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

Published online by Cambridge University Press:  09 September 2014

Laurent Desvillettes ,
François Golse  and
Valeria Ricci
Laurent Desvillettes
Affiliation:
Ecole Normale Supérieure de Cachan, CMLA, 61 Av. du Pdt. Wilson, 94235 Cachan cedex, France. . desville@cmla.ens-cachan.fr
François Golse
Affiliation:
Ecole Polytechnique, Centre de Mathématiques L. Schwartz, 91128 Palaiseau cedex, France.; francois.golse@math.polytechnique.fr
Valeria Ricci
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy.; valeria.ricci@unipa.it
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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, Collège de France Seminar, vol. II. Paris 1979–1980; vol. 60 of Res. Notes Math. Pitman, Boston, London (1982) 98–138].

Keywords

Heat equationhomogenizationinfinite diffusion limitthermal nonequilibrium models
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 6 , November 2014 , pp. 1583 - 1613
Copyright
© EDP Sciences, SMAI 2014

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