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1、FullyDevelopedHeatTransfertoFluidFlowinRectangularPassagesFilledWithPorousMaterialsA.Haji-SheikhDepartmentofMechanicalandAerospaceThisisatheoreticalandnumericalstudyoffullydevelopedforcedconvectioninvariousEngineering,rectangularducts.EachductisfilledwithporousmaterialsandtheBrinkmanmode
2、lTheUniversityofTexasatArlington,describesthelaminarfluidflowinsidethisfullysaturatedporouspassage.AFourierArlington,TX76019-0023seriessolutionprovidestheexactsolutionforthevelocityfield.Also,aFourierseriessolutioncanproducethetemperatureprofileforaconditionofconstantenergyinputperunitlengt
3、h.Thisincludestwodifferentwallconditions:auniformwalltemperatureatanyaxiallocationandalocallyuniformheatfluxovertheboundary.Thecaseofconstantwalltemperatureovertheentirepassageisalsoaccommodatedusingaspecialanalytical/numericalsolution.DOI:10.1115/1.2188507Keywords:ductflow,porousmedia,
4、fullydeveloped,forcedconvection,rectangularducts1Introduction2u2upe2+2−u−=01AstudyofßowinrectangularporouspassagesisofinterestinyzKxavarietyofheattransferapplicationssuchaselectroniccooling.withaconstantpressuregradient=−p/x.Inthisequation,theThefundamentalsofsteadyßowinp
5、orousmediaarereportedin1Ð4.Recently,comprehensivestudiesofheattransferindevel-effectiveviscosityise,theßuidviscosityis,andtheperme-opingsectionsofporousplatechannelsandcirculartubesareabilityisK.UsingainFig.1asthecharacteristiclength,Eq.1,reportedintheliterature,e.g,5Ð9.indimens
6、ionlessform,becomesThispaperstudiesthefullydevelopedtemperatureÞeldsin2¯u2¯u1rectangularchannelswithclassicalboundaryconditions.These+−¯u+1=02boundaryconditionsforfreeßowinrectangularductsarewell¯y2¯z2MDadocumentedintheliterature.Forthelocallyconstantwallheatwhere¯y=y/a,¯z=z/a,M
7、=/,¯u=u/a2,andDa=K/a2isßuxattheboundaries,SparrowandSiegel10studiedthevaria-eetionsoftheheattransfercoefÞcientinrectangularducts.AnothertheDarcynumber.Theboundaryconditionsare¯u0at¯y=±1andmodelthathasbeenstudiedconsiderstheheatßuxperunitlengthat¯z=±¯b=±b/awhile¯u/¯y=
