Approximate solution to radiative transfer in two-dimensional cylindrical media

The development of an approximate solution to radiative transfer in two-dimensional, absorbing, emitting, scattering, cylindrical media is presented. The approach is based on an isolation of the discontinuities of the intensity prior to specifying the set of discrete ordinates. The discontinuities in the intensity or its slope at any point within the medium or at the bounding wall may be because of property variation along a bounding wall or at a corner, or the bounding geometry. The chosen set of discrete ordinates is based on Gaussian quadratures, and integrations are performed over solid angles over which the intensity is continuous and possesses continuous derivatives. Results for the incident radiation and radiative heat flux are presented for different physical configurations, and they are in good agreement with those available in the literature. In particular, approximately an order-of-magnitude fewer unknown intensities are involved in the solution to obtain results of accuracy comparable to the discrete-ordinates method.