《传热学综合传热》PPT课件.ppt

ChapterTwelve MultimodeHeatAndMassTransfer Thatmosttechnicallyimportantproblemsinvolvemultimodeheattransfereffects Tosolvesuchproblems itmaybenecessarytosimultaneouslyworkwithheatequation surfaceenergybalance overallenergybalances andappropriteraterateequationsforconduction convectionandradiationheattransfer Example12 1TherearwindowofanautomobileisofthicknessL 8mmandheightH 0 5mandcontainsfine meshedheatingwiresthatcaninducenearlyvolumetricheating Considersteady stateconditionsforwhichtheinteriorsurfaceofthewindowisexposedtoairat10 whiletheexteriorsurfaceisexposedtoairat 10 andaverycoldskywithaneffectivetemperatureof 33 Theairmovesinparallelflowoverthesurfacewithavelocityof20m s DeterminethevolumetricheatingrateneededmaintaintheinteriorwindowsurfaceatTs i 15 solutionKnown Boundaryconditionsassociatedwitharearwindowexperiencinguniformvolumetricheating Find VolumetricheatingrateneededtomaintaininnersurfacetemperatureatTs i 15 Schematic Assumptions steady state one dimensionalconditions Constantproperties Uniformvolumetricheatinginwindow Convectionheattransferfrominteriorsurfaceofwindowtointeriorairmaybeapproximatedasfreeconvectionfromaverticalplate Radiationexchangewithautomobileinteriorisnegligible Heattransferfromoutersurfaceisduetoforcedconvectionoveraflatplateandradiationexchangewiththesky Boundarylayerseparationontheoutersurfaceinnegligible Outersurfaceisdiffuseandgray Properties Glass Air k v Pr lookattables Analysis Thetemperaturedistributionintheglassisgovernedbytheappropriateformoftheheatequation Boundaryconditions Applyinganenergybalancetotheinnersurface Hence Applyinganenergybalancetotheoutersurface 1 2 3 TheinsideconvectioncoefficientmaybeobtainedfromEquation TheoutsideconvectioncoefficientmaybeobtainedbyfirstevaluatingtheReynoldsnumber Mixedboundarylayerconditions 4 5 Equation5maybeexpressedas 6 Substitutingintoequation4 Example12 2Thecompositeinsulationshownisbeingconsideredasaroofingmaterial Known Dimensionsofacompositeinsulationconsistingofahoneycombcoresandwichedbetweensolidslabs Find Totalthermalresistance Schematic becauseisnolateralheatfromcelltocell anditsufficestoconsidertheheattransferacrossasinglecell Assumptions 1 One dimensional steady stateconditions 2 Equivalentconditionsforeachcell 3 Constantproperties 4 Diffuse graysurfacebehavior Properties Analysis Thetotalresistanceofthecompositeisdeterminedbyconduction convectionandradiationprocessesoccurringwithinthehoneycombandbyconductionacrosstheinnerandouterslabs Thecorrespondingthermalcircuitisshown Thetotalresistanceofthecompositeis Theequivalentresistanceforthehonecombis Thecellformsanenclosurethatmaybeclassifiedasahorizontalcavityheatedfrombelow andtheappropriateformoftheRayleighnumberis Theresistancetoheattransferbyradiationmaybeobtainedbyfirstnotingthatthecellformsathree surfaceenclosureforwhichthesidewallsarereradiating Example12 3Cylindricaldry bulbthermometerisinstalledinalargediameterducttoobtainthetemperatureTairflowingthroughtheductatavelocityV theductinsidesurfaceisatknowntemperatureTswhichlessthenT Known Dry bulbtemperatureassociatedwithairflowthroughalargediameterductofprescribedsurfacetemperature Find Temperatureofairflow Schematic Dry bulbthermometer Assumption Steady stateconditionsexit Heattransferbyconductionalongthethermometersisnegligible Ductwallformsalargeenclosureaboutthethermometer Thermometersurfacearediffusegray Properties air v k Pr Analysis SinceTdb Ts thereisnetradiationtransferfromthesurfaceofthedry bulbthermometertotheductwall Hencetomaintainsteady stateconditions thethermometertemperaturemustbelessthanthatoftheairtoallowforconvectionheattransferfromtheair Fromapplicationofasurfaceenergybalancetothethermometer Theairt