A solution for the non-linear SN radiative-conductive problem in a grey plane-parallel participating medium

In the present work an analytical approach to the non-linear SN radiative-conductive transfer problem in plane-parallel geometry using a composite method by the Laplace transform and the Adomian decomposition is discussed. The present study may be considered a guideline on how to distribute the influence of the boundary conditions and the non-linearity in order to solve the SN problem. The resulting scheme is manifest exact and converges in the limit of the complete expansion to the exact analytical solution. Comparison of our findings with solutions in the literature show that the approximate analytical expressions with finite M are valid solutions for conductive-radiative heat transfer.