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Homogenization of a conductive and radiative heat transfer problem

Grégoire Allaire 1, 2 K. El Ganaoui
2 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
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.
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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. ⟨10.1137/080714737⟩. ⟨hal-00784061⟩



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