Application of the spatial averaging theorem to radiative heat transfer in two-phase media

The spatial averaging theorem is applied to rigorously derive continuum-scale equations of radiative transfer in two-phase media consisting of arbitrary-type phases in the limit of geometrical optics. The derivations are based on the equations of radiative transfer and the corresponding boundary conditions applied at the discrete-scale to each phase, and on the discrete-scale radiative properties of each phase and the interface between the phases. The derivations confirm that radiative transfer in two-phase media consisting of arbitrary-type phases in the range of geometrical optics can be modeled by a set of two continuum-scale equations of radiative transfer describing the variation of the average intensities associated with each phase. Finally, a Monte Carlo based methodology for the determination of average radiative properties is discussed in the light of previous pertinent studies.