English

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

Analysis of PDEs 2019-02-20 v1

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.]

Keywords

Cite

@article{arxiv.1305.6920,
  title  = {Derivation of a homogenized two-temperature model from the heat equation},
  author = {Laurent Desvillettes and François Golse and Valeria Ricci},
  journal= {arXiv preprint arXiv:1305.6920},
  year   = {2019}
}

Comments

31 pages, no figures