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arXiv · 1305.6920

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

Laurent Desvillettes·François Golse·Valeria Ricci
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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: Coll\`ege 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. 2013-05-29. Derivation of a homogenized two-temperature model from the heat equation. https://doi.org/10.1051/m2an%2F2014011

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