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

Laurent Desvillettes; François Golse; Valeria Ricci

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 6, page 1583-1613
  • ISSN: 0764-583X

Abstract

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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].

How to cite

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Desvillettes, Laurent, Golse, François, and Ricci, Valeria. "Derivation of a homogenized two-temperature model from the heat equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.6 (2014): 1583-1613. <http://eudml.org/doc/273228>.

@article{Desvillettes2014,
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].},
author = {Desvillettes, Laurent, Golse, François, Ricci, Valeria},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {heat equation; homogenization; infinite diffusion limit; thermal nonequilibrium models; two-temperatures model},
language = {eng},
number = {6},
pages = {1583-1613},
publisher = {EDP-Sciences},
title = {Derivation of a homogenized two-temperature model from the heat equation},
url = {http://eudml.org/doc/273228},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Desvillettes, Laurent
AU - Golse, François
AU - Ricci, Valeria
TI - Derivation of a homogenized two-temperature model from the heat equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 6
SP - 1583
EP - 1613
AB - 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].
LA - eng
KW - heat equation; homogenization; infinite diffusion limit; thermal nonequilibrium models; two-temperatures model
UR - http://eudml.org/doc/273228
ER -

References

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