An Evaluation of the Differential Approximation for Spherically Symmetric Radiative Transfer

The problem of radiative transfer between concentric spheres enclosing a gray gas has been solved for the case of unequal temperature walls with uniform heat generation in the gas by using a differential approximation based upon half-range moments. Comparison of the results with exact calculations illustrates the deficiencies of the differential approximation for the spherically symmetric case. Large errors exist in the optically thin limit for walls of different temperature. Smaller but appreciable errors are also found at all optical depths for equal temperature walls with heat generation in the gas.