P-N approximation for radiative heat transfer in a nongray medium

Using the rectangular model to characterize the specral dependence of the absorption coefficient, the P-N approximation is extended to treat nongray radiative transfer problems in planar media. Specifically, the P-1 and P-3 approximation formulations are developed for a medium with any number of bands. Analytical solutions are derived for the special case of a single-level absorption coefficient. Numerical solutions are obtained for a medium with a two-level absorption coefficient. Comparisons with the available exact solutions for radiative equilibrium show that the P-1 and P-3 approximations generate accurate results. Solutions for internal heat generation are also discussed.