Development of approximate solutions to radiative transfer in slabs and spheres

The development of an approximate solution to radiative heat transfer in absorbing, emitting and anisotropically scattering media is presented. The method of approach is applied to both plane-parallel and concentric spherical media. The radiative properties are assumed to be gray, with the walls emitting and reflecting the incoming radiant energy, and the temperature is known. The approach is based on the isolation of the discontinuity in the intensity of radiation. Once the discontinuity has been isolated, the equation of radiative transfer is discretized by considering angular intervals over which the intensity is continuous and has continuous derivatives. Results from calculations of the net radiative heat flux and incident radiation at the walls are presented. Good agreement is obtained between the results of this approach and the results calculated using other methods described in the literature.