Homogenization of a Conductive, Convective, and Radiative Heat Transfer Problem in a Heterogeneous Domain

We are interested in the homogenization of heat transfer in periodic porous media where the fluid part is made of long thin parallel cylinders, the diameter of which is of the same order as the period. The heat is transported by conduction in the solid part of the domain and by conduction, convection, and radiative transfer in the fluid part (the cylinders). A nonlocal boundary condition models the radiative heat transfer on the cylinder walls. To obtain the homogenized problem we first use a formal two-scale asymptotic expansion method. The resulting effective model is a convection-diffusion equation posed in a homogeneous domain with homogenized coefficients evaluated by solving so-called cell problems where radiative transfer is taken into account. In a second step we rigorously justify the homogenization process by using the notion of two-scale convergence. One feature of this work is that it combines homogenization with a three dimensional (3D) to two dimensional (2D) asymptotic analysis since the ra...

[1]  U. Hornung.  Homogenization and porous media , 1996 .

[2]  A. A. Amosov,et al.  Stationary nonlinear nonlocal problem of radiative–conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency , 2010 .

[3]  G. Allaire.  Homogenization and two-scale convergence , 1992 .

[4]  Alain Damlamian,et al.  Two-Scale Convergence On Periodic Surfaces And Applications , 1995 .

[5]  P. Donato,et al.  An introduction to homogenization , 2000 .

[6]  G. Allaire,et al.  Homogenization of the Neumann problem with nonisolated holes , 1993 .

[7]  G. D. Maso,et al.  An Introduction to-convergence , 1993 .

[8]  Jacques-Louis Lions,et al.  Some Methods in the Mathematical Analysis of Systems and Their Control , 1981 .

[9]  Philippe G. Ciarlet,et al.  Plates And Junctions In Elastic Multi-Structures , 1990 .

[10]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[11]  Pierre Charrier,et al.  Asymptotic Transport Models for Heat and Mass Transfer in Reactive Porous Media , 2003, Multiscale Model. Simul..

[12]  A. Amosov,et al.  Nonstationary nonlinear nonlocal problem of radiative–conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency , 2010 .

[13]  Luc Tartar,et al.  The General Theory of Homogenization: A Personalized Introduction , 2009 .

[14]  N. Bakhvalov,et al.  Homogenisation: Averaging Processes in Periodic Media , 1989 .

[15]  Karima El Ganaoui.  Homogénéisation de modèles de transferts thermiques et radiatifs : application au coeur des réacteurs à caloporteur gaz , 2006 .

[16]  Patrizia Donato,et al.  On the homogenization of some nonlinear problems in perforated domains , 1990 .

[17]  V. Zhikov,et al.  Homogenization of Differential Operators and Integral Functionals , 1994 .

[18]  P. Heckbert.  Simulating Global Illumination Using Adaptive Meshing , 1991 .

[19]  G. Nguetseng.  A general convergence result for a functional related to the theory of homogenization , 1989 .

[20]  G. Rybicki.  Radiative transfer , 2019, Climate Change and Terrestrial Ecosystem Modeling.

[21]  Doina Cioranescu,et al.  Asymptotic behavior of elliptic problems in perforated domains with nonlinear boundary conditions , 2007, Asymptot. Anal..

[22]  E. Sanchez-Palencia.  Non-Homogeneous Media and Vibration Theory , 1980 .

[23]  Grégoire Allaire,et al.  Homogenization of a Conductive and Radiative Heat Transfer Problem , 2008, Multiscale Model. Simul..

[24]  Maria Neuss-Radu,et al.  Some extensions of two-scale convergence , 1996 .

[25]  M. Modest.  Radiative heat transfer , 1993 .