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1、9RadiativeTransferinParticipatingMediaInthelastchapter,surface(orexternal)radiationexchangebetweenthewallsofanenclosurewasconsidered.Animportantassumptionassociatedwithexternalradiativeheattransferisthattheenclosureeitherboundsavacuumorisfilledwithnon-participatingmedia.Amediumisconsidere
2、dparticipatinginradiativethermaltransferifitabsorbs,emits,orscattersathermalrayasittravelsthroughthemedium.Radiativeheattransferinaparticipatingmediumisalsoreferredtoasinternalradiation,whichoccursinmanyengineeringthermalsystems.Anexampleofinternalradiationisahightemperaturecombustiongasm
3、ixture,whichisknowntoabsorb,emit,andscatterthethermalenergy.Anotherexampleisthesemitransparentmeltfromwhichopticalsinglecrystalsarepulledout.Fortheproblemsofradiativetransferinaparticipatingmedium,theabsorption,emissionandscatteringeffectsmustbeconsideredinordertoprovideanaccurateestimate
4、ofthermalenergytransferinthesystem.Thermalradiationinparticipatingmediaisgovernedbytheradiativetransferequation,whichdescribestheenergybalancealongathermalray.Owingtotheimportanceofinternalradiationtransferinthermalengineeringapplications,manynumericaltechniqueshavebeendevelopedtopredictt
5、hephenomenaandtoassistinthermaldesignsinvolvingradiativeheattransfer.Thewidelyusednumericalalgorithmsincludethefinitedifference,discreteordinates,MonteCarlo,zonalmethod,andfiniteelementmethodsaswellasotherapproximationmethodssuchasexponentialkernelapproximation,directnumericalintegration,
6、reductionoftheintegralorder,andtheYLXmethod.Thesemethodshavebeendocumentedindetailintworecentmonographsonradiationheattransfer[1,2].ThischapterdiscussesthediscontinuousGalerkinfiniteelementmethodforthesolutionofthermalradiativetransferproblemsinvolvingparticipatingmedia.Theapplicationofth
7、ediscontinuousmethodtothesolutionoftheinternalradiativeheattransferproblemshasattractedattentiononlyrecently,andtheliteratureisstillexpanding.Itstartswiththedifferential-integralequationgoverningthetransferoftheradiationintensityandtheboundaryconditionsrequiredforth