On the use of the Rosseland and Planck mean absorption coefficients in the non-equilibrium radiative transfer equation

The use of the Rosseland and Planck mean absorption coefficients in the non-equilibrium (time-dependent) radiative transfer equation is investigated in the gray approximation for a prescribed temperature distribution. The corresponding gray radiative flux at the surface of a halfspace is compared to an exact (multi-frequency) solution obtained from multiple collision theory. An improved mean absorption coefficient is then obtained using the exact angle integrated intensity at the surface, and the corresponding gray approximation is shown to be markedly accurate.