Convection in porous media PDF
Preview Convection in porous media
Convection in Porous Media Convection in Porous Media Third Edition Donald A. Nield UniversityofAuckland Auckland,NewZealand and Adrian Bejan DukeUniversity Durham,NorthCarolina,USA Donald.A.Nield AdrianBejan AssociateProfessor J.A.JonesProfessorofMechanicalEngineering DepartmentofEngineeringScience DepartmentofMechanicalEngineeringand UniversityofAuckland MaterialsScience PrivateBag92019,Auckland DukeUniversity NewZealand Durham,NorthCarolina27708 [email protected] USA [email protected] LibraryofCongressControlNumber:2005932308 10digitISBN:0-387-29096-6 13digitISBN:978-0387-29096-6 (cid:1)C 2006SpringerScience+BusinessMedia,Inc. Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Use in connection with any form of information storage and retrievel, electronic adaptation, computer software,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.The useinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenot identifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject toproprietaryrights. PrintedintheUnitedStatesofAmerica (BS/DH) 9 8 7 6 5 4 3 2 1 springer.com To our wives Rachel Nield and Mary Bejan Our children Cherry, Alexandra, and Peter Nield Cristina, Teresa, and William Bejan Our grandchildren Michael and Rachel van der Mark Charlotte and Susan Nield Elizabeth and John Hayman Preface to the Third Edition Papersonconvectioninporousmediacontinuetobepublishedattheratethatis nowover200peryear.Theindicationofthecontinuedimportanceofthesubject, togetherwiththewideacceptanceofthefirstandsecondeditionsofthisvolume, hasencouragedustoprepareanexpandedthirdedition.Wehaveretainedtheba- sicstructureandmostofthetextofthesecondedition.Wehavebeensomewhat selectiveinourchoiceofreferences,butneverthelessthereareover1400newref- erences.Again,wehavemadeanefforttohighlightnewconceptualdevelopments andengineeringapplications. Wefoundthatitwaspossibletofitalotofthenewmaterialundertheexisting sectionheadings.However,wenowhavenewsectionsonbidisperseporousmedia, localthermalnonequilibrium,electrodiffusion,transverseheterogeneityinchan- nels,thermaldevelopmentofforcedconvection,effectsoftemperature-dependent viscosity,constructalmultiscaleflowstructures,optimalspacingsforplatessep- arated by porous structures, control of convection using vertical vibration, and bioconvection. Onceagainwedecidedthat,exceptforabriefmention,convectioninunsaturated mediahadtobebeyondthescopeofthisbook.Also,weareawarethatthereare sometopicsintheareaofhydrologythatcouldberegardedascomingunderthe umbrellaofthetitleofourbookbutarenottreatedhere. Wearegratefultoalargenumberofpeoplewhoprovidedus,priortopublication, withcopiesoftheirchaptersofbooksthatsurveyresearchonvarioustopics.Other colleagueshavecontinuedtoimproveourunderstandingofthesubjectofthisbook inwaystoonumeroustomentionhere. Wewishtothankouremployers,theUniversityofAucklandandDukeUniver- sity,fortheirongoingsupport. OnceagainwereliedontheexpertiseandhardworkofLindaHayesandDeborah Frazeforthepreparationoftheelectronicversionofourmanuscript. D.A.Nield A.Bejan Preface to the Second Edition Papersonconvectioninporousmediacontinuetobepublishedattherateofover 100peryear.Thisindicationofthecontinuedimportanceofthesubject,together with the wide acceptance of the first edition, has encouraged us to prepare an expandedsecondedition.Wehaveretainedthebasicstructureandmostofthetext ofthefirstedition.Withspaceconsiderationsinmind,wehavebeenselectivein ourchoiceofreferences,butneverthelessthereareover600newreferences.We also made an effort to highlight new conceptual developments and engineering applications. In the introductory material, we judged that Chapters 2 and 3 needed little alteration (though there is a new Section 2.6 on other approaches to the topic), butourimprovedunderstandingofthebasicmodelingofflowthroughaporous mediumhasledtoanumberofchangesinChapter1,bothwithintheoldsections andbytheadditionofasectiononturbulenceinporousmediaandasectionon fracturedmedia,deformablemedia,andcomplexporousstructures. InChapter4,onforcedconvection,wehaveaddedmajornewsectionsoncom- pactheatexchangers,onheatlinesforvisualizingconvection,andonconstructal treenetworksforthegeometricminimizationoftheresistancetovolume-to-point flowsinheterogeneousporousmedia. InChapter5(externalnaturalconvection)thereisasubstantialamountofnew materialinsertedintheexistingsections.InChapters6and7,oninternalnatural convection,wenowhaveincludeddescriptionsoftheeffectsofamagneticfield and rotation, and there are new sections on periodic heating and on sources in confinedorpartlyconfinedregions;thelatterisareflectionofthecurrentinterest intheproblemofnuclearwastedisposal.InChapter8,onmixedconvection,there arenonewsections,butinanewsubsectionwehavegivensomeprominencetothe unifiedtheorythathasbeendevelopedforboundarylayersituations.InChapter9, ondouble-diffusiveconvection(heatandmasstransfer)thereisanewsectionon convectionproducedbyinclinedgradients,atopicthatalsohasbeengivenwider coverageintherelatedsectioninChapter7. InChapter10,whichdealswithconvectionwithchangeofphase,wehaveanew subsectiononthesolidificationofbinaryalloys,aresearchareathathasblossomed inthelastdecade.Wealsohaveanewsectiononspacesfilledwithfluidandfibers coatedwithaphase-changematerial.Inthefirsteditionwehadlittletosayabout two-phaseflow,despiteitsimportanceingeothermalandothercontexts.Wenow haveincludedasubstantialdiscussiononthistopic,whichwehaveplacedatthe x PrefacetotheSecondEdition endofChapter11(geophysicalaspects).Onceagainwedecidedthat,exceptfora briefmention,convectioninunsaturatedmediahadtobebeyondthescopeofthis book. D.A.N.againenjoyedthehospitalityoftheDepartmentofMechanicalEngineer- ingandMaterialsScienceatDukeUniversitywhileonResearchandStudyLeave from the University of Auckland, and both of those institutions again provided financialsupport. WearegratefulforcommentsfromGrahamWeirandRogerYoungonadraft ofSection11.9,atopiconwhichwehadmuchtolearn.Wealsoaregratefulto alargenumberofpeoplewhoprovideduswithpreprintsoftheirpaperspriorto publication.Othercolleagueshaveimprovedourunderstandingofthesubjectof thisbookinwaystoonumeroustomentionhere. Once again we relied on the expertise and hard work of Linda Hayes for the preparation of the electronic version of our manuscript, and again the staff at theEngineeringLibraryofDukeUniversitymadeoursearchoftheliteraturean enjoyableexperience. D.A.Nield A.Bejan Preface to the First Edition Inthisbookwehavetriedtoprovideauser-friendlyintroductiontothetopicof convectioninporousmedia.Wehaveassumedthatthereaderisconversantwith thebasicelementsoffluidmechanicsandheattransfer,butotherwisethebookis self-contained. Only routine classic mathematics is employed. We hope that the bookwillbeusefulbothasareview(forreference)andasatutorialwork(suitable asatextbookinagraduatecourseorseminar). This book brings into perspective the voluminous research that has been per- formed during the last two decades. The field recently has exploded because of worldwideconcernwithissuessuchasenergyself-sufficiencyandpollutionofthe environment.Areasofapplicationincludetheinsulationofbuildingsandequip- ment,energystorageandrecovery,geothermalreservoirs,nuclearwastedisposal, chemical reactor engineering, and the storage of heat-generating materials such asgrainandcoal.Geophysicalapplicationsrangefromtheflowofgroundwater aroundhotintrusionstothestabilityofsnowagainstavalanches. We believe that this book is timely because the subject is now mature in the sensethatthereisacorpusofmaterialthatisunlikelytorequiremajorrevisionin thefuture.Asthereaderwillfind,therelationsforheattransfercoefficientsand flowparametersforthecaseofsaturatedmediaarenowknownwellenoughfor engineeringdesignpurposes.Thereisasoundbasisofunderlyingtheorythathas been validated by experiment. At the same time there are outstanding problems in the cases of unsaturated media and multiphase flow in heterogeneous media, whicharerelevanttosuchtopicsasthedryingofporousmaterialsandenhanced oilrecovery. The sheer bulk of the available material has limited the scope of this book. It hasforcedustoomitadiscussionofconvectioninunsaturatedmediaandalsoof geothermalreservoirmodeling;referencestoreviewsofthesetopicsaregiven.We alsohaveexcludedmentionofseveralhundredadditionalpapers,includingsome ofourown.Wehaveemphasizedreportsofexperimentalwork,whichareinrela- tivelyshortsupply(andinsomeareasarestilllacking).Wehavealsoemphasized simpleanalysiswherethisilluminatesthephysicsinvolved.Theexcludedmaterial includessomegoodearlywork,whichhasnowbeensuperseded,andsomerecent numericalworkinvolvingcomplexgeometry.Alsoexcludedarepapersinvolving theadditionaleffectsofrotationormagneticfields;weknowofnoreportedex- perimentalworkorsignificantapplicationsoftheseextensions.Weregretthatour surveycouldnotbeexhaustive,butwebelievethatthisbookgivesagoodpicture ofthecurrentstateofresearchinthisfield. xii PrefacetotheFirstEdition Thefirstthreechaptersprovidethebackgroundfortherestofthebook.Chap- ters4through8formthecorematerialonthermalconvection.Ouroriginalplan, whichwastoseparatefoundationalmaterialfromapplications,provedtobeim- practical,andthesechaptersareorganizedaccordingtogeometryandtheformof heating.Chapter9dealswithcombinedheatandmasstransferandChapter10with convectioncoupledwithchangeofphase.Geophysicalthemesinvolveadditional physical processes and have given rise to additional theoretical investigations; thesearediscussedinChapter11. * * * ThisbookwaswrittenwhileD.A.N.wasenjoyingthehospitalityoftheDepart- mentofMechanicalEngineeringandMaterialsScienceatDukeUniversity,while onResearchandStudyLeavefromtheUniversityofAuckland.Financialsupport forthisleavewasprovidedbytheUniversityofAuckland,DukeUniversity,and theUnitedStates–NewZealandCooperativeScienceProgram.Weareparticularly grateful to Dean Earl H. Dowell and Prof. Robert M. Hochmuth, both of Duke University,fortheirhelpinmakingthisbookprojectpossible. LindaHayesdidalltheworkofconvertingourroughhandwrittennotesintothe current high-quality version on computer disk. She did this most efficiently and withtremendousunderstanding(i.e.,patience!)forthemanyinstancesinwhich wechangedourmindsandmodifiedthemanuscript. Atvariousstagesinthepreparationofthemanuscriptandthefigureswewere assistedbyLindaHayes,KathyVickers,JongS.Lim,JoseL.Lage,andLaurens Howle. Eric Smith and his team at the Engineering Library of Duke University wenttogreatlengthstomakeourliteraturesearcheasier.Weareverygratefulfor alltheassistancewehavereceived. D.A.Nield A.Bejan Contents Nomenclature xxi 1 MechanicsofFluidFlowthroughaPorousMedium 1 1.1 Introduction 1 1.2 Porosity 3 1.3 SeepageVelocityandtheEquationofContinuity 4 1.4 MomentumEquation:Darcy’sLaw 4 1.4.1 Darcy’sLaw:Permeability 6 1.4.2 DeterministicModelsLeadingtoDarcy’sLaw 6 1.4.3 StatisticalModelsLeadingtoDarcy’sLaw 7 1.5 ExtensionsofDarcy’sLaw 8 1.5.1 AccelerationandOtherInertialEffects 8 1.5.2 QuadraticDrag:Forchheimer’sEquation 10 1.5.3 Brinkman’sEquation 14 1.5.4 Non-NewtonianFluid 16 1.6 HydrodynamicBoundaryConditions 17 1.7 EffectsofPorosityVariation 21 1.8 TurbulenceinPorousMedia 23 1.9 FracturedMedia,DeformableMedia,andComplex PorousStructures 25 1.10 BidispersePorousMedia 25 2 HeatTransferthroughaPorousMedium 27 2.1 EnergyEquation:SimpleCase 27 2.2 EnergyEquation:ExtensionstoMoreComplexSituations 28 2.2.1 OverallThermalConductivityofaPorousMedium 28 2.2.2 EffectsofPressureChanges,ViscousDissipation,and AbsenceofLocalThermalEquilibrium 30 2.2.3 ThermalDispersion 33 2.3 Oberbeck-BoussinesqApproximation 35 2.4 ThermalBoundaryConditions 36 2.5 Hele-ShawAnalogy 36 2.6 OtherApproaches 37
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