http://www.paper.edu.cnTheApplicationofNumericalSimulationintheDeterminationofThermalconductivityofMetalsandAlloys1YingYangJieminZhouSchoolofEnergyandPowerEngineeringSchoolofEnergyandPowerEngineeringCentralSouthUniversityCentralSouthUniversityChangsha,Hunan,PRC410083Changsha,Hunan,PRC410083yangying_csu@hotmail.comProf_zhou@hotmail.comyangying_csu@126.comAbstractInthisresearch,atransientexperimentalsystemwasdesignedtodeterminethethermalconductivityofthemetalsandalloyswhosetheoreticalfoundationwasanaxialperiodicheatflowtechnique.Meanwhile,mathematiccalculationwasappliedtointuitivelysimulatetheheattransferandtemperatureperiodicchangeprocess�tocorrecttheerrorandthentoincreasetheresultprecisiontosomeextent.Inverificationexperiment,comparedwiththerecommendeddatafromreference,theerrorofthecorrectedexperimentalresultsiswithin�5%atthetemperaturerangeof300~800K�whichmeansthecompetitivemethodandthemeasuringsystemhavethecomparativereliability.Theresearchonthemethodandthemeasuringsystemwillpavethewaytothesubsequentresearchonthemetalsandnewalloyssuchaslead-freeeutecticsolders.1IntroductionAlthoughsometraditionalmetalandalloyssuchaslead,Sn-Pbsoldersplayedadominantroleinjointingtechniqueofallelectronicspackagingindustryduringthepastseveraldecadesbecauseoftheirbetterphysicalperformances,itisaninevitableinternationaltrendtodevelopthereplacersofleadsolderoutoftheconsiderationofenvironmentalprotectionandsociallong-termbenefit[1],[2].ItisessentialforthepromisingreplacerstohaveenoughandcredibledatatoverifytheequalorbetterreliabilityandtheoverallperformancesascomparedwiththeSn-Pbsolders.Withsuchapurpose,atransientexperimentalsystemwasdesignedinthisresearchtodeterminethethermalconductivityofthemetalsandalloyswhosetheoreticalfoundationwasanaxialperiodicheatflowtechnique[3],[4].Meanwhile,numericalmethodwasappliedtoanalysistheheattransferandthedeviationfromtheidealconditionandthentomodifytheinitialexperimentalresults.Itisasignificantattemptonacquiringmoreprecisedeterminingresultbycombiningexperimentaldeterminingandnumericalanalysis.2Experimentalprincipleandinstrument2.1MethodsformeasuringthermalconductivityBasedupontheassumptionsthatthespecimencouldbeconsideredasasemi-infinitebodyandtheheatconductionprocessinitisofonedimensionthethermaldiffusivityofthespecimencouldbecalculatedby1SupportbytheSpecialFoundationforDoctorateDisciplineofChina(ContractNo.:20010533009)http://www.paper.edu.cnmeasuringthedecreasingamplitudeorincreasingphaselagbetweenthedifferentpositionsastheheatwavepropagatedthroughthespecimensinitsaxialdirection.Whentheoneendofthespecimenwasexposedtoaperiodicheatflow,thethermaldiffusivityprocesscouldbeformulatedmathematically[5],[6]as()()224tXPaL∆∆=π(1)()()1222lnθθπPXaa∆=(2)whereaListhermaldiffusivityduetothephaselag,m2�s-1;aaisthermaldiffusivityduetoamplitudedecrement,m2�s-1;Pistheperiodofthewaveofaxialheatflow,s;X∆isaxialdistancebetweenthethermocouples,m;t∆isthephasetimelag,sand�1,���areamplitudeatthermocouple1,2,K.Thevaluesofthediffusivity,calculatedfromtheexpression,maydifferfromeachotherduetoradicalheattransferbetweenthespecimenandthesurroundings,whichcanbetakenintoaccountbyacorrectionfactor,()()12ln2θθπPtFL∆=(3)andLaFF1=(4)whereFL,FaarethecorrectionfactorsofaL,aa.ThecorrectedvalueisevaluatedbyLLFaa=oraaFaa=.Theothercorrectioncanbedescribedbyfollowingequation()...
