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

This work studies the heat equation in a two-phase material withspherical inclusions. Under some appropriate scaling on the size, volume frac-tion and heat capacity of the inclusions, we derive a coupled system of partialdifferential equations governing the evolution of the temperature of each phaseat a macroscopic level of description. The coupling terms describing the ex-change of heat between the phases are obtained by using homogenization tech-niques originating from [D. Cioranescu, F. Murat: Coll`ege de France Seminarvol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98–138. Pitman,Boston, London, 1982.]