Partition-extrapolation integration applied to radiative transfer in cylindrical media

An integration technique constructed to treat integrands with singularity has been extended to the solutions of the equation of radiative transfer in integral form. To illustrate the technique, radiative transfer is considered in an absorbing and isotropic scattering solid cylinder exposed to diffuse radiation, as well as radiative equilibrium in a participating medium between concentric cylinders with unequal surface temperatures. The integral equations for the two problems are solved by using the collocation method. Since the integral equations have singular kernels, the partition-extrapolation technique is employed. The technique yields estimates of the integration with singularity by extrapolation of the integration results of several subdomains without singularity. Comparisons of the results obtained by the present method with those obtained by the F-N method and the Monte Carlo method show that the partition-extrapolation technique generates accurate results.