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1、8ExternalRadiativeHeatTransferThermaltransferbyradiationisanimportantheattransfermechanisminthermalsystems.Unlikeheatconductionandconvection,thermalradiationdoesnotrequiredirectcontactbetweentheheattransferparties.Rather,itisaresultoftheelectromagneticenergyradiatedfromabodya
2、tatemperatureaboveabsolutezero.Ingeneral,thermalradiationproblemsareclassifiedintotwocategories.Thefirstcategoryisconcernedwiththethermalradiationexchangebetweensurfaces,whichinvolvesnointerveningmedia.Thesecondcategorydealswiththethermalradiationtransferthroughabsorbingandsc
3、atteringmedia.Intheheattransferliterature,theformerisoftenreferredtoasexternalradiation,whilethelatterasinternalradiation.Themathematicalformulationsaredifferentforthesetwocategories,andtherefore,naturallyleadtotheuseofdifferentcomputationalapproaches.Thermalradiationproblems
4、canbedifficulttosolve,andthusthereareonlylimitedcaseswheresimplesolutionsarepossible.Formostpracticalapplications,inwhichheatflowsandtemperaturesneedtobefound,numericalsolutionsareoftenneeded,andmayrequireconsiderablecomputationaleffort.Manymethodshavebeenreportedintheliterat
5、ureandanextensivereviewofthemethodsavailabletodayisdocumentedinModest[1]andSiegalandHowell[2].HerewefocusonthenumericalalgorithmsthathavebeendevelopedonthebasisofthediscontinuousGalerkinfiniteelementformulationforthesolutionofthermalradiationproblems.Sincetheexternalandintern
6、althermalradiationproblemsaredescribedusingdifferentmathematicalequations,itisconvenienttodiscussthesubjectintwoconsecutivechapters.Inthischapter,weconsiderthesolutionoftheexternalradiationexchangeproblemsbythediscontinuousGalerkinfiniteelementmethod.Westartwiththebasicconcep
7、tofexternalradiationbetweensurfaces,anddevelopanintegralrepresentationofthesurfaceenergyexchangeinanenclosure,onthebasisofthermalenergybalance.TheuseofthediscontinuousGalerkinmethodforthesolutionoftheintegralequationisthendiscussedfor2-D,2-Daxisymmetricand3-Dgeometries.Perhap
8、sthemostimportantpartofalgorithmdevelopmentforthenumericalsolutionof
