Volume 48, Number 6, November-December 2014
|Page(s)||1583 - 1613|
|Published online||09 September 2014|
Derivation of a homogenized two-temperature model from the heat equation
1 Ecole Normale Supérieure de Cachan,
CMLA, 61 Av. du Pdt.
2 Ecole Polytechnique, Centre de Mathématiques L. Schwartz, 91128 Palaiseau cedex, France.
3 Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy.
Revised: 4 February 2014
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].
Mathematics Subject Classification: 35K05 / 35B27 / 76T05 / 35Q79, 76M50
Key words: Heat equation / homogenization / infinite diffusion limit / thermal nonequilibrium models
© EDP Sciences, SMAI 2014
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