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Model of two-temperature convective transfer in porous media

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Abstract

In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an \(\varepsilon \)-periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are \(\varepsilon \)-periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.

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Authors and Affiliations

  1. Université de Rennes 1, I.R.M.A.R, Campus de Beaulieu, 35042, Rennes Cedex, France

    Isabelle Gruais

  2. Inst. Math. “S.Stoilow”, Romanian Academy, P.O. Box 1-764, Bucharest, Romania

    Dan Poliševski

Authors
  1. Isabelle Gruais
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  2. Dan Poliševski
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Correspondence to Isabelle Gruais.

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Gruais, I., Poliševski, D. Model of two-temperature convective transfer in porous media. Z. Angew. Math. Phys. 68, 143 (2017). https://doi.org/10.1007/s00033-017-0889-2

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  • DOI: https://doi.org/10.1007/s00033-017-0889-2

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