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Derivation of a Homogenized Two-Temperature Model from the Heat Equation

2014

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pitman, Boston, London, 1982.]

01 natural sciencesHomogenization (chemistry)Heat capacity010305 fluids & plasmasTwo temperatureMathematics - Analysis of PDEsThermal nonequilibrium models0103 physical sciencesFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsScalingMSC 35K05 35B2776T05 (35Q79 76M50)35K05 35B27 76T05 (35Q79 76M50)MathematicsNumerical AnalysisHomogenizationPartial differential equationInfinite diffusion limitApplied MathematicsHeat equationMathematical analysis010101 applied mathematicsComputational MathematicsThermal non-equilibrium modelsModeling and SimulationVolume fractionHeat equationAnalysisAnalysis of PDEs (math.AP)
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