On the entropy inequality

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1、OntheEntropyInequalityINGOMOLLERCommunicatedbyJ.L.ERICKSENContentsPage1.Introduction.................................1182.BasicConcepts................................1193.HomogeneousSimpleMaterialswithFadingMemory...............1214.RestrictionsImposedontheConstitutiveEqua

2、tionsfortheEntropyFluxbytheEntropyInequality..................................1255.FurtherRestrictionsbythePrincipleofInvarianceunderSuperposedRigidMotion..1276.MaterialSymmetry..............................1307.HeatConductioninaHomogeneousThermoelasticMaterial............1

3、328.DipolarFluid.................................135Acknowledgements................................141References...................................1411.IntroductionTheThermodynamicsofIrreversibleProcessesasaphenomenologicaltheorydescribingprocessesincontinuawasinitiatedbyE

4、CKART[1]in1940.IndependentlyofECKART'Swork,MEIXNERproposedessentiallythesametheoryinaseriesofpapersbetween1939and1943".Bothauthorsintroduceanequationofbalanceofentropywithpositiveproductiondensity.Animportantfeatureofthisbalanceequationisthattheentropyfluxisassumedtobeequal

5、totheheatfluxdividedbythetemperature,althoughthisrelationdoesnotresultfromthetheory;onecansuggestpossiblymeaningfulgeneralizationsofthisassumption[3].Themotivationforthisrelationrestsuponthedefinitionofentropyinthermo-staticsandonanapproximatecalculationoftheentropyfluxbase

6、donthekinetictheoryofgases.Inrecentyears,COLEMAN&NOLL[4]havedevelopedanimprovedmethodforexploitingtheentropybalance.ThismethodwasappliedtosimplematerialswithfadingmemorybyCOLEMAN[5].Hereagainthepostulateismadethatentropyfluxandheatfluxovertemperatureareequal.Inthepresentpap

7、erthisassumptionisomitted.Instead,weintroduceanindependententropyflux,subjecttoconstitutiveassumptionslikethosemadeforheatflux,internalenergy,stress,andentropy.Byevaluationoftheentropyin-equalityandapplicationofanaturalinvarianceprinciple,wearethenabletoderivearelationbetwe

8、enentropyfluxandheatfluxwhich,forsimplematerialswithfadingmemory,reducestothatusua