大學(xué)教學(xué)講解課件：chapter-6(Heat-TransferJPHolman-)

Chapter6CollegeofNuclearScienceandTechnologyEmpiricalandPracticalRelationsforForced-ConvectionHeatTransfer

1Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology26-1Introduction

ThediscussionandanalysesofChapter5haveshownhowforced-convectionheattransfermaybecalculatedforseveralcasesofpracticalinterest;however,theproblemsconsideredwerethosethatcouldsolvedinananalyticalfashion.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology3But,itisnotalwayspossibletoobtainanalyticalsolutionstoconvectionproblems,andtheindividualisforcedtoresorttoexperimentalmethodstoobtaindesigninformation,aswellastosecurethemoreelusivedatethatincreasethephysicalunderstandingoftheprocess.Whatwehavetodo:Generalizetheresultsofone’sexperimentsinformofsomeempiricalcorrelationChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology4DifficultiesWhichvariablesshouldwemeasure?Whatfunctionalformshouldthedatabeorganizedinto?It’shardandexpensivetodotheexperiments,so,howmanyexperimentsshouldwedo?Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology5SimilarityConsiderationsPurpose:todoresearchontherelationshipbetweensimilarphysicalphenomena.Forsimilarphysicalphenomena:atcorrespondingtimewithcorrespondinglocationonthephysicalquantityrelatedwiththephenomenoncorrespondenceproportional.Forsametypeofphenomena:Phenomenondescribedbydifferentialequationswiththesameformandcontent.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology6CharacteristicsforphysicalphenomenasimilarityThesamecharacteristicnumbersareequalThereissomewhatrelationshipbetweendifferentcharacteristics.ForexampleChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology7TheconditionsforphysicalphenomenasimilaritySameidentifiedcharacteristicnumbersareequalIt’ssimilarforMonodromyconditions,whichincludesinitialconditions,boundaryconditionsandGeometricconditionsChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology8HowtogetdimensionlessgroupsSimilarityConsiderations:Toestablishthecolumnproportioncoefficientbetweenthetwophenomena,relationshipbetweentheexportofthesesimilaritycoefficientandobtainadimensionlessquantitybasedonKnownmathematicaldescriptionofthephysicalphenomena.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology9Phenomenon1：Phenomenon2：mathematicaldescriptionChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology10EstablishsimilarmultiplesRelationshipbetweenthemChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology11BerkeleynumberToobtaindimensionlessgroups

Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology12DimensionalAnalysisIndimensionalanalysis,dimensionalgroupssuchastheReynoldsandPrandtlnumbersarederivedfrompurelydimensionalandfunctionalconsiderations.FundamentalBasisTheoremof,Aconsistentdimensionlessequationshowingtherelationshipbetweenthenphysicalquantitiescouldbetransferredtoarelationshipwhichcontains(n-r)independentdimensionlessgroups.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology13AdvantagesofdimensionlessanalysisSimpleWecanstillobtaindimensionlessgroupswithoutknowingtheDifferentialEquationsFundamentalquantityintheSIUnitsLength[m]，MASS[kg]，time[s]，ELECTRICCURRENT[A]，thermodynamictemperature[K]，amountofsubstance[mol]，luminousintensity[cd]Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology14NowwecomebacktothedifficultiesWhichvariablesshouldwemeasure?

OnlyvariablesthatarecontainedincharacteristicnumbersWhatfunctionalformshouldthedatabeorganizedinto?

ArrangethedataaccordingtotherelationshipbetweenthecharacteristicnumbersIt’shardandexpensivetodotheexperiments,so,howmanyexperimentsshouldwedo?

ModularExperimentsundertheguidanceofthesimilarconsiderationChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology15Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology166-2EmpiricalRelationsForPipeAndTubeFlowCasesofUndevelopedFlowThecasesofundevelopedlaminarflowsystemswherethefluidpropertiesvarywidelywithtemperature,andturbulent-flowsystemsareconsiderablymorecomplicatedbutareofveryimportantpracticalinterestinheatexchangersandassociatedheat-transferequipment.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology17Fordesignandengineeringpurposes,empiricalcorrelationsareusuallyofgreatestpracticalutility.Forlaminarflow,thelengthoftheundevelopedpartundevelopeddeveloped(Averagefrom0tox)Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology18Forturbulentflow,thelengthoftheundevelopedpartundevelopeddeveloped(Averagefrom0tox)Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology19FurtherconsiderationtoBulktemperatureChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology20FortubeinFigure6-1thetotalenergyaddedcanbeexpressedintermsofbulk-temperaturebyIndifferentialequation,TheTwandTbherearethewallandbulktemperatureattheparticularxlocation.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology21Thetotalheattransfercanalsobeexpressedas[6-3]whereAisthetotalsurfaceareaforheattransfer.BecausebothTwandTbcanvaryalongthelengthofthetube,asuitableaveragingprocessmustbeadoptedforusewithEquation(6-3).Inchapter10we’lldiscussdifferentmethodsfortakingproperaccountoftemperaturevariationsinheatexchangers.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology22AtraditionexpressionforcalculationofheattransferinfullydevelopedturbulentflowinsmoothtubesForheatingofthefluidForcoolingofthefluidChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology23ConditionsChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology24WidetemperaturedifferencesThesepropertyvariationsmaybeevidencedbyachangeinthevelocityprofileasindicatedinthefigure.1.Inothermalflow2.Gasheating,Liquidcooling3.Liquidheating,gascoolingChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology25SomerelationstakepropertyvariationsintoaccountGasheatingGascoolingLiquidHeatingLiquidCoolingChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology26ConditionsChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology27ConditionsChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology28Ifthechannelthroughwhichthefluidflowsisnorcircularcrossthesection,itisrecommendedthattheheat-transfercorrelationsbebasedonthehydraulicdiameter.VariousSectionsDefinitionHydraulicdiameterAiscross-sectionalareaoftheflowPisthewettedperimeterChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology29ThehydraulicdiametershouldbeusedincalculatingtheNusseltandReynoldsnumbers,andinestablishingthefrictioncoefficientforusewithReynoldsanalogy.AverageNusseltnumberforuniformheatfluxinflowdirectionanduniformwalltemperatureatparticularflowcrosssectionAverageNusseltnumberforuniformwalltemperatureProductoffrictionfactorandReynoldsnumberbasedonhydraulicdiameterChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology30ConstantaxialwallheatfluxConstantaxialwalltemperatureHeattransferandfluidfrictionforfullydevelopedflowinductsofvariouscrosssectionsGeometryTriangleSquareRegularHexagonCircleRectanglewithb=2aChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology31Airat2atmand200℃isheatedasitflowsthroughatubewithadiameterof1in(2.54cm)atvelocityof10m/s.Calculatetheheattransferperunitlengthoftubeisconstant-heat-fluxconditionismaintainedatthewallandthewallandthewalltemperatureis20℃,abovetheairtemperature,allalongthelengthofthetube.Howmuchwouldthebulktemperatureincreasea3-mlengthofthetube?ExampleChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology32SolutionWefirstcalculatetheReynoldsnumbertodetermineiftheflowislaminarorturbulent,andthenselecttheappropriateempiricalcorrelationtocalculatetheheattransfer.Thepropertiesofairatabulktemperatureof200℃areChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology33Sotheflowisturbulent.WethereforeuseEquation(6-4a)tocalculatetheheat-transfercoefficientChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology34Theheat-flowperunitlengthisthenChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology35Wecannowmakeanenergybalancetocalculatetheincreaseinbulktemperatureina3.0-mlengthofthetubeChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology36SotheheattransferperunitlengthisChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology376-3FlowAcrossCylindersAndSpheresBoundary-layerSeparationLookatFigure6-7,itisnecessarytoincludethepressuregradientintheanalysisbecausethisinfluencestheboundary-layervelocityandcausesseparatedflowregiontodeveloponthebacksideofthecylinderwhenthefreestreamvelocityissufficientlylarge.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology38Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology39Figure6—8VelocitydistributionsindicatingflowseparationonacylinderincrossflowBoundaryLayerSeparationRegionChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology40Incaseofcylinder,onemightmeasurexdistancefromthefrontstagnationpointofthecylinder.Thusthepressureintheboundarylayershouldfollowthatofthefreestreamforpotentialflowaroundacylinder,providedthisbehaviorwouldnotcontradictsomebasicprinciple.Astheincreaseflowprogressesalongthefrontsideofthecylinder,thepressurewoulddecreaseandthenincreasealongthebacksideofthecylinder,resultinginanincreaseinfree-streamvelocityonthefrontsideofthecylinderandadecreaseonthebackside.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology41ThedetailedbehavioroftheheattransferfromaheatedcylindertoairaresummarizedinFigure6-11Thechangeofheat-transfercoefficientthroughcircularCylindersChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology42AtthelowerRenumbers,aminimumpointintheheat-transfercoefficientoccursatapproximatelythepointofseparation.Thereisasubsequentincreaseintheheat-transfercoefficientontherearsideofthecylinder,resultingfromtheturbulenteddymotionintheseparatedflow.AthigherRenumbers,

twominimumpointsareobservedChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology43Becauseofthecomplicatednatureoftheflow-separation,itisnotpossibletocalculateanalyticallytheaveragecoefficientsincrossflow.KnudsenandKatzsuggestedthatthecorrelationbeextendedtoliquidsbyinclusionofTheresultingcorrelationforaverageheat-transfercoefficientsincrossflowovercircularcylindersisTherelationshipofFlowAcrossCylinders[6-17]Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology44TheconstantCandnaretabulatedintheTable6-2ReCn0.4～40.9890.3304～400.9110.38540～40000.6830.4664000～400000.1930.61840000～4000000.02660.805℃，℃

BulktemperatureChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology45StillamorecomprehensiverelationisgivenbyChurchillandBernsteinwhichisapplicableoverthecompleterangeofavailabledata.ForBulktemperatureChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology46NoncircularCylindersEquation[6-17]isemployedinordertoobtainanempiricalcorrelationforgases,andtheconstantsforusewiththisequationaresummarizedinTable6-3.ThedatauponwhichTable6-3isbasedwereforgaseswithPr~0.7andweremodifiedbysame1.11factoremployedfortheinformationpresentedinTable6-2Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology47Table6-3constantsforheattransferfromnoncircularcylindersforusewithEquation(6-17)FlatSquareRegularHexagonChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology48SpheresAsingleEquationforgasesandliquidsflowingpastspheresAtfree-streamtemperatureChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology49ExampleAirat1atmand35℃flowsacrossa5.0-cm-diametercylinderatavelocityof50m/s.Thecylindersurfaceismaintainedatatemperatureof150℃.CalculatetheheatlossperunitlengthofthecylinderChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology50SolutionWefirstdeterminetheRenumberandthenfindtheapplicableconstantsfromTable6-2forusewithEquation(6-17).Thepropertiesofairareevaluatedatthefilmlengthofcylinder.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology51FromTable6-2,wehaveChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology526-4FlowAcrossTubeBanksDifferentArrangementofBanksUsually,therearetwokindsofarrangementofbanks,theyareInline&StaggeredFigure6-14In-lineStaggeredChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology53ForStaggeredtubebanks,theyhavebetterheat-transferperformance,buthardtocleanandhavemoreresistanceloss.[6-17]Onthebasisofacorrelationoftheresultsofvariousinvestigators,GrimsonwasabletorepresentdatainformofEquation6-17Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology54NumberoftheRows>10TheRenumberisbasedonthemaximumvelocityoccurringinthetubebank,thatis,thevelocitythroughtheminimum-flowarea.ThevalueofCandnarelistedinthefollowingtableChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology55In-lineStaggeredChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology56ZhukauskassuggestedagroupofformulawhichcouldbeusedforawiderangeofPrnumbersThebulktemperatureTheRenumbersarebasedonOutsidediameterofthetubeandonthevelocitythroughtheminimum-flowarea.RangeofPrnumberChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology57Fornumberoftubebanks<16rows,hesuggestedaratioεEquationsforheat-transferintubebanksof16rowsormore(IN-LINEarrangement)EquationsRangeofRenumberChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology58Equationsforheat-transferintubebanksof16rowsormore(Staggeredarrangement)Raitofortubebanks<16rowsEquationsRangeofReNumberNumberofRowsIn-lineStaggeredChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology596-5Liquid-MetalHeatTransferLet’sfirstconsiderthesimpleflatplatewithaliquidmetalflowingacrossit.ThePrandtlnumberforliquidmetalsisverylow,oftheorderof0.01,sothatthethermal–boundary-layerthicknessshouldbesubstantiallylargerthanthehydrodynamic-boundarylayerthickness.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology60ThissituationresultsfromthehighvaluesofthermalconductivityforconductivityforliquidmetalsandisdepictedinFigure6-15.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology61Sincetheratioofissmall,thevelocityprofilehasaverybluntshapeovermostofthethermalboundarylayer.Asafirstapproximation,then,wemightassumeaslug-flowmodelforcalculationoftheheattransfer;thatis,wetakeThroughoutthethermalboundarylayerforpurposesofcomputingtheenergy-transporttermintheintegralenergyequationChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology62Theconditionsonthetemperatureprofilearethesameasthoseinsection5-6,sothatweusethecubicparabolaasbefore:Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology63InsertingEquationsgivesThatmaybeintegratedtogiveChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology64ThesolutiontothisdifferentialequationsisForaplateheatedoveritsentirelength.Theheat-transfercoefficientmaybeexpressedbyChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology65ItmaybeputindimensionlessformasUsingEquation(5-21)forthehydrodynamic-boundary-layerthickness,Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology66WemaycomputetheratioUsingPr~0.01,weobtainItisthereasonableagreementwithourslug-flowmodel.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology67Itisimportanttonotethattheheat-transferisdependentonthePecletnumber.Empiricalcorrelationsareusuallyexpressedintermsofparameter,fourofwhichwepresentbelow.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology68ConditionsInFullydevelopedturbulentflowofliquidmetalsInsmoothtubesWithuniformheatfluxatwallPropertiesareevaluatedatbulktemperatureValidforChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology69ConditionsIntubeswithconstantwalltemperatureAllpropertiesareevaluatedatbulktemperatureConditionsConstant-heat-fluxconditionValidforChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology70TheheattransferfromaspheretoliquidsodiumForcedconvectionValidforConditionsChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology716-5SummaryEstablishthegeometryofthesituationMakeapreliminarydeterminationofappropriatefluidpropertiesEstablishtheflowregimebycalculatingtheReynoldsorPecletnumberSelectanequationthatfitsthegeometryandflowregimeandreevaluateproperties,ifnecessary,inaccordancewithstipulationsandtheequation.Processtocalculatethevalueofheat-transferrateChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnologyEmpiricalandPracticalRelationsforForced-ConvectionHeatTransfer

72Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology736-1Introduction

ThediscussionandanalysesofChapter5haveshownhowforced-convectionheattransfermaybecalculatedforseveralcasesofpracticalinterest;however,theproblemsconsideredwerethosethatcouldsolvedinananalyticalfashion.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology74But,itisnotalwayspossibletoobtainanalyticalsolutionstoconvectionproblems,andtheindividualisforcedtoresorttoexperimentalmethodstoobtaindesigninformation,aswellastosecurethemoreelusivedatethatincreasethephysicalunderstandingoftheprocess.Whatwehavetodo:Generalizetheresultsofone’sexperimentsinformofsomeempiricalcorrelationChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology75DifficultiesWhichvariablesshouldwemeasure?Whatfunctionalformshouldthedatabeorganizedinto?It’shardandexpensivetodotheexperiments,so,howmanyexperimentsshouldwedo?Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology76SimilarityConsiderationsPurpose:todoresearchontherelationshipbetweensimilarphysicalphenomena.Forsimilarphysicalphenomena:atcorrespondingtimewithcorrespondinglocationonthephysicalquantityrelatedwiththephenomenoncorrespondenceproportional.Forsametypeofphenomena:Phenomenondescribedbydifferentialequationswiththesameformandcontent.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology77CharacteristicsforphysicalphenomenasimilarityThesamecharacteristicnumbersareequalThereissomewhatrelationshipbetweendifferentcharacteristics.ForexampleChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology78TheconditionsforphysicalphenomenasimilaritySameidentifiedcharacteristicnumbersareequalIt’ssimilarforMonodromyconditions,whichincludesinitialconditions,boundaryconditionsandGeometricconditionsChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology79HowtogetdimensionlessgroupsSimilarityConsiderations:Toestablishthecolumnproportioncoefficientbetweenthetwophenomena,relationshipbetweentheexportofthesesimilaritycoefficientandobtainadimensionlessquantitybasedonKnownmathematicaldescriptionofthephysicalphenomena.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology80Phenomenon1：Phenomenon2：mathematicaldescriptionChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology81EstablishsimilarmultiplesRelationshipbetweenthemChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology82BerkeleynumberToobtaindimensionlessgroups

Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology83DimensionalAnalysisIndimensionalanalysis,dimensionalgroupssuchastheReynoldsandPrandtlnumbersarederivedfrompurelydimensionalandfunctionalconsiderations.FundamentalBasisTheoremof,Aconsistentdimensionlessequationshowingtherelationshipbetweenthenphysicalquantitiescouldbetransferredtoarelationshipwhichcontains(n-r)independentdimensionlessgroups.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology84AdvantagesofdimensionlessanalysisSimpleWecanstillobtaindimensionlessgroupswithoutknowingtheDifferentialEquationsFundamentalquantityintheSIUnitsLength[m]，MASS[kg]，time[s]，ELECTRICCURRENT[A]，thermodynamictemperature[K]，amountofsubstance[mol]，luminousintensity[cd]Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology85NowwecomebacktothedifficultiesWhichvariablesshouldwemeasure?

OnlyvariablesthatarecontainedincharacteristicnumbersWhatfunctionalformshouldthedatabeorganizedinto?

ArrangethedataaccordingtotherelationshipbetweenthecharacteristicnumbersIt’shardandexpensivetodotheexperiments,so,howmanyexperimentsshouldwedo?

ModularExperimentsundertheguidanceofthesimilarconsiderationChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology86Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology876-2EmpiricalRelationsForPipeAndTubeFlowCasesofUndevelopedFlowThecasesofundevelopedlaminarflowsystemswherethefluidpropertiesvarywidelywithtemperature,andturbulent-flowsystemsareconsiderablymorecomplicatedbutareofveryimportantpracticalinterestinheatexchangersandassociatedheat-transferequipment.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology88Fordesignandengineeringpurposes,empiricalcorrelationsareusuallyofgreatestpracticalutility.Forlaminarflow,thelengthoftheundevelopedpartundevelopeddeveloped(Averagefrom0tox)Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology89Forturbulentflow,thelengthoftheundevelopedpartundevelopeddeveloped(Averagefrom0tox)Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology90FurtherconsiderationtoBulktemperatureChapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology91FortubeinFigure6-1thetotalenergyaddedcanbeexpressedintermsofbulk-temperaturebyIndifferentialequation,TheTwandTbherearethewallandbulktemperatureattheparticularxlocation.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology92Thetotalheattransfercanalsobeexpressedas[6-3]whereAisthetotalsurfaceareaforheattransfer.BecausebothTwandTbcanvaryalongthelengthofthetube,asuitableaveragingprocessmustbeadoptedforusewithEquation(6-3).Inchapter10we’lldiscussdifferentmethodsfortakingproperaccountoftemperaturevariationsinheatexchangers.Chapter6CollegeofNuclear

Chapter6CollegeofNuclearScienceandTechnology93AtraditionexpressionforcalculationofheattransferinfullydevelopedturbulentflowinsmoothtubesForheatingofthefluidForcoolingofthefluidChapter6CollegeofNuclear

Cha