A generalized successive improvement of the modified differential approximation in participating radiative heat transfer

A generalized successive improvement of the modified differential approximation (MDA) first proposed by Olfe is extended to the treatment of a medium with isotropic scattering and boundary reflection. The method can be used to readily generate successive improvement of solutions. In this work, the procedure is applied to compute the transmissivity and hemispherical reflectivity of an absorbing, isotropically scattering slab with one reflecting boundary. Comparison of present computational results with existing exact solutions shows that, in general, the MDA is superior to the unmodified differential approximation, and that one or two applications of the improvement of the MDA produces results very close to the exact solution. The present method also gives accurate solutions for an optically thin medium. The general concept of the current method appears to be adaptable to the treatment of multi-dimensional cases.