The multiphase radiation transfer model for two-phase layered systems

Abstract

The multiphase model, where each phase is characterized by its own average radiation intensity, is known to be perspective and useful to take into account the dependent scattering. It has not been applied to statistically anisotropic materials, which is a serious theoretical gap. The system of equations for radiation transfer in layered two-phase systems is derived in the assumption of geometrical optics. No internal scattering in the layers is considered. The obtained model is validated by comparison with the known rigorous solutions for the reflectance/transmittance problem. The results of the model for a single optical window are rigorous in the four limiting cases of small and high internal transmittance and surface reflectivity. The model is not precise but still reasonable at intermediate values of these two parameters. In the case of multiple windows, the initial distribution of the radiative energy between phases has a small impact on the calculated reflectance and transmittance. The variations of the reflectance and transmittance due to the variation of the initial distribution decrease with the number of windows. Chapman–Enskog expansion of the model equations for emitting media gives the generalized Fourier law for radiative heat transfer. Radiative interaction between phases is shown to depend on the specific surface of interfaces. In the case of the same refractive index of the phases and completely transparent interfaces, the radiative thermal conductivity tensor is obtained, and its anisotropy factor is calculated for gray media.