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

Abstract

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume frac- tion 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 ex- change of heat between the phases are obtained by using homogenization tech- niques 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.]