(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
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