Radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and particles using the modified discrete-ordinates method

The radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and a cloud of particles is investigated by using the combined finite-volume and discrete-ordinates method, named modified discrete-ordinates method (MDOM), which integrates the radiative transfer equation (RTE) over a control volume and a control angle simultaneously like in the finite-volume method (FVM) and treats the angular derivative terms due to spherical geometry as the conventional discrete-ordinates method (DOM). The radiative properties involving non-gray gas and particle behavior are modeled by using the extended weighted sum of gray gases model (WSGGM) with particles. Mathematical formulation and final discretization equations for the RTE are introduced by considering the behavior of a two-phase mixture of non-gray gas and particles in a spherically symmetric concentric enclosure. The present approach is validated by comparing with the results of previous works including gray and non-gray radiative heat transfer. Finally, a detailed investigation of the radiative heat transfer with non-gray gases and/or a two-phase mixture is conducted to examine the dependence of the radiative heat transfer upon temperature ratio between inner and outer spherical enclosure, particle concentration, and particle temperature.