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1、FullyDevelopedHeatTransfertoFluidFlowinRectangularPassagesFilledWithPorousMaterialsA.Haji-SheikhDepartmentofMechanicalandAerospaceThisisatheoreticalandnumericalstudyoffullydevelopedforcedconvectioninvariousEngineering,rectangularducts.Eachductis?lledwithporousmaterialsandtheBrinkmanmode
2、lTheUniversityofTexasatArlington,describesthelaminar?uid?owinsidethisfullysaturatedporouspassage.AFourierArlington,TX76019-0023seriessolutionprovidestheexactsolutionforthevelocity?eld.Also,aFourierseriessolutioncanproducethetemperaturepro?leforaconditionofconstantenergyinputperunitlengt
3、h.Thisincludestwodifferentwallconditions:auniformwalltemperatureatanyaxiallocationandalocallyuniformheat?uxovertheboundary.Thecaseofconstantwalltemperatureovertheentirepassageisalsoaccommodatedusingaspecialanalytical/numericalsolution.DOI:10.1115/1.2188507Keywords:duct?ow,porousmedia,
4、fullydeveloped,forcedconvection,rectangularducts1Introduction2u2upe2+2?u?=01Astudyof?owinrectangularporouspassagesisofinterestinyzKxavarietyofheattransferapplicationssuchaselectroniccooling.withaconstantpressuregradient=?p/x.Inthisequation,theThefundamentalsofsteady?owinp
5、orousmediaarereportedin1D4.Recently,comprehensivestudiesofheattransferindevel-effectiveviscosityise,the?uidviscosityis,andtheperme-opingsectionsofporousplatechannelsandcirculartubesareabilityisK.UsingainFig.1asthecharacteristiclength,Eq.1,reportedintheliterature,e.g,5D9.indimens
6、ionlessform,becomesThispaperstudiesthefullydevelopedtemperatureTeldsin2ˉu2ˉu1rectangularchannelswithclassicalboundaryconditions.These+?ˉu+1=02boundaryconditionsforfree?owinrectangularductsarewellˉy2ˉz2MDadocumentedintheliterature.Forthelocallyconstantwallheatwhereˉy=y/a,ˉz=z/a,M
7、=/,ˉu=u/a2,andDa=K/a2is?uxattheboundaries,SparrowandSiegel10studiedthevaria-eetionsoftheheattransfercoefTcientinrectangularducts.AnothertheDarcynumber.Theboundaryconditionsareˉu0atˉy=±1andmodelthathasbeenstudiedconsiderstheheat?uxperunitlengthatˉz=±ˉb=±b/awhileˉu/ˉy=
