Homogenization of a conductive and radiative heat transfer problem

Grégoire Allaire 1, 2 K. El Ganaoui
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : This paper is devoted to the homogenization of a heat conductionproblem in a periodically perforated domain with a nonlinear andnonlocal boundary condition modeling radiative heat transfer inthe perforations. Because of the critical scaling considered it isessential to use a method of two-scale asymptotic expansionsinside the variational formulation of the problem. We obtain anonlinear homogenized problem of heat conduction with effectivecoefficients which are computed via a cell problem featuring aradiative heat transfer boundary condition. We rigorously justifythis homogenization process for the linearized problem by usingtwo-scale convergence. We perform numerical simulations in twodimensions: we reconstruct an approximate temperature field byadding to the homogenized temperature a corrector term. Thecomputed numerical errors agree with the theoretical predictederrors and prove the effectiveness of our method for multiscalesimulation of conductive and radiative heat transfer problems inperiodically perforated domains.
Type de document :
Article dans une revue
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2009, 7 (3), pp.1148-1170
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Soumis le : dimanche 3 février 2013 - 13:57:59
Dernière modification le : mercredi 14 novembre 2018 - 15:22:35

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  • HAL Id : hal-00784061, version 1

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Grégoire Allaire, K. El Ganaoui. Homogenization of a conductive and radiative heat transfer problem. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2009, 7 (3), pp.1148-1170. 〈hal-00784061〉

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