Derivation of a homogenized two-temperature model from the heat equation

Laurent Desvillettes, François Golse, Valeria Ricci
2014 Mathematical Modelling and Numerical Analysis  
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.
more » ... 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.]
doi:10.1051/m2an/2014011 fatcat:anz5rrwiavbn7i76kaqvs4h3za