(5.5)--Chapter 5 Theoretical Basis for传热学传热学传热学.ppt

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1、Chapter5Theoretical Basis for Convective Heat TransfernIntroductiontoconvectiveheattransfernMathematicaldescriptionofconvectiveheattransferproblemsnMathematicaldescriptionofconvectiveheattransferproblemsinboundary-layertypenAnalyticalsolutionandanalogytheoryofheattransferforlaminarflowoveraplatenSim

2、ilarityprincipleanddimensionanalysisnApplicationofsimilarityprinciple5-1 Introduction to convectiveheattransfer1 Definition and properties of convective heat transferConvective heat transfer referstothephenomenonofheattransferbetweenafluidandasolidsurfaceasfluidflowsthroughthesolid.Convectiveheattra

3、nsferexamples:1)heating;2)electronicdevicecooling;3)electricfan.Convectiveheattransferisdifferentfromheatconvection,withbothconvectionandconduction;notabasicheattransfermode.(1)Complexheattransferprocesswithconductionandconvection(2)Directcontact(fluidandwall)andmacroscopicmotion;temperaturedifferen

4、ce(3)Duetoviscosityoffluidandfrictionalresistanceofwallsurface,aboundarylayerwithalargevelocitygradientformsclosetowallsurface.2 characteristics of convective heat transfer3 Basic calculation formula for convective heat transferNewtonslawofcooling:4 surface heat transfer coefficient (convective heat

5、 transfer coefficient)Physicalmeaning:amountofheattransferperunitwallareaandperunittimewitha1Ktemperaturedifferencebetweenfluidandwall.How to determine h and enhance heat transfer is the core problem of convective heat transferW/(m2K)Forcedconvection:causedbyexternalforces(suchas:pumps,fans,hydrauli

6、chead).5 Factors affecting convective heat transferThere are five main influencing factors:(1)flow cause;(2)flowstate;(3)fluidphasechange;(4)geometricalfactorsofheattransfersurface;(5)thermophysicalpropertiesoffluid.(1)flowcauseFreeconvection:causedbyadensitydifferenceinsidefluid.(2)Flowstate:(3)Flu

7、idphasechange:Laminarflow:FluidlumpsfollowthemainstreamdirectionforregularstratifiedflowTurbulentflow:DramaticmixingbetweenvariouspartsofthefluidSinglephase:NophasechangePhasechangeheattransfer:Condensation,boiling,sublimation,solidification,melting,etc.(4)Geometricfactorsofheattransfersurface:Inter

8、nalflowconvectiveheattransfer:IntubesorgroovesExternalflowconvectiveheattransfer:Overaflatplate,roundtube,tubebanks(5)Thermophysicalpropertiesoffluids:DensitySpecificheatcapacityDynamicviscosityKinematicviscosityBodyexpansioncoefficientThermalConductivity W/(mK)Smallthermalconductivityinsidefluidand

9、betweenfluidandwallMoreenergyperunitvolumeoffluidRetardfluidflow,notconducivetoheatconvectionNaturalconvectionheattransferenhancementInsummary,surfaceheattransfercoefficientisafunctionofmanyfactors:ConvectiveheattransferclassificationConvectiveheattransferPhasechangeNophasechangeForcedconvectionFree

10、convectionInternalflowInfinitespaceForcedflowinnon-circulartubeForcedflowincirculartubeMixedconvection(bothforcedandfree)ExternalflowFinitespaceMezzaninespaceOveraplateOveratubeOvertubebanksVerticalwallandtubeCrosstubeHorizontalwall(upanddownsurfaces)CondensationheattransferBoilingheattransferVertic

11、alwallHorizontaltubeandtubebanksInsidetubeInsidetube(crossandvertical)Largespace(6)Methodsofstudyingconvectiveheattransfer:(2)Experimental method(1)Analytical method(3)Analogymethod(4)NumericalmethodFocus on(7)DifferentialequationsforconvectiveheattransferprocessInthisextremelythinadherent-wall flui

12、d layer,heatcanonlybetransferredinmodeofheatconduction.AccordingtoFourierslaw:ThermalconductivityoffluidChangerateoffluidtemperature in thenormaldirectionofnear-wallsurfaceAccordingtoNewtonscoolinglaw:ByFourierslawandNewtonscoolinglaw:DifferentialequationforconvectiveheattransferprocessnThetemperatu

13、regradientortemperaturefielddependsonthermalpropertiesofthefluid,flowstate(laminarorturbulent),magnitudeanddistributionofflowvelocity,surfaceroughness,etc.TemperaturefielddependsonflowfieldnThevelocityandtemperaturefieldsaredeterminedbytheconvectiveheattransferdifferentialequations:hdependsonthermal

14、conductivityoffluid,temperaturedifferenceandtemperaturegradientofnear-wallfluid.MassconservationequationMassconservationequationMomentumconservationequationMomentumconservationequationEnergyconservationequationEnergyconservationequation(2)FluidisanincompressibleNewtonianfluidNamely:fluidobeysNewtons

15、lawofviscosity:(3)Allphysicalparameters(,cp,)areconstant,nointernalheatsource(1)Thefluidistwo-dimensionalAssumptions:5-2 Mathematical description ofconvectiveheattransferproblemsPaint,mud,etc.do not comply with this law,called non-Newtonian fluid(4)Heatdissipationcausedbyviscousdissipationisnegligib

16、le1.Massconservationequation(continuityequation)ContinuousflowoffluidfollowsthelawofconservationofmassMassflowsintothemicrounitinthexdirection:Massflowsoutofthemicrounitinthexdirection:Netmassflowsintothemicrounitinthexdirectionperunittime:Masschangeoffluidinthemicrounit:Conservationoffluidmassinthe

17、microunit:Net mass flows into the micro unit=mass change of fluid in the micro unitMassflowsintothemicrounitinthexdirection:Two-dimensional continuity equationThree-dimensional continuity equationFortwo-dimensional,steady-stateflow,andconstantdensity:2MomentumconservationequationNewtons second law o

18、f motion:sumoftheexternalforcesactingonthemicrounitisequaltothechangerateoffluidmomentuminthecontrolvolume.Differencebetweenpressurepandnormalviscousstressiia)pexistsregardlessofflow;iionlyexistswhenfluidflowsb)pisthesameinalldirectionsatthesamepoint;iiisrelatedtothesurfaceorientationForce=massaccel

19、eration(F=ma)ForcemainlyincludesvolumeforceandsurfaceforceVolumeforce:gravity,centrifugalforce,electromagneticforceSurfaceforce:normalstressincludespressurepandnormalviscousstressiiSurfaceforcesonthemicrounitMomentumdifferentialequationNavier-Stokesequation(N-Sequation)(1)inertiaterm(ma);(2)volumefo

20、rce;(3)pressuregradient;(4)viscousforceForsteadystateflow:Onlyingravityfield:3EnergyconservationequationEnergyconservationofmicrounit:netheatimportedandexported+netheattransferredbyheatconvection+Heatgenerationbyinnerheatsource=Totalenergyincrease+expansionworkQ=E+W W Workofvolumeforce(gravity)andsu

21、rfaceforce(1)Allthermalpropertiesoffluidareconstant,andfluiddoesnotwork.(2)fluidisnotcompressible(4)NointernalheatsourcesuchaschemicalreactionUK=0Qinternalheatsource=0(3)LowflowvelocityforgeneralengineeringproblemsW0 Assumption:Netheattransferredtothemicrounitbyheatconvectioninthexdirectionperunitti

22、me:Netheattransferredtothemicrounitbyheatconvectionintheydirectionperunittime:Energyconservationequation:Thermodynamicenergy:Differentialequationsofconvectiveheattransfer(Constantproperties,nointernalheatsource,two-dimensional,incompressibleNewtonianfluid)n4equations,4unknowns-thevelocityfield(u,v)a

23、ndtemperaturefield(t)andthepressurefield(p)canbeobtained;bothforlaminarflowandturbulence(instantaneousvalues).nAfterthefirstfourequationsareusedtofindthetemperaturefield,Newtonscoolingdifferentialequationcanbeused:n Calculatelocalconvectiveheattransfercoefficient4Methodfordeterminingsurfaceheattrans

24、fercoefficient(1)Mathematicalsolutionofdifferentialequationa）Exactsolution(analyticalsolution):accordingtotheboundarylayertheory:b)Approximateintegrationmethod:Assumevelocitydistributionandtemperaturedistributionintheboundarylayer,andsolvetheintegralequationc)Numericalsolution:rapiddevelopmentinrece

25、ntyearsCansolveverycomplexproblems:three-dimensional,turbulent,variableproperties,supersonicBoundarylayerdifferentialequationsOrdinarydifferentialequationsSolution(2)AnalogymethodofmomentumandheattransferUsing the similar law of momentum and heat transfer inturbulence,the local surface heat transfer

26、 coefficient is inferredfromthelocalsurfacefrictioncoefficientinturbulentflow.(3)ExperimentalmethodGuidedbytheanalogytheory5DefiniteconditionsforconvectiveheattransferprocessThedefiniteconditionsincludefouritems:geometry,physics,time,andboundary.(1)Geometryconditions:Describegeometryandsizeofconvect

27、iveheattransferFlatplate,tube;verticalorhorizontaltube;length,diameter,etc.(2)Physicsconditions:DescribephysicalcharacteristicsofconvectiveheattransferprocessSuchas:properties,c and whetherchangewithtemperatureandpressure;whetherhasinternalheatsourceanditssizeanddistribution(3)Timeconditions:Describ

28、etimecharacteristicsofconvectiveheattransferSteady-stateconvectiveheattransferprocessdoesnotrequiretimeconditionsindependentoftime(4)Boundaryconditions:DescribeboundarycharacteristicsofconvectiveheattransferprocessBoundaryconditionscanbedividedintotwocategories:thefirstkindandthesecondkindaBoundaryc

29、onditionsofthefirstkindKnowntemperaturevalueatboundaryinconvectiveheattransferprocessatanymomentbBoundaryconditionsofthesecondkindKnown heat flux value at boundary in convectiveheat transferprocessatanymomentBoundarylayer:Whenviscousfluidflowsthroughsurfaceofanobject,avelocityboundarylayerwithalarge

30、velocitygradientforms;whenthereisatemperaturedifferencebetweenwallandfluid,atemperatureboundarylayer(orathermalboundarylayer)withalargetemperaturegradientalsoforms.5-3Differentialequationsofboundarylayerforconvectiveheattransfer1VelocityboundarylayernDue to viscosity,flow velocity near the wallsurfa

31、ce gradually decreases as the distance fromthe wall surface decreases;it is stagnated at thenear-wallandinanon-slipstate.nFromy=0,u=0,uincreasesrapidlyasthedistancefromwallsurfaceintheydirectionincreases;uclosestothemainstreamvelocityuthroughathinlayerofthickness.Define:Thedistancefromthewallsurface

32、atu/u=0.99isthethicknessofboundarylayer.y=ThinlayerFlowboundarylayerorvelocityboundarylayer ThicknessofboundarylayerSmall :Airflowsoveraplate,u=10m/sIn the boundary layer:theaveragevelocitygradientislarge;thevelocitygradientaty=0isthelargestByNewtonslawofviscosity:Largevelocitygradientandlargeviscou

33、sstressBeyond the boundary layer:udoesntchangeinthey direction,Viscousstressiszeromainstream u/y=0Theflowfieldcanbedividedintotworegions:theboundarylayerregionandthemainstreamBoundarylayerregion:Theviscouseffectoffluidplaysaleadingrole,andthemotionoffluidcanbedescribedbythemotiondifferentialequation

34、s(N-Sequation)ofviscousfluidMainstream:Velocitygradientis0,=0;canberegardedasnon-viscousidealfluid;EulerequationCriticaldistance:thedistanceoflaminarboundarylayerbeyondwhichthelaminarlayerbeginstotransittoturbulentboundarylayer,xcTurbulent boundary layer:CriticalReynoldsnumber:Laminar bottom layer:c

35、losetothewall,viscousforcedominates,sothataverythinlayeradheringtowallwillstillmaintainlaminarcharacteristicswithmaximumvelocitygradientForflowintube:Rec2300Re104,TurbulentflowForflowoveraplate:generallytakeRec=105Severalimportantcharacteristicsofflowboundarylayer(1)Thethicknessofboundarylayerisextr

36、emelysmallcomparedtocharacteristicdimensionLofwall,1,whichisu a:;Pr1,whichisu a:。Example:two-dimensional,steadystate,forcedconvection,laminarflow,neglectofgravitymeansequivalentuchangesfrom0toualongthicknessofboundarylayer:Bythecontinuityequation:Two-dimensionalsteady-stateequationsignoringgravityIt

37、showsthatpressuregradientinboundarylayerchangesonlyinxdirection,whilenormalpressuregradientinboundarylayerisextremelysmall.Thepressureinanysectionofboundarylayerisindependentofyandequalstomainstreampressure.AnothercharacteristicofboundarylayerSincepressurechangeinydirectionisneglected,thepressurecha

38、ngeinboundarylayerinxdirectionisthesameasmainstream,andcanbedeterminedbyBernoulliequationofidealfluidinmainstream:Differentialequationsof laminar boundarylayerinconvectiveheattransfer:3equations,3unkown:u,v,t,equationsclosedWithcorrespondingdefinitionconditions,equationscanbesolved.If,thenFormainstr

39、eamwithaveragevelocity,averagetemperature,andgivenconstantwalltemperature,theboundaryconditionsofheattransferforflowoverplateare:5-4Analyticalsolutionandanalogytheoryofheattransferforlaminarflowoveraplate1AnalyticalsolutionforlaminarflowoffluidoveranisothermalplateA dimensionless amount of ratio of

40、local shear stress tohydrodynamic head is often used in engineering called theFanning friction coefficient,abbreviated as the frictioncoefficient:Solvingmomentumdifferentialequationcanobtainexactsolutionof,whichare:Thicknessofboundarylayeratx awayfromleading-edge:Note:laminar Anexpressionforlocalsur

41、faceheattransfercoefficient:Characteristicnumberequationorcriterionequationwhere:Nusselt numberReynolds numberPrandtl numberNote:Characteristiclengthislocalcoordinatesx.Besuretonoticetheapplicableconditionsofthecriterionequation:Externallyflowoveranisothermalplate,nointernalheatsource,laminarflowFor

42、laminarflowoveraplate:Itshowsthatthelawofmomentumtransferissimilartoheattransferinthiscase.In particular:for a fluid with=a(Pr=1),velocity field will be completelysimilartothedimensionlesstemperaturefield,whichisanotherphysicalmeaningofPr,indicatingthatthicknessesofflowboundarylayerandtemperaturebou

43、ndarylayerarethesame.Energyequation:Momentumequation:Theconvectivesurfaceheattransfercoefficientoftheentireplatecanbeobtainedbyintegratingthelocalsurfaceheattransfercoefficientfrom0to1:experimentpointCharacteristiclength:full-lengthofplatelQualitativetemperature:theaveragetemperatureoffluidinboundar

44、ylayerScopeofapplication:Re21052BasicideasofanalogytheoryPurpose:Toestablisharelationshipof.Byanalogy,theuneasilydeterminedheattransfercoefficienthisobtainedbyusingeasilydetermineddragcoefficient(byexperiment).Because measuring flow resistance coefficient is much easier than measuring heat transfer

45、coefficient.Princple:Foraturbulentflow,whenoneofmicellesinfluidpulsatesfromalocationtoanother,itwillcreatetwoeffects:(1)Additionalmomentumexchangebetweenlayersofdifferentflowvelocitiess,resultinginadditionalshearstress;(2)Fluidbetweendifferenttemperaturelayerscreatesanadditionalheatexchange.Thisaddi

46、tionalshearstressandheattransferduetoturbulentpulsationiscalledturbulentshearstressandturbulentheatflux.Sincetheadditionalshearstressandheatfluxinturbulentflowareduetopulsationoffluidmicelles,theremustbeanintrinsicrelationship between heat transfer and flow resistance inturbulentflow.Taketurbulenthe

47、attransferofflowoveranisothermalplateasanexample.ThemomentumandenergyequationsofturbulentboundarylayerareTurbulentmomentumdiffusivityIntroducethefollowingdimensionlessquantities:TurbulentthermaldiffusivitythenReynoldsbelievesthatsinceturbulentshearstresstandturbulentheatflux qtarebothcausedbypulsati

48、on,itcanbeassumedthat:TurbulentPrandtlnumberWhenPr=1,thenu*andshouldhavethesamesolution,thus:andSimilarly:Thedragcoefficientofturbulentboundarylayeronaplatebyexperimentaldeterminationis:This is the famous Reynolds Analogy and premise of its establishment is Pr=1.WhenPr1,theanalogyneedstobecorrected,

49、sothereisChilton-ColburnAnalogy(revisedReynoldsAnalogy):whereStiscalledStantonnumberandisdefinedasjiscalledjfactorandiswidelyusedindesignofheatexchangersforrefrigerationandlowtemperatureindustries.Whenlengthofplatelisgreaterthanthecriticallengthxc,theboundarylayeronplateconsistsofalaminarsegmentanda

50、turbulentsegment.TheirNuare:Thentheaverageconvectiveheattransfercoefficienthmis:Iftake,thenabovebecomes:,laminar,turbulent,5-5SimilarityprincipleanddimensionanalysisExperimentisanindispensabletool.However,thefollowingtwoproblemsareoftenencountered:(1)Toomanyvariables1.ProposaloftheproblemA.Whatvaria