Homogenized models of conduction-advection-radiation heat transfer in porous media. (15th September 2022) - Le, T.D.; Moyne, C.; Sans, M.
Highlights: Upscaled models for conduction-convection-radiation problem in porous media The homogenization technique is used to rigorously derive macroscopic laws Surface-to-surface radiation is investigated for closed and connected-pore systems Radiation effect modifies the effective coefficient in the macroscopic equations Abstract: Upscaled models are derived from the periodic homogenization technique for conduction-convection-radiation problem in porous media for the case of an opaque solid and transparent fluid. Thermal radiation at the pore-scale level is first described through a differential view factor between elementary surfaces. Such heat transfer mode is coupled with the conduction-convection mechanisms by a radiative flux in the fluid phase and a jump of conductive fluxes at the solid/fluid interface. In the framework of the periodic homogenization procedure, a macroscopic model is built with upscaled effective coefficients. Both cases of closed and open pores are studied. In the second case the radiative transfer cannot be restricted to the central unit cell. The radiation at the macroscale only affects the effective conductivity. The validity of the approach is illustrated by some simple examples. The main objective of this work is to establish the macroscopic equation form of the conduction-convection-radiation problem and to understand how the radiation affects the macroscopic behavior.