Treatment Of Radiative Transfer In Glass Melts: Validity Of Rosseland And P-1 Approximations

The Rosseland (or diffusion) approximation for the radiative transfer in glass melts has been widely used in the numerical simulation of flow and heat tranfer in glass furnaces and forming processes. Its validity is not well confirmed, however, and it is necessary to verify to which limit it is applicable. A simple but realistic problem of steadily cooled flowing glass layer is analysed using two Rosseland approximations, one with prescribed boundary temperature and another with Deissler jump boundary condition, and also using the P-1 approximation and an exact solution scheme. The three approximate methods are compared to the exact solution and their validities are scrutinised.