A multi-dimensional differential approximation for absorbing/emittingand anisotropically scattering media with collimated irradiation.

By considering the intensity within a medium to consist of a collimated and a fairly diffuse part, the overall problem of radiative transfer is reduced to two simpler ones: first the collimated intensity is obtained (equivalent in complexity to a nonscattering medium); for the evaluation of the diffuse part of the radiation (due to emission and scattering), a new differential approximation has been developed. To demonstrate the accuracy and simplicity of the present method, two sample cases are presented for which some exact solutions can be found in the literature: results are presented (1) for cosine-varying irradiation incident upon a two-dimensional, isotropically scattering slab and (2) for irradiation with a Gaussian intensity distribution of a two-dimensional, anisotropically scattering semi-infinite cylindrical medium.