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AA HHEEAATT TTRRAANNSSFFEERR TTEEXXTTBBOOOOKK TTHHIIRRDD EEDDIITTIIOONN JJoohhnn HH.. LLiieennhhaarrdd IIVV // JJoohhnn HH.. LLiieennhhaarrdd VV AA HHeeaatt TTrraannssffeerr TTeexxttbbooookk (cid:2)(cid:2) LLiieennhhaarrdd && LLiieennhhaarrdd Phlogiston Press ISBN 0-9713835-0-2 PSB 01-04-0249 A Heat Transfer Textbook A Heat Transfer Textbook Third Edition by John H. Lienhard IV and John H. Lienhard V Phlogiston Cambridge Press Massachusetts ProfessorJohnH.LienhardIV DepartmentofMechanicalEngineering UniversityofHouston 4800CalhounRoad HoustonTX77204-4792U.S.A. ProfessorJohnH.LienhardV DepartmentofMechanicalEngineering MassachusettsInstituteofTechnology 77MassachusettsAvenue CambridgeMA02139-4307U.S.A. Copyright©2003byJohnH.LienhardIVandJohnH.LienhardV Allrightsreserved PleasenotethatthismaterialiscopyrightedunderU.S.CopyrightLaw. The authorsgrantyoutherighttodownloadandprintitforyourpersonaluseor fornon-profitinstructionaluse. Anyotheruse,includingcopying, distributingormodifyingtheworkforcommercialpurposes,issubjecttothe restrictionsofU.S.CopyrightLaw. Internationalcopyrightissubjecttothe BerneInternationalCopyrightConvention. Theauthorshaveusedtheirbesteffortstoensuretheaccuracyofthe methods,equations,anddatadescribedinthisbook,buttheydonot guaranteethemforanyparticularpurpose. Theauthorsandpublisheroffer nowarrantiesorrepresentations,nordotheyacceptanyliabilitieswith respecttotheuseofthisinformation. Pleasereportanyerratatotheauthors. Lienhard,JohnH.,1930– Aheattransfertextbook/JohnH.LienhardIVand JohnH.LienhardV—3rded. —Cambridge,MA: PhlogistonPress,c2003 Includesbibliographicreferencesandindex. 1.Heat—Transmission 2.MassTransfer I.Lienhard,JohnH.,V,1961– II.Title TJ260.L4452003 PublishedbyPhlogistonPress Cambridge,Massachusetts,U.S.A. ThisbookwastypesetinLucidaBrightandLucidaNewMathfonts(designed byBigelow&Holmes)usingLATEXundertheY&YTEXSystem. Forupdatesandinformation,visit: http://web.mit.edu/lienhard/www/ahtt.html Thiscopyis: Version 1.12 dated January 19, 2003 Preface Thisbookismeantforstudentsintheirintroductoryheattransfercourse —studentswhohavelearnedcalculus(throughordinarydifferentialequa- tions)andbasicthermodynamics. Weincludetheneededbackgroundin fluid mechanics, although students will be better off if they have had an introductory course in fluids. An integrated introductory course in thermofluid engineering should also be a sufficient background for the material here. Ourmajorobjectivesinrewritingthe1987editionhavebeentobring thematerialuptodateandmakeitasclearaspossible. Wehavesubstan- tially revised the coverage of thermal radiation, unsteady conduction, and mass transfer. We have replaced most of the old physical property data with the latest reference data. New correlations have been introduced for forced and natural convection and for convective boiling. The treatment of thermal resistance has been reorganized. Dozens of new problemshavebeenadded. Andwehaverevisedthetreatmentofturbu- lentheattransfertoincludetheuseofthelawofthewall. Inanumberof places we have rearranged material to make it flow better, and we have made many hundreds of small changes and corrections so that the text will be more comfortable and reliable. Lastly, we have eliminated Roger Eichhorn’s fine chapter on numerical analysis, since that topic is now most often covered in specialized courses on computation. This book reflects certain viewpoints that instructors and students alike should understand. The first is that ideas once learned should not be forgotten. We have thus taken care to use material from the earlier parts of the book in the parts that follow them. Two exceptions to this are Chapter 10 on thermal radiation, which may safely be taught at any pointfollowingChapter2,andChapter11onmasstransfer,whichdraws only on material through Chapter 8. v vi Webelievethatstudentsmustdevelopconfidenceintheirownability toinventmeansforsolvingproblems. Theexamplesinthetexttherefore do not provide complete patterns for solving the end-of-chapter problems. Students who study and absorb the text should have no unusual troubleinworkingtheproblems. Theproblemsvaryinthedemandthat theylayonthestudent,andwehopethateachinstructorwillselectthose that best challenge their own students. The first three chapters form a minicourse in heat transfer, which is applied in all subsequent chapters. Students who have had a previous integrated course thermofluids may be familiar with this material, but to most students it will be new. This minicourse includes the study of heat exchangers, which can be understood with only the concept of the overall heat transfer coefficient and the first law of thermodynamics. Wehaveconsistentlyfoundthatstudentsnewtothesubjectaregreatly encouragedwhentheyencounterasolidapplicationofthematerial,such asheatexchangers,earlyinthecourse. Thedetailsofheatexchangerde- sign obviously require an understanding of more advanced concepts — fins, entry lengths, and so forth. Such issues are best introduced after the fundamental purposes of heat exchangers are understood, and we develop their application to heat exchangers in later chapters. This book contains more material than most teachers can cover in three semester-hours or four quarter-hours of instruction. Typical one- semestercoveragemightincludeChapters1through8(perhapsskipping some of the more specialized material in Chapters 5, 7, and 8), a bit of Chapter 9, and the first four sections of Chapter 10. We are grateful to the Dell Computer Corporation’s STAR Program, theKeckFoundation,andtheM.D.AndersonFoundationfortheirpartial support of this project. JHL IV, Houston, Texas JHL V, Cambridge, Massachusetts August 2002 Contents I The General Problem of Heat Exchange 1 1 Introduction 3 1.1 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Relation of heat transfer to thermodynamics. . . . . . . . . . 6 1.3 Modes of heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 A look ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2 Heatconductionconcepts, thermalresistance, andtheoverall heat transfer coefficient 49 2.1 The heat diffusion equation . . . . . . . . . . . . . . . . . . . . . . . 49 2.2 Solutions of the heat diffusion equation. . . . . . . . . . . . . . 58 2.3 Thermal resistance and the electrical analogy . . . . . . . . . 62 2.4 Overall heat transfer coefficient, U . . . . . . . . . . . . . . . . . . 78 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3 Heat exchanger design 99 3.1 Function and configuration of heat exchangers . . . . . . . . 99 3.2 Evaluation of the mean temperature difference in a heat exchanger. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.3 Heat exchanger effectiveness . . . . . . . . . . . . . . . . . . . . . . 120 3.4 Heat exchanger design. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 vii viii Contents II Analysis of Heat Conduction 139 4 Analysisofheatconductionandsomesteadyone-dimensional problems 141 4.1 The well-posed problem . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.2 The general solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.3 Dimensional analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.4 Anillustrationofdimensionalanalysisinacomplexsteady conduction problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 4.5 Fin design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 5 Transient and multidimensional heat conduction 193 5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 5.2 Lumped-capacity solutions . . . . . . . . . . . . . . . . . . . . . . . . 194 5.3 Transient conduction in a one-dimensional slab . . . . . . . 203 5.4 Temperature-response charts . . . . . . . . . . . . . . . . . . . . . . 208 5.5 One-term solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 5.6 Transient heat conduction to a semi-infinite region. . . . . 220 5.7 Steady multidimensional heat conduction . . . . . . . . . . . . 235 5.8 Transient multidimensional heat conduction. . . . . . . . . . 247 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 III Convective Heat Transfer 267 6 Laminar and turbulent boundary layers 269 6.1 Some introductory ideas . . . . . . . . . . . . . . . . . . . . . . . . . . 269 6.2 Laminar incompressible boundary layer on a flat surface 276 6.3 The energy equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 6.4 The Prandtl number and the boundary layer thicknesses 296 6.5 Heattransfercoefficientforlaminar,incompressibleflow over a flat surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 6.6 The Reynolds analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 6.7 Turbulent boundary layers . . . . . . . . . . . . . . . . . . . . . . . . 313 6.8 Heat transfer in turbulent boundary layers . . . . . . . . . . . 322 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338