Radiative transfer within strongly non homogeneous porous media: Application to a slab of packed particles

The original radiation transfer model is dedicated to strongly non homogeneous porous media with a transparent phase and an opaque one, characterised by a diffuse reflection law at local scale. It is only based on radiative statistical functions of extinction and scattering and a general phase function, which completely characterise the radiation properties of the medium. The model is a generalisation for these media, under integral formulation, of the Generalised Radiative Transfer Equation (GRTE). A rigorous expression of the emission source term from the radiation reciprocity principle is the key point. The model is developed and applied in the case of a slab of a packed bed of spherical particles, by using a statistical Monte Carlo method. It has been validated by comparison with results of the bibliography in the academic case of purely absorbing media and in the case of optically thick slabs. The model has finally been applied to realistic cases of scattering, absorbing and emitting porous media. The model also accurately accounts for local configurations resulting in non-monotonous temperature profiles.