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1、12FluidFlowandHeatTransferinElectromagneticFieldsInmanythermalandfluidssystems,externalfieldssuchastheelectromagneticfieldsareimposedtoachieveacertaindesiredperformancethroughtheinteractionofthefluids,orfluidmotionwiththeimposedfields.Practicalsystemsincludeinductionandm
2、icrowaveheating,electromagneticstirring,magneticcontrolofturbulentflowsandthermalfluctuations,plasmaspayingandmicroactuationinfluidicdevices,etc.Strictlyspeaking,thegeneral,rigorousmathematicaldescriptionoftheelectromagneticfieldinamovingmediumanditsmutualcouplingwiththe
3、thermalfieldandfluidmotionsinthemediumshouldbemadewithintheframeworkofEinstein’srelativistictheory.Formostengineeringapplications,however,thespeedofthemotionismuchsmallerthanthatofthelight,andthusthecommonlyknownmagnetohydrodynamictheoryprovidesanadequatetheoreticalbasis
4、forthedescriptionoftheelectromagnetic,thermalandfluidflowfieldsandtheirinteractions.ThemagnetohydrodynamicequationsareanonlinearsetconsistingoftheMaxwellequations,theNavier-Stokesequationsandthethermalandspeciestransportequations,withthecouplingbetweenthefieldsmadethroug
5、hconstitutiverelationsandsources/sinks.Inordertoaccuratelyinterpretthebehaviorofanelectromagneticallyassistedthermalfluidsystemforbothfundamentalunderstandingandprocessdesign,informationonthedistributionofthethermal,fluidflowandelectromagneticfieldsisrequired.Thisinturnr
6、equiresthesolutionofthemagnetohydrodynamicgoverningequations.Thusfar,wehavediscussedextensivelytheapplicationofthediscontinuousfiniteelementmethodstothesolutionofthethermalandfluidflowequationsforvarioussystems.Thesemethods,aswillbeshownbelow,maybeappliedwithstraightforw
7、ardmodificationsinthesource/sinkterms,fortheanalysisofthermalandfluidflowsystemsundertheinfluenceofanelectromagneticfield.ThesolutionoftheMaxwellequationsisasubjectofcomputationalelectromagneticsandmanydifferenttechniques,bothanalyticalandnumerical,havebeendeveloped.Rece
8、ntly,thediscontinuousfiniteelementformulationhasalsobeenextendedtosolvethecompletesetoftheMaxwellequati
