Analytical Solution Under Two-Flux Approximation to Radiative Heat Transfer in Absorbing Emitting and Anisotropically Scattering Medium

Radiative transfer in absorbing, emitting, and highly anisotropically scattering media is widely encountered in high temperature applications such as pulverized coal firing furnaces and high temperature thermal protection materials. Efficient and effective solution methods for the transfer process are very crucial, especially in thermal radiation related reverse problems and optimization designs. In this study, the analytical solution for radiative heat transfer in an absorbing, emitting, and anisotropically scattering slab between two parallel gray walls are derived under the two-flux approximation. Explicit expression for the radiative heat flux in a slab is obtained under two-flux approximation. The reliability and adaptability of an analytical solution is examined in case studies by comparing with the Monte Carlo results. Comparative studies indicate that the analytical solution can be used in radiative transfer calculation in an absorbing emitting and anisotropically scattering slab. It is much more applicable in a forward and isotropic scattering slab than in an absorbing one, especially in a forward scattering slab. Because of simplicity and high computing efficiency with the analytical solution, it may be useful in reverse radiative transfer problems, in optimization design, and in developing some numerical schemes on radiative heat transfer.