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化工原理
PrinciplesofChemicalIndustry化工原理HeattransfertofluidswithoutphasechangeHeattransfertofluidswithouRegimesofheattransferinfluidsAfluidbeingheatedorcooledmaybeflowingindifferentflowpatterns.Also,thefluidmaybeflowinginforcedornaturalconvection.RegimesofheattransferinflAtordinaryvelocitiestheheatgeneratedfromfluidfrictionisnegligibleincomparisonwiththeheattransferredbetweenthefluids.AtordinaryvelocitiestheBecausethesituationsofflowattheentrancetoatubediffersfromthosewelldownstreamfromtheentrance,thevelocityfieldandassociatedtemperaturefieldmaydependonthedistancefromthetubeentranceBecausethesituationsofflowThepropertiesofthefluid-viscosity,thermalconductivity,specificheat,anddensityareimportantparametersinheattransfer.Eachofthese,especiallyviscosity,istemperature-dependent.Thepropertiesofthefluid-viHeattransferbyforcedconvectioninturbulentflowPerhapsthemostimportantsituationinheattransferistheheatflowinastreamoffluidinturbulentflow.HeattransferbyforcedconvecSincetherateofheattransferisgreaterinturbulentflowthaninlaminarflow,mostequipmentisoperatedintheturbulentrange.Sincetherateofheattran
Adimensionalanalysisoftheheatflowtoafluidinturbulentflowthroughastraightpipeyieldsdimensionlessrelations.
(12-27)AdimensionalanalysisoftThethreegroupsinEq(12-27)arerecognizedastheNusselt(Nu),Reynolds(Re),andPrandtl(Pr)numbersrespectively.ThethreegroupsinEq(12-2
TheNusseltnumberforheattransferfromafluidtoapipeorfromapipetoafluidequalsthefilmcoefficientmultipliedbyd/kThefilmcoefficienthistheaveragevalueoverthelengthofthepipeTheNusseltnumberforheat
PrandtlnumberPristheratioofthediffusivityofmomentumμ/ρ
tothethermaldiffusivityk/ρcpPrandtlnumberPristheraThePrandtlnumberofagasisusuallycloseto1(0.69forair,1.06forsteam).ThePrandtlnumberofgasesisalmostindependentoftemperaturebecausetheviscosityandthermalconductivitybothincreasewithtemperatureataboutthesamerate.ThePrandtlnumberofagasEmpiricalequationForheattransfertoandfromfluidsthatfollowthepower-lawrelation,thedimensionlessrelationbecomesTousethedimensionlessrelation,theconstantcandindexm,nmustbeknown.EmpiricalequationForheattra
Arecognizedempiricalcorrelation,forlongtubeswithsharp-edgedentrances,istheDittus-Boelterequation
Wherenis0.4whenthefluidisbeingheatedand0.3whenitisbeingcooled.Arecognizedempiricalcorr
AbetterrelationshipforturbulentflowisknownastheSieder-Tateequation
(12-32)AbetterrelationshipfortEquation(12-32)shouldnotbeusedforReynoldsnumbersbelow6000orformoltenmetals,whichhaveabnormallylowPrandtlnumber.Equation(12-32)shouldnotEffectoftubelengthNearthetubeentrance,wherethetemperaturegradientsarestillforming,thelocalcoefficienthxisgreaterthanhforfullydevelopedflow.EffectoftubelengthNeartheInentrance,hxisquitelarge,buthxvaluedropsrapidlytowardhinacomparativelyshortlengthoftube.Averagevalueofhiinturbulentflow.
Sincethetemperatureofthefluidchangesfromoneendofthetubetotheotherandfluidpropertiesµ
,cpandkareallfunctionoftemperature,thelocalvalueofhialsovariesfrompointtopointalongthetube.
Inentrance,hxisquitelaTherelationoflocalheattransfercoefficienthiandlongtubehisasfollowsWhenLapproachesinfinite,hiisclosetothehoflongtube.TherelationoflocalheattraForlaminarflow,therelationofNuandPrandReis(12.25)Forlaminarflow,therelationForgasestheeffectoftemperatureonhiissmall.Theincreaseinconductivityandheatcapacitywithtemperatureoffsettheriseinviscosity,givingaslightincreaseinhi.ForgasesForliquids
theeffectoftemperatureismuchgreaterthanforgasesbecauseoftherapiddecreaseinviscositywithrisingtemperature.ForliquidsTheeffectsofk,cp,andµinEq(12-36)allactinthesamedirection,buttheincreaseinhiwithtemperatureisduemainlytotheeffectoftemperatureonviscosity.Theeffectsofk,cp,andµInpractice,anaveragevalueofhiiscalculatedandusedasaconstantincalculatingtheoverallcoefficientU.Inpractice,anaveragevaltheaveragevalueofhiiscomputedbyevaluatingthefluidpropertiesk,cp,andµataveragefluidtemperature,definedasthearithmeticmeanbetweentheinletandoutlettemperatures.theaveragevalueofhiisEstimationofwalltemperature
tw
TheestimationoftwrequiresaniterativecalculationbasedontheresistanceequationEstimationofwalltemperature
TodeterminetwthewallresistancecanusuallybeneglectedTodeterminetwthewallrSubstitutingUo,gives
(12-38)SubstitutingUo,givesCrosssectionsotherthancircularTouseEq(12-30)forcrosssectionotherthancircularitisonlynecessarytoreplacethediameterinbothReynoldsandNusseltnumberbytheequivalentdiameterde.Crosssectionsotherthancirc
de
isdefinedas4timesthehydraulicradiusrH.Themethodisthesameasthatusedincalculatingfrictionloss.deisdefinedas4timesthHeattransferintransitionregionbetweenlaminarandturbulentflowEquation(12-32)appliesonlyforReynoldsnumbersgreaterthan6000.TherangeofReynoldsnumbersbetween2100and6000iscalledthetransitionregion,andnosimpleequationapplieshere.Heattransferintransitionre
Agraphicalmethodthereforeisused.ThemethodisbasedonacommonplotoftheColburnjfactorversusRe,withlinesofconstantvalueofL/DAgraphicalmethodtherefor
TheheattransfercoefficientcanbecalculatedbyfollowingequationTheheattransfercoefficieHeatingandcoolingoffluidsinforcedconvectionoutsidetubesThemechanismofheatflowinforcedconvectionoutsidetubesdiffersfromthatofflowinsidetubes.Thelocalvalueofheat-transfercoefficientvariesfrompointtopointaroundcircumferenceinforcedconvectionoutsidetube.HeatingandcoolingoffluidsInFig12.5,thelocalvalueoftheNusseltnumberisplottedradiallyforallpointsaroundcircumferenceofthetube.InFig12.5,thelocalvaluNuθismaximumatthefrontandbackofthetubeandaminimumatthesides.Inpractice,thevariationsinthelocalcoefficientareoftennoimportance,andaveragevaluesbasedontheentirecircumferenceareused.NuθismaximumatthefrontafluidsflowingnormaltoasingletubeThevariablesaffectingthecoefficientofheattransfertoafluidinforcedconvectionoutsideatubeareDo,theoutsidediameterofthetube;cp,μ,andk,thespecificheat,theviscosity,andthermalconductivity,respectively,ofthefluid;andG,themassvelocity.fluidsflowingnormaltoasinDimensionalanalysisgivesNusseltnumberisonlyafunctionoftheReynoldsnumber.DimensionalanalysisgivesTheexperimentaldataforairareplottedinthiswayinFig12.6TheexperimentaldataforairForheatingandcoolingliquidsflowingnormaltosinglecylindersthefollowingequationisusedForheatingandcoolingliquidNaturalconvectionConsiderahot,verticalplateincontactwiththeairinaroom.Thedensityoftheheatedairimmediatelyadjacenttotheplateislessthanthatoftheunheatedairatadistancefromtheplate,andthebuoyancyofthehotaircausesanunbalancebetweentheverticallayersofairofdifferingdensity.NaturalconvectionConsiderTemperaturedifferencebetweenthesurfaceofplateandtheaircausesaheattransfer.Naturalconvectioninliquidfollowsthesamepattern.Thebuoyancyofheatedliquidlayersnearahotsurfacegeneratesconvectioncurrentsjustasingases.TemperaturedifferencebetwForsinglehorizontalcylinders,theheattransfercoefficientcanbecorrelatedbyequationcontainingthreedimensionlessgroupsNu=f(Pr,Gr)Gr:GrashofnumberPr:PrandtlnumberForsinglehorizontalcylind(12-67)Thecoefficientofthermalexpansionβ
isapropertyoffluid(12-67)ThecoefficientoftherFig12.8showsarelationship,whichsatisfactorilycorrelatesexperimentaldataforheattransferfromasinglehorizontalcylindertoliquidsorgasesFig12.8showsarelationsh化工原理英文教材传热无相变传热Heattransfertofluidswithoutphasechange课件FormagnitudesoflogGrProf4ormore,thelineofFig12.8followscloselytheempiricalequationFormagnitudesoflogGrPrNaturalconvectiontoairfromverticalshapesandhorizontalplatesEquationsforheattransferinnaturalconvectionbetweenfluidsandsolidsofdefinitegeometricshapeareoftheform(12-73)ValuesoftheconstantsbandnforvariousconditionsaregiveninTable12.4NaturalconvectiontoairfromAdoublepipeheatexchangerisusedtocondensethesaturatedtoluenevapor(2000kg/h)intosaturatedliquid.Thecondensationtemperatureandlatentheatoftolueneare110oCand363kJ/kg,respectively.Thecoldwaterat20oC(inlettemperature)and5000kg/hgoesthroughthepipe(di=50mm)fullyturbulently.Iftheindividualheattransfercoefficienthiofwatersideis2100w/(m2K),andheatresistancesofpipewallaswellastoluenesidearemuchlargerthanthatofwaterside(thismeansbothresistancescanbeignored),find:Outlettemperatureofcoldwater,inoC.Pipelengthofexchanger.Inorderformassflowrateoftoluenetobedouble,ifthemassflowrateofcoldwateratthesameinlettemperature(20oC)isdouble,whatisthepipelengthofnewexchangertoberequired?AdoublepipeheatexchangeriSolution:Heatbalanceq=m1=m2Cp(Tcb-Tca)2000363=50004.19(Tcb-20)(1)OutlettemperatureofcoldwaterTcb=54.65oC(2)U=h(fromtheproblem)∆T1=110-54.65=55.35,∆T2=110-20=90∆T=(∆T1+∆T2)/2=72.68(since∆T2/∆T1<2)L=q/(Ud∆T)=20003631000/3600/(21000.0572.68)=8.42m(3)q’=2qm1=2m2Cp(T’cb-Tca)OutlettemperatureofcoldwaterTcb=54.65oC∆T’=(∆T1+∆T2)/2=72.68Fullydevelopedturbulentflow,hRe0.8~m0.8~u0.8h’/h=20.8,h’=1.74hq’=1.74hdL’∆T’=2m1q=hdL∆T=m1L’/L=2/1.74soL’=28.42/1.74=9.68mSolution:Heatbalanceq=m1=mAsinglepass(1-1)shell-tubeexchangerismadeofmany252.5mmtubes.Organicsolution,u=0.5m/s,m(massflowrate)=15000kg/h,Cp=1.76kJ/kg.oC,=858kg/m3,passesthroughthetube.Thetemperaturechangesfrom20to50oC.Thesaturatedvaporat130oCcondensestothesaturatedwater,whichgoesthroughtheshell.Theindividualheattransfercoefficientshiandhointhepipeandshellare700andis10000W/m2oC,respectively.Thethermalconductivitykofpipewallis45W/m.oC.Iftheheatlossandresistancesoffoulingcanbeignored,find(1)OverallheattransfercoefficientUo.(basedonoutsidetubearea)andLMTD.(2)Heattransferarea,numberofpipesandlengthofpipes.Asinglepass(1-1)shell-tube化工原理英文教材传热无相变传热Heattransfertofluidswithoutphasechange课件化工原理
PrinciplesofChemicalIndustry化工原理HeattransfertofluidswithoutphasechangeHeattransfertofluidswithouRegimesofheattransferinfluidsAfluidbeingheatedorcooledmaybeflowingindifferentflowpatterns.Also,thefluidmaybeflowinginforcedornaturalconvection.RegimesofheattransferinflAtordinaryvelocitiestheheatgeneratedfromfluidfrictionisnegligibleincomparisonwiththeheattransferredbetweenthefluids.AtordinaryvelocitiestheBecausethesituationsofflowattheentrancetoatubediffersfromthosewelldownstreamfromtheentrance,thevelocityfieldandassociatedtemperaturefieldmaydependonthedistancefromthetubeentranceBecausethesituationsofflowThepropertiesofthefluid-viscosity,thermalconductivity,specificheat,anddensityareimportantparametersinheattransfer.Eachofthese,especiallyviscosity,istemperature-dependent.Thepropertiesofthefluid-viHeattransferbyforcedconvectioninturbulentflowPerhapsthemostimportantsituationinheattransferistheheatflowinastreamoffluidinturbulentflow.HeattransferbyforcedconvecSincetherateofheattransferisgreaterinturbulentflowthaninlaminarflow,mostequipmentisoperatedintheturbulentrange.Sincetherateofheattran
Adimensionalanalysisoftheheatflowtoafluidinturbulentflowthroughastraightpipeyieldsdimensionlessrelations.
(12-27)AdimensionalanalysisoftThethreegroupsinEq(12-27)arerecognizedastheNusselt(Nu),Reynolds(Re),andPrandtl(Pr)numbersrespectively.ThethreegroupsinEq(12-2
TheNusseltnumberforheattransferfromafluidtoapipeorfromapipetoafluidequalsthefilmcoefficientmultipliedbyd/kThefilmcoefficienthistheaveragevalueoverthelengthofthepipeTheNusseltnumberforheat
PrandtlnumberPristheratioofthediffusivityofmomentumμ/ρ
tothethermaldiffusivityk/ρcpPrandtlnumberPristheraThePrandtlnumberofagasisusuallycloseto1(0.69forair,1.06forsteam).ThePrandtlnumberofgasesisalmostindependentoftemperaturebecausetheviscosityandthermalconductivitybothincreasewithtemperatureataboutthesamerate.ThePrandtlnumberofagasEmpiricalequationForheattransfertoandfromfluidsthatfollowthepower-lawrelation,thedimensionlessrelationbecomesTousethedimensionlessrelation,theconstantcandindexm,nmustbeknown.EmpiricalequationForheattra
Arecognizedempiricalcorrelation,forlongtubeswithsharp-edgedentrances,istheDittus-Boelterequation
Wherenis0.4whenthefluidisbeingheatedand0.3whenitisbeingcooled.Arecognizedempiricalcorr
AbetterrelationshipforturbulentflowisknownastheSieder-Tateequation
(12-32)AbetterrelationshipfortEquation(12-32)shouldnotbeusedforReynoldsnumbersbelow6000orformoltenmetals,whichhaveabnormallylowPrandtlnumber.Equation(12-32)shouldnotEffectoftubelengthNearthetubeentrance,wherethetemperaturegradientsarestillforming,thelocalcoefficienthxisgreaterthanhforfullydevelopedflow.EffectoftubelengthNeartheInentrance,hxisquitelarge,buthxvaluedropsrapidlytowardhinacomparativelyshortlengthoftube.Averagevalueofhiinturbulentflow.
Sincethetemperatureofthefluidchangesfromoneendofthetubetotheotherandfluidpropertiesµ
,cpandkareallfunctionoftemperature,thelocalvalueofhialsovariesfrompointtopointalongthetube.
Inentrance,hxisquitelaTherelationoflocalheattransfercoefficienthiandlongtubehisasfollowsWhenLapproachesinfinite,hiisclosetothehoflongtube.TherelationoflocalheattraForlaminarflow,therelationofNuandPrandReis(12.25)Forlaminarflow,therelationForgasestheeffectoftemperatureonhiissmall.Theincreaseinconductivityandheatcapacitywithtemperatureoffsettheriseinviscosity,givingaslightincreaseinhi.ForgasesForliquids
theeffectoftemperatureismuchgreaterthanforgasesbecauseoftherapiddecreaseinviscositywithrisingtemperature.ForliquidsTheeffectsofk,cp,andµinEq(12-36)allactinthesamedirection,buttheincreaseinhiwithtemperatureisduemainlytotheeffectoftemperatureonviscosity.Theeffectsofk,cp,andµInpractice,anaveragevalueofhiiscalculatedandusedasaconstantincalculatingtheoverallcoefficientU.Inpractice,anaveragevaltheaveragevalueofhiiscomputedbyevaluatingthefluidpropertiesk,cp,andµataveragefluidtemperature,definedasthearithmeticmeanbetweentheinletandoutlettemperatures.theaveragevalueofhiisEstimationofwalltemperature
tw
TheestimationoftwrequiresaniterativecalculationbasedontheresistanceequationEstimationofwalltemperature
TodeterminetwthewallresistancecanusuallybeneglectedTodeterminetwthewallrSubstitutingUo,gives
(12-38)SubstitutingUo,givesCrosssectionsotherthancircularTouseEq(12-30)forcrosssectionotherthancircularitisonlynecessarytoreplacethediameterinbothReynoldsandNusseltnumberbytheequivalentdiameterde.Crosssectionsotherthancirc
de
isdefinedas4timesthehydraulicradiusrH.Themethodisthesameasthatusedincalculatingfrictionloss.deisdefinedas4timesthHeattransferintransitionregionbetweenlaminarandturbulentflowEquation(12-32)appliesonlyforReynoldsnumbersgreaterthan6000.TherangeofReynoldsnumbersbetween2100and6000iscalledthetransitionregion,andnosimpleequationapplieshere.Heattransferintransitionre
Agraphicalmethodthereforeisused.ThemethodisbasedonacommonplotoftheColburnjfactorversusRe,withlinesofconstantvalueofL/DAgraphicalmethodtherefor
TheheattransfercoefficientcanbecalculatedbyfollowingequationTheheattransfercoefficieHeatingandcoolingoffluidsinforcedconvectionoutsidetubesThemechanismofheatflowinforcedconvectionoutsidetubesdiffersfromthatofflowinsidetubes.Thelocalvalueofheat-transfercoefficientvariesfrompointtopointaroundcircumferenceinforcedconvectionoutsidetube.HeatingandcoolingoffluidsInFig12.5,thelocalvalueoftheNusseltnumberisplottedradiallyforallpointsaroundcircumferenceofthetube.InFig12.5,thelocalvaluNuθismaximumatthefrontandbackofthetubeandaminimumatthesides.Inpractice,thevariationsinthelocalcoefficientareoftennoimportance,andaveragevaluesbasedontheentirecircumferenceareused.NuθismaximumatthefrontafluidsflowingnormaltoasingletubeThevariablesaffectingthecoefficientofheattransfertoafluidinforcedconvectionoutsideatubeareDo,theoutsidediameterofthetube;cp,μ,andk,thespecificheat,theviscosity,andthermalconductivity,respectively,ofthefluid;andG,themassvelocity.fluidsflowingnormaltoasinDimensionalanalysisgivesNusseltnumberisonlyafunctionoftheReynoldsnumber.DimensionalanalysisgivesTheexperimentaldataforairareplottedinthiswayinFig12.6TheexperimentaldataforairForheatingandcoolingliquidsflowingnormaltosinglecylindersthefollowingequationisusedForheatingandcoolingliquidNaturalconvectionConsiderahot,verticalplateincontactwiththeairinaroom.Thedensityoftheheatedairimmediatelyadjacenttotheplateislessthanthatoftheunheatedairatadistancefromtheplate,andthebuoyancyofthehotaircausesanunbalancebetweentheverticallayersofairofdifferingdensity.NaturalconvectionConsiderTemperaturedifferencebetweenthesurfaceofplateandtheaircausesaheattransfer.Naturalconvectioninliquidfollowsthesamepattern.Thebuoyancyofheatedliquidlayersnearahotsurfacegeneratesconvectioncurrentsjustasingases.TemperaturedifferencebetwForsinglehorizontalcylinders,theheattransfercoefficientcanbecorrelatedbyequationcontainingthreedimensionlessgroupsNu=f(Pr,Gr)Gr:GrashofnumberPr:PrandtlnumberForsinglehorizontalcylind(12-67)Thecoefficientofthermalexpansionβ
isapropertyoffluid(12-67)ThecoefficientoftherFig12.8showsarelationship,whichsatisfactorilycorrelatesexperimentaldataforheattransferfromasinglehorizontalcylindertoliquidsorgasesFig12.8showsarelationsh化工原理英文教材传热无相变传热Heattransfertofluidswithoutphasechange课件FormagnitudesoflogGrProf4ormore,thelineofFig12.8followscloselytheempiricalequationFormagnitudesoflogGrPrNaturalconvectiontoairfromverticalshapesandhorizontalplatesEquationsforheattransferinnaturalconvectionbetweenfluidsandsolidsofdefinitegeometricshapeareoftheform
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