Discrete-ordinate solutions for radiative transfer in a cylindrical enclosure with Fresnel boundaries

This work considers radiative heat transfer in a 2-D cylindrical scattering medium with Fresnel boundaries. The present analysis divides the radiative intensity into the attenuated incident and in-scattering components, solves the resulting problem of the former analytically, and that of the latter by the discrete-ordinale method (DOM). In addition, the present analysis rationalizes the distribution of the quadrature points used by the DOM to treat relevantly the strongly angular dependence of radiative intensity around the critical angles. Comparisons of the results obtained by the different methods show that the above techniques can improve the discrete-ordinale solutions. The present results reveal that the gradient of radiative heat flux in a cylindrical medium with Fresnel boundaries may vary abruptly at some locations.