The radiative conductive transfer equation in cylinder geometry: Semi-analytical solution and a point analysis of convergence

Highlights: • The radiative conductive transfer equation in cylinder geometry was solved for a solid cylinder. • The solution was obtained for the SN approximation in a semi-analytical fashion. • Consistency and stable convergence of the recursive solution are discussed. • The parameter dependence on convergence was analised. • Numerical results were compared to results in the literature and novel results were obtained. In this work we present a solution for the radiative conductive transfer equation in cylinder geometry for a solid cylinder. We discuss a semi-analytical approach to the non-linear S_N problem, where the solution is constructed by Laplace transform and a decomposition method. In the present work we prove consistency and convergence of the discussed solution inspired by stability analysis criteria and taking into account the influence of the parameter sets. Finally, we report on some problem studies with numerical results for the solutions and convergence behaviour. Some of the results are compared with available data in the literature.