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化工原理英文教材傳熱無相變傳熱Heattransfertofluidswithoutphasechange課件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化工原理英文教材傳熱無相變傳熱Heattransfertofluidswithoutphasechange課件化工原理

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化工原理英文教材傳熱無相變傳熱Heattransfertofluidswithoutphasechange課件FormagnitudesoflogGrProf4ormore,thelineofFig12.8followscloselytheempiricalequationFormagnitudesoflogGrPrNaturalconvectiontoairfromverticalshapesandhorizontalplatesEquationsforheattransferinnaturalconvectionbetweenfluidsandsolidsofdefinitegeometricshapeareoftheform