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1、Chap2IntroductiontoconductionObjectives:1.TodevelopadeeperunderstandingofFourier’slaw.Whatformdoesittakefordifferentgeometries?2.Todevelopthegeneralequation,termedtheheatequation,whichgovernsthetemperaturedistributioninamedium.temperaturedistributiondeterminetheheatflux2.1Theconductionratee
2、quationOrigin:Fourier’slawisphenomenological.Evaluatingthisexpressioninthelimitas,weobtainfortheheatrateorfortheheatfluxk--thethermalconductivity(w/m.k)Recallthattheminussignisnecessarybecauseheatisalwaystransferredinthedirectionofdecreasingtemperature.Theheatfluxisdirectionalquantity.Thedi
3、rectionofheatflowwillalwaysbenormaltoasurfaceofconstanttemperature,calledanisothermal(等温)surface.Theheatfluxisvectorquantity,sothemoregeneralstatementoftheFourier’slawisasfollows:is3-Ddeloperatorandisthescalar(标量)temperaturefield.Analternativeformiswhereistheheatfluxinadirectionn,whichisnor
4、mal(perpendicular)toanisotherm.Theheatfluxvectorcanberesolvedintocomponentssuchthat,inCartesiancoordinates,thegeneralexpressionisFromEquation2.3,itfollowsthatEachoftheseexpressionsrelatestheheatfluxacrossasurfacetothetemperaturegradientinadirectionperpendiculartothesurface.2.2Thethermalprop
5、ertiesofmatterTransportproperties2.2.1ThermalconductivityDefinition:Thermalconductivityassociatedwithconductioninthex-directionisdefinedasForanisotropic(各向同性)material:Usually,asillustratedinFig2.4.ThesolidstateAccordingly,transportofthermalenergyisduetotwoeffects:themigrationoffreeelectrons
6、andlatticevibrationalwaves.Forpuremetals,ismuchlagerthanForalloys,isnolongernegligibleFornonmetallicsolids,canbeverylarge,suchasdiamond.Theconductivityvarywiththetemperature.Fig2.5.InsulationSystemThermalinsulationsarecomprisedoflowthermalconductivitymaterialscombinedtoachieveanevenlowersys
7、temthermalconductivity.Foamedinsulation,reflectiveinsulationThefluidstateGasTheeffectoftemperature,pressure,andchemicalspeciesonthethermalconductivityofagasmaybeexplainedintermsofthekinetictheoryofgases.n,thenumberofparticlesperunitvolume;c,themeanmolecu
