Comparison between local and homogenized models of radiative transfer in a set of parallel ducts considered as a porous medium

A set of parallel ducts of various cross-sections in a diffuse opaque solid medium is modeled as a continuous absorbing and isotropically scattering porous medium. Simple expressions of the absorption and scattering coefficients of this equivalent medium have been determined by identification of the Fourier transforms of the radiative power per unit volume, obtained from the continuous medium model and from a reference local model, in the case of an infinite system. Comparisons of radiative transfer results of the continuous medium model with those of the local model have been carried out for finite configurations typical of combustion applications. Typical discrepancies of a few percent have been observed both for the radiative power per unit volume and boundary radiative flux calculations. The continuous medium model, although practically equivalent to the local model, leads to much faster computation.