Statistical Approach to Radiative Transfer in the Heterogeneous Media of Thin-Wall Morphology—I: Theory

Abstract

Foams, three-dimensional (3D)-printed cellular and honeycomb structures, and very oblate particles dispersed in a matrix are the examples of heterogeneous media with thin-wall morphology. Phase boundaries can also be considered by this approach. Statistical description is proposed to estimate the effective radiative properties of such media. Three orientation models are studied: (i) isotropic, (ii) surface elements parallel to a plane, and (iii) surface elements parallel to an axis. Radiative transfer equations (RTEs) are obtained and analyzed in the framework of the homogeneous phase approach (HPA) and the multiphase approach (MPA). Analytical expressions are obtained for the absorption, extinction, and scattering coefficients, the scattering phase function, and the radiative thermal conductivity for very oblate particles dispersed in an absorbing scattering matrix. The reflective properties of the platelets and their preferential orientation can be used to optimize the radiative thermal conductivity.