Momentum and heat transfer in helical coils

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1、TheChemicalEngineeringJournal,5(1973)117-1271170ElsevierSequoiaS.A.,Lausanne.PrintedintheNetherlandsMomentumandHeatTransferinHelicalCoilsJOHNM.TARBELLandMICHAELR.SAMUELS*DepartmentofChemicalEngineering,Universit,vofDelaware,Newark,Del.1971I(USA)(Received24July1972)Abstractutionoftheappropriatemoment

2、um(Navier-Stokes)andenergyequations(eqns.(12)-(17))forthegeo-TheequationsofmotionandenergyforflowandheatmetrydepictedinFig.1.Themomentumandenergytransferincurvedtubeshavebeensolvednumericallybyequationsaredecoupledbyassumingthephysicalthealternatingdirection-implicittechnique.Detaileddescriptionsoft

3、hevelocityandtemperatureprofilesasfunctionsofRe,PrandXareprovidedinelucidatingthesignificantroleofsecondaryconvection.Africtionfactorcorrelationwhichproperlyaccountsfortheeffectofcurvatureisdevelopedforapplicationintherange20

4、ationisgivenbelow.f7.964x1O-3A=1.0t8.279x1O-4tRe-f,xI-2.096xlo-Re*Fig.1.Thetoroidalgeometry.ResultsfortheasymptoticNusseltnumberarepropertiestobeindependentoftemperature.ThecomparedwiththerecentexperimentalworkofNavier-Stokesequationsarethensolvedindepen-Dravidetal.andwithKalbandSeadersrecentdently,

5、andtheresultingsteadystatefullydevelopednumericalstudy.ForPr<5,theresultshereareinvelocityprofilesareincorporatedinthesubsequentgoodagreementwithKalbandSeader’sworkandtheirsolutionoftheenergyequation.TheresultsarelimitingNucorrelationsarerecommended.AtlowPrstrictlyapplicabletotoroidalflowandshouldbe

6、thedifferenceinthethermalboundaryconditionssatisfactoryforhelicalcoilsofsmallpitch.usedinthisworkandinthatofKalbandSeaderProfilesforthethreevelocitycomponentsandtheappearstobesigni’cantanddifferencesinlimitingNusecondaryflowstreamfunctionaredeterminedfor33arenoted.OscillationofthelocalNuasafunctiono

7、fcasesinwhichtheaspectratioXisvariedfrom3to30,axialpositionisobservedtobecharacteristicofallandtheReynoldsnumberisvariedupto1723.ThishighPeflows.Thisresultisqualitativelyconfirmedbyrangeofparametersre