PN solutions of radiative heat transfer in a slab with reflective boundaries

The spherical harmonics method is used to obtain solution for the radiative heat transfer equation for a slab with reflective boundaries. An absorbing, emitting, non-isothermal, gray medium is considered with linearly anisotropic scattering. Under the condition of the thermal equilibrium, the slab boundaries are subjected to specular and diffuse reflection. The analytical form of solutions is obtained for both conservative and non-conservative cases. The accuracy of the method was verified by benchmark comparisons against the solutions of an earlier work performed by the normal-mode expansion technique. The present predictions of heat flux were found to be in good agreement with the benchmark data.