to calculate heat transfer rates.In this chapter we lay the foundation for much of the material treated in thetext. We do so by raising several questions. What is heat transfer? How is heattransferred? Why is it important?One objective is to develop an appreciation forthe fundamental concepts and principles that underlie heat transfer processes. Asecond objective is to illustrate the manner in which a knowledge of heat transfermay be used with the Þrst law of thermodynamics (conservation of energy) to solveproblems relevant to technology and society.1.1What and How?A simple, yet general, deÞnition provides sufÞcient response to the question: Whatis heat transfer?Whenever there exists a temperature difference in a medium or between media, heattransfer must occur.As shown in Figure 1.1, we refer to different types of heat transfer processesas modes.When a temperature gradient exists in a stationary medium, which maybe a solid or a ßuid, we use the term conductionto refer to the heat transfer thatwill occur across the medium. In contrast, the term convectionrefers to heat trans-fer that will occur between a surface and a moving ßuid when they are at differentHeat transfer (or heat) is thermal energy in transit due to a spatial temperature difference.T2T1T1T2>q"q"Conduction through a solidor a stationary fluidConvection from a surfaceto a moving fluidNet radiation heat exchangebetween two surfacesSurface, T1Surface, T2Ts > T
Tsq"1q"2Moving fluid, T
FIGURE1.1Conduction, convection, and radiation heat transfer modes.c01.qxd 3/6/06 10:21 AM Page 2www.konkur.in

temperatures. The third mode of heat transfer is termed thermal radiation.All sur-faces of finite temperature emit energy in the form of electromagnetic waves. Hence,in the absence of an intervening medium, there is net heat transfer by radiationbetween two surfaces at different temperatures.1.2Physical Origins and Rate EquationsAs engineers it is important that we understand the physical mechanismswhich un-derlie the heat transfer modes and that we be able to use the rate equations thatquantify the amount of energy being transferred per unit time.1.2.1 ConductionAt mention of the word conduction, we should immediately conjure up concepts ofatomicand molecular activity, for it is processes at these levels that sustain thismode of heat transfer. Conduction may be viewed as the transfer of energy from themore energetic to the less energetic particles of a substance due to interactions be-tween the particles.The physical mechanism of conduction is most easily explained by consideringa gas and using ideas familiar from your thermodynamics background. Consider agas in which there exists a temperature gradient and assume that there is no bulk,ormacroscopic, motion.The gas may occupy the space between two surfaces that aremaintained at different temperatures, as shown in Figure 1.2. We associate the tem-perature at any point with the energy of gas molecules in proximity to the point. Thisenergy is related to the random translational motion, as well as to the internal rota-tional and vibrational motions, of the molecules.1.2?Physical Origins and Rate Equations3xoxTT2T1 > T2q"xq"xFIGURE1.2Association of conduction heat transfer with diffusion of energy due tomolecular activity.c01.qxd 3/6/06 10:21 AM Page 3www.konkur.in

Higher temperatures are associated with higher molecular energies, and whenneighboring molecules collide, as they are constantly doing, a transfer of energyfrom the more energetic to the less energetic molecules must occur. In the presenceof a temperature gradient, energy transfer by conduction must then occur in thedirection of decreasing temperature. This would even be true in the absence ofcollisions, as is evident from Figure 1.2. The hypothetical plane at is constantlybeing crossed by molecules from above and below due to their randommotion.However, molecules from above are associated with a larger temperature thanthose from below, in which case there must be a nettransfer of energy in the posi-tive xdirection. Collisions between molecules enhance this energy transfer. Wemay speak of the net transfer of energy by random molecular motion as a diffusionof energy.The situation is much the same in liquids, although the molecules are moreclosely spaced and the molecular interactions are stronger and more frequent. Simi-larly, in a solid, conduction may be attributed to atomic activity in the form of lat-tice vibrations. The modern view is to ascribe the energy transfer to lattice wavesinduced by atomic motion. In an electrical nonconductor, the energy transfer is ex-clusively via these lattice waves; in a conductor it is also due to the translationalmotion of the free electrons. We treat the important properties associated with con-duction phenomena in Chapter 2 and in Appendix A.Examples of conduction heat transfer are legion. The exposed end of a metalspoon suddenly immersed in a cup of hot coffee will eventually be warmed due tothe conduction of energy through the spoon. On a winter day there is significantenergy loss from a heated room to the outside air. This loss is principally due toconduction heat transfer through the wall that separates the room air from the out-side air.It is possible to quantify heat transfer processes in terms of appropriate rateequations.These equations may be used to compute the amount of energy beingtransferred per unit time. For heat conduction, the rate equation is known asFourierÕs law.For the one-dimensional plane wall shown in Figure 1.3, having atemperature distribution T(x), the rate equation is expressed as(1.1)The heat ßux(W/m2) is the heat transfer rate in the xdirection perunit area per-pendicularto the direction of transfer, and it is proportional to the temperature gra-dient, dT/dx, in this direction. The parameter kis a transportproperty known as thethermal conductivity(W/m
K) and is a characteristic of the wall material. Theminus sign is a consequence of the fact that heat is transferred in the direction of de-creasing temperature. Under the steady-state conditionsshown in Figure 1.3, wherethe temperature distribution is linear, the temperature gradient may be expressed asand the heat flux is thenq
x
k T2  T1LdTdx
T2  T1Lq
xq
x
k dTdxxo4Chapter 1
Introductionq"xLT1T(x)TxT2FIGURE1.3One-dimensional heat transfer by conduction (diffusion of energy).c01.qxd 3/6/06 10:21 AM Page 4www.konkur.in

or(1.2)Note that this equation provides a heat ßux, that is, the rate of heat transfer per unitarea.The heat rateby conduction, qx(W), through a plane wall of area Ais then theproduct of the flux and the area, .EXAMPLE1.1The wall of an industrial furnace is constructed from 0.15-m-thick fireclay brickhaving a thermal conductivity of 1.7 W/m
K. Measurements made during steady-state operation reveal temperatures of 1400 and 1150 K at the inner and outer sur-faces, respectively. What is the rate of heat loss through a wall that is 0.5 m by1.2 m on a side?SOLUTIONKnown:Steady-state conditions with prescribed wall thickness, area, thermalconductivity, and surface temperatures.Find:Wall heat loss.Schematic:Assumptions:1.Steady-state conditions.2.One-dimensional conduction through the wall.3.Constant thermal conductivity.Analysis:Since heat transfer through the wall is by conduction, the heat fluxmay be determined from Fourier's law. Using Equation 1.2, we haveq
x
k TL
1.7 W/m
K  250 K0.15 m
2833 W/m2T1 = 1400 KT2 = 1150 Kk = 1.7 W/m¥KxL = 0.15 mqx''xLW = 1.2 mH = 0.5 mWall area, Aqxqx
q
x
Aq
x
k T1  T2L
k TL1.2
Physical Origins and Rate Equations5c01.qxd 3/6/06 10:21 AM Page 5www.konkur.in

The heat ßux represents the rate of heat transfer through a section of unit area, and itis uniform (invariant) across the surface of the wall. The heat loss through the wallof area is thenComments:Note the direction of heat flow and the distinction between heat fluxand heat rate.1.2.2ConvectionThe convection heat transfer modeis comprised of two mechanisms.In addition toenergy transfer due to random molecular motion(diffusion), energy is also trans-ferred by the bulk, or macroscopic, motionof the fluid. This fluid motion is associ-ated with the fact that, at any instant, large numbers of molecules are moving col-lectively or as aggregates. Such motion, in the presence of a temperature gradient,contributes to heat transfer. Because the molecules in the aggregate retain their ran-dom motion, the total heat transfer is then due to a superposition of energy transportby the random motion of the molecules and by the bulk motion of the fluid. It iscustomary to use the term convectionwhen referring to this cumulative transportand the term advectionwhen referring to transport due to bulk fluid motion.We are especially interested in convection heat transfer, which occurs betweena fluid in motion and a bounding surface when the two are at different temperatures.Consider fluid flow over the heated surface of Figure 1.4. A consequence of thefluid-surface interaction is the development of a region in the fluid through whichthe velocity varies from zero at the surface to a finite value uassociated with theflow. This region of the fluid is known as the hydrodynamic, or velocity, boundarylayer.Moreover, if the surface and flow temperatures differ, there will be a regionof the fluid through which the temperature varies from at to in the outerflow. This region, called the thermal boundary layer, may be smaller, larger, or thesame size as that through which the velocity varies. In any case, if convec-tion heat transfer will occur from the surface to the outer flow.The convection heat transfer mode is sustained both by random molecular mo-tion and by the bulk motion of the fluid within the boundary layer. The contributiondue to random molecular motion (diffusion) dominates near the surface where theTs  T,Ty ? 0Tsqx ? (HW) q
x ? (0.5 m  1.2 m) 2833 W/m2 ? 1700 WA ? H  W6Chapter 1
Introductionyu(y)T(y)xTsHeatedsurfaceu?yT?TemperaturedistributionT(y)Velocitydistributionu(y)q"FluidFIGURE1.4Boundary layer development inconvection heat transfer.c01.qxd 3/6/06 10:21 AM Page 6www.konkur.in

ßuid velocity is low. In fact, at the interface between the surface and the ßuidthe ßuid velocity is zero and heat is transferred by this mechanism only.The contribution due to bulk ßuid motion originates from the fact that the boundarylayer growsas the flow progresses in the xdirection. In effect, the heat that is con-ducted into this layer is swept downstream and is eventually transferred to the fluidoutside the boundary layer. Appreciation of boundary layer phenomena is essentialto understanding convection heat transfer. It is for this reason that the discipline offluid mechanics will play a vital role in our later analysis of convection.Convection heat transfer may be classified according to the nature of the flow.We speak of forced convectionwhen the flow is caused by external means, such asby a fan, a pump, or atmospheric winds. As an example, consider the use of a fan toprovide forced convection air cooling of hot electrical components on a stack ofprinted circuit boards (Figure 1.5a). In contrast, for free(or natural) convectiontheflow is induced by buoyancy forces, which are due to density differences caused bytemperature variations in the fluid. An example is the free convection heat transferthat occurs from hot components on a vertical array of circuit boards in air (Figure1.5b). Air that makes contact with the components experiences an increase in tem-perature and hence a reduction in density. Since it is now lighter than the surround-ing air, buoyancy forces induce a vertical motion for which warm air ascendingfrom the boards is replaced by an inflow of cooler ambient air.While we have presumed pureforced convection in Figure 1.5aand purenat-ural convection in Figure 1.5b, conditions corresponding to mixed(combined)forcedand natural convectionmay exist. For example, if velocities associated with( y
0 ),1.2
Physical Origins and Rate Equations7Hot componentson printedcircuit boardsAirAirForcedflowBuoyancy-drivenflowq''q''q"WaterHot plateColdwaterWaterdropletsMoist airVaporbubbles(a)(b)(c)(d)q''FIGURE1.5Convection heat transfer processes. (a) Forced convection. (b) Natural convection. (c) Boiling. (d) Condensation.c01.qxd 3/6/06 10:21 AM Page 7www.konkur.in

the ßow of Figure 1.5aare small and/or buoyancy forces are large, a secondaryflow that is comparable to the imposed forced flow could be induced. In this case,the buoyancy-induced flow would be normal to the forced flow and could have asignificant effect on convection heat transfer from the components. In Figure 1.5b,mixed convection would result if a fan were used to force air upward between thecircuit boards, thereby assisting the buoyancy flow, or downward, thereby opposingthe buoyancy flow.We have described the convection heat transfer mode as energy transfer occur-ring within a fluid due to the combined effects of conduction and bulk fluid motion.Typically, the energy that is being transferred is the sensible, or internal thermal,energy of the fluid. However, there are convection processes for which there is, inaddition, latentheat exchange. This latent heat exchange is generally associatedwith a phase change between the liquid and vapor states of the fluid. Two specialcases of interest in this text are boilingand condensation.For example, convectionheat transfer results from fluid motion induced by vapor bubbles generated at thebottom of a pan of boiling water (Figure 1.5c) or by the condensation of watervapor on the outer surface of a cold water pipe (Figure 1.5d).Regardless of the particular nature of the convection heat transfer process, theappropriate rate equation is of the form(1.3a)where , the convective heat ßux(W/m2), is proportional to the difference betweenthe surface and fluid temperatures, Tsand T, respectively. This expression isknown as NewtonÕs law of cooling, and the parameter h(W/m2
K) is termed theconvection heat transfer coefÞcient.It depends on conditions in the boundary layer,which are influenced by surface geometry, the nature of the fluid motion, and an as-sortment of fluid thermodynamic and transport properties.Any study of convection ultimately reduces to a study of the means by which hmay be determined. Although consideration of these means is deferred to Chapter 6,convection heat transfer will frequently appear as a boundary condition in the solu-tion of conduction problems (Chapters 2 through 5). In the solution of such prob-lems we presume hto be known, using typical values given in Table 1.1.q
q

h(Ts  T)8Chapter 1
IntroductionTABLE1.1Typical values of theconvection heat transfer coefÞcientProcessh(W/m2
K)Free convectionGases2-25Liquids50-1000Forced convectionGases25-250Liquids100-20,000Convection with phase changeBoiling or condensation 2500-100,000c01.qxd 3/6/06 10:21 AM Page 8www.konkur.in

When Equation 1.3a is used, the convection heat ßux is presumed to be positiveif heat is transferred fromthe surface and negativeif heat is transferred tothe surface . However, if , there is nothing to preclude us from ex-pressing Newton's law of cooling as(1.3b)in which case heat transfer is positive if it is to the surface.1.2.3RadiationThermal radiation is energy emittedby matter that is at a nonzero temperature. Al-though we will focus on radiation from solid surfaces, emission may also occurfrom liquids and gases. Regardless of the form of matter, the emission may be at-tributed to changes in the electron configurations of the constituent atoms or mole-cules. The energy of the radiation field is transported by electromagnetic waves (oralternatively, photons). While the transfer of energy by conduction or convectionrequires the presence of a material medium, radiation does not. In fact, radiationtransfer occurs most efficiently in a vacuum.Consider radiation transfer processes for the surface of Figure 1.6a. Radiationthat is emittedby the surface originates from the thermal energy of matter boundedby the surface, and the rate at which energy is released per unit area (W/m2) istermed the surface emissive power E.There is an upper limit to the emissive power,which is prescribed by the StefanÐBoltzmann law(1.4)where Tsis the absolute temperature(K) of the surface and
is the StefanÐBoltzmann constant. Such a surface is called an idealradiator or blackbody.The heat flux emitted by a real surface is less than that of a blackbody at thesame temperature and is given by(1.5)E

T 4s(

5.67  108 W/m2 ? K4)Eb

T 4sq

h(T  Ts)T  Ts(T  Ts)(Ts  T)1.2
Physical Origins and Rate Equations9Surroundingsat TsurTs > Tsur, Ts > T
q"convq"convq"radGasT
, hGasT
, hGE(a)(b)Surface of emissivity , absorptivity , andtemperature TsSurface of emissivity = , area A, andtemperature TsFIGURE1.6Radiation exchange: (a) at a surface and (b) between a surface and large surroundings.c01.qxd 3/6/06 10:21 AM Page 9www.konkur.in

where is a radiative property of the surface termed the emissivity.With values inthe range , this property provides a measure of how efficiently a surfaceemits energy relative to a blackbody. It depends strongly on the surface materialand finish, and representative values are provided in Appendix A.Radiation may also be incidenton a surface from its surroundings. The radia-tion may originate from a special source, such as the sun, or from other surfaces towhich the surface of interest is exposed. Irrespective of the source(s), we designatethe rate at which all such radiation is incident on a unit area of the surface as the ir-radiation G(Figure 1.6a).A portion, or all, of the irradiation may be absorbedby the surface, thereby in-creasing the thermal energy of the material. The rate at which radiant energy is ab-sorbed per unit surface area may be evaluated from knowledge of a surface radia-tive property termed the absorptivity. That is,(1.6)where . If and the surface is opaque, portions of the irradiation arereßected.If the surface is semitransparent, portions of the irradiation may also betransmitted.However, while absorbed and emitted radiation increase and reduce, re-spectively, the thermal energy of matter, reflected and transmitted radiation have noeffect on this energy. Note that the value of depends on the nature of the irradiation,as well as on the surface itself. For example, the absorptivity of a surface to solar radi-ation may differ from its absorptivity to radiation emitted by the walls of a furnace.In many engineering problems (a notable exception being problems involvingsolar radiation or radiation from other very high temperature sources), liquids canbe considered opaque, and gases can be considered transparent, to radiation heattransfer. Solids can be opaque (as is the case for metals) or semitransparent(as isthe case for thin sheets of some polymers and some semiconducting materials).A special case that occurs frequently involves radiation exchange between asmall surface at Tsand a much larger, isothermal surface that completely surroundsthe smaller one (Figure 1.6b). The surroundingscould, for example, be the walls of aroom or a furnace whose temperature Tsurdiffers from that of an enclosed surface. We will show in Chapter 12 that, for such a condition, the irradiation maybe approximated by emission from a blackbody at Tsur, in which case . Ifthe surface is assumed to be one for which (a gray surface), the netrate of ra-diation heat transfer fromthe surface, expressed per unit area of the surface, is(1.7)This expression provides the difference between thermal energy that is released dueto radiation emission and that which is gained due to radiation absorption.There are many applications for which it is convenient to express the net radia-tion heat exchange in the form(1.8)where, from Equation 1.7, the radiation heat transfer coefÞcient hris(1.9)Here we have modeled the radiation mode in a manner similar to convection. In thissense we have linearizedthe radiation rate equation, making the heat rate proportionalhr  
(Ts  Tsur)(T 2s  T 2sur)qrad
hr A(Ts  Tsur)q
rad
qA
Eb(Ts)  G

(T 4s  T 4sur)
G

T 4sur(Tsur  Ts)  10    1Gabs
G0    110Chapter 1
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to a temperature difference rather than to the difference between two temperaturesto the fourth power. Note, however, that hrdepends strongly on temperature, whilethe temperature dependence of the convection heat transfer coefficient his generallyweak.The surfaces of Figure 1.6 may also simultaneously transfer heat by convectionto an adjoining gas. For the conditions of Figure 1.6b, the total rate of heat transferfromthe surface is then(1.10)EXAMPLE1.2An uninsulated steam pipe passes through a room in which the air and walls are at25°C. The outside diameter of the pipe is 70 mm, and its surface temperature andemissivity are 200°C and 0.8, respectively. What are the surface emissive powerand irradiation? If the coefficient associated with free convection heat transfer fromthe surface to the air is 15 W/m2
K, what is the rate of heat loss from the surfaceper unit length of pipe?SOLUTIONKnown:Uninsulated pipe of prescribed diameter, emissivity, and surface tem-perature in a room with fixed wall and air temperatures.Find:1.Surface emissive power and irradiation.2.Pipe heat loss per unit length, .Schematic:Assumptions:1.Steady-state conditions.2.Radiation exchange between the pipe and the room is between a small surfaceand a much larger enclosure.3.The surface emissivity and absorptivity are equal.h = 15 W/m2¥KD = 70 mmT
= 25°C Ts = 200°C Tsur = 25°C = 0.8Lq'GEAirqq
qconv  qrad
hA(Ts  T)  A
(T 4s  T 4sur)1.2
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Analysis:1.The surface emissive power may be evaluated from Equation 1.5, while the ir-radiation corresponds to . Hence2.Heat loss from the pipe is by convection to the room air and by radiation ex-change with the walls. Hence, and from Equation 1.10, withA
DL,The heat loss per unit length of pipe is thenComments:1.Note that temperature may be expressed in units of ¡C or K when evaluatingthe temperature difference for a convection (or conduction) heat transfer rate.However, temperature must be expressed in kelvins (K) when evaluating a ra-diation transfer rate.2.The net rate of radiation heat transfer from the pipe may be expressed as3.In this situation the radiation and convection heat transfer rates are comparablebecause Tsis large compared to Tsurand the coefÞcient associated with free con-vection is small. For more moderate values of Tsand the larger values of hasso-ciated with forced convection, the effect of radiation may often be neglected.The radiation heat transfer coefÞcient may be computed from Equation 1.9, andfor the conditions of this problem its value is .4.This example is provided as a tutorial sessi