Homogenization of a Conductive and Radiative Heat Transfer Problem, Simulation with Cast3m
نویسندگان
چکیده
We are interested in conductive and radiative transfer of energy in the core of gas cooled reactors. Two scales characterize the problem: macroscopic and microscopic. We want to consider the domain like an equivalent homogenous medium. So we use homogenization theory to compute the effective macroscopic properties which take into account the microscopic structure. We first present a full mathematical study of a simpler conduction problem with non linear boundary condition and its simulation with the CEA’s (French Atomic Energy Commissariat) computer code CAST3M. Then we present the homogenization of the real physical problem (including radiative boundary condition). NOMENCLATURE d dimension of the space. σ Stefan-Boltzmann constant. K conductivity matrix. K∗ homogenized conductivity matrix. Ωε perforated periodic domain. Ω non perforated domain. ε period of the domain = size of the cell size of the domain . Γε,i boundary of a given channel i in Ωε. x macroscopic variable. y = xε microscopic variable. Tε temperature, solution of the real problem. T temperature, solution of the homogenized problem. f volumetric source. g Neumann imposed flux. Id identity operator. ress all correspondence to this author.
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