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 theinclusions, we derive a coupled system of partial differential equations governing theevolution of the temperature of each phase at a macroscopic level of description. Thecoupling terms describing the exchange of heat between the phases are obtained by usinghomogenization techniques originating from [D. Cioranescu, F. Murat, Collège de FranceSeminar, vol. II. Paris 1979–1980; vol. 60 of Res. Notes Math. Pitman,Boston, London (1982) 98–138].
