On the Integro-Differential Radiative Conductive Transfer Equation: A Modified Decomposition Method
In this work we present a solution for the radiative conductive transfer equation in spherical geometry. We discuss a semi-analytical approach to the non-linear SN problem, where the solution is constructed by Laplace transform and a decomposition method. In the present discussion, we report on arithmetic stability issues for the recursive scheme. In order to stabilise convergence by virtue of limited arithmetic precision, we propose a modification of the Adomian decomposition method by splitting terms responsible for instability by the specific choice of the source terms in the recursive scheme. This procedure results then in a finite number of modified recursion steps controlled by a splitting parameter α, whereas for all subsequent recursion steps the usual recursion scheme is used. Finally, we report on some case studies with numerical results for the solutions and convergence behaviour.
- [HoEtAl16]Howell, J. R., Menguc, M. P., and Siegel, R.: Thermal Radiation Heat Transfer, CRC Press, New York (2016).Google Scholar
- [ViEtAl11]Vilhena, M. T. M. B., Bodmann, B. E. J., and Segatto, C. F.: Non-linear radiative-conductive heat transfer in a heterogeneous gray plane-parallel participating medium. In: Ahasan, A. (ed.) Convection and Conduction Heat Transfer. InTech, New York (2011).Google Scholar
- [Oz73]Ozisik, M.N.: Radiative Transfer and Interaction with Conductions and Convection, John Wiley & Sons Inc., New York (1973).Google Scholar
- [El09]Elghazaly, A.: Conductive-Radiative Heat Transfer in a Scattering Medium with Angle-Dependent Reflective Boundaries. J. Nucl. Radiation Phys. 4, 31–41 (2009).Google Scholar