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 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: Collège de France Seminar vol. 2 (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pitman, Boston, London, 1982.]
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Laurent Desvillettes, François Golse, Valeria Ricci. Derivation of a homogenized two-temperature model from the heat equation. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2014, 48 (2014), pp.1583-1613. ⟨10.1051/m2an/2014011⟩. ⟨hal-00827912⟩

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