On the transient radiative transfer in a one-dimensional planar medium subjected to radiative equilibrium

The transient radiative heat transfer in one-dimensional slabs separated by a participating media is investigated with the finite volume method (FVM). Especially, the transient behavior of the absorbing, emitting, and isotropically scattering medium in radiative equilibrium is examined in terms of temporal and spatial evolutions of the incident radiation, radiative heat flux, and temperature of the medium. Commonly used convection schemes in computational fluid dynamics (CFD) such as step, diamond, 2nd order upwind, QUICK, and CLAM are introduced to capture the physics of the radiative wave propagation. After mathematical formulations for the transient radiative transfer equation (TRTE) are derived, corresponding final discretization equations are summarized by treating the convection terms with a simple step scheme. The present approach is then validated by comparing with published data, and applied to problems of participating medium in cold or radiative equilibrium subjected to continuous diffuse and collimated irradiation. It is found that when the medium is in radiative equilibrium the temporal and spatial evolutions of the radiative behavior is quite different from those in the cold medium.