AN IMPROVED DIFFERENTIAL APPROXIMATION FOR RADIATIVE TRANSFER WITH SPHERICAL SYMMETRY.
Scientific interim rept.,
MARTIN MARIETTA CORP BALTIMORE MD RESEARCH INST FOR ADVANCED STUDIES
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An improved closure condition is used to construct a purely differential equation which, with associated boundary conditions, describes radiative transfer with spherical symmetry. The method is equivalent in degree of complexity to the P4 moment approximation, that is, a spherical harmonic expansion retaining four terms. The improved closing conditions are especially constructed to allow both isotropic radiation and unidirectional, beam-like radiation. The method is applied to the problem of radiative equilibrium of a grey gas between two concentric black spheres maintained at different temperatures. Both radiative heat flux and temperature distribution from the present model are compared to known exact results, and it is shown that trends are correctly predicted by the improved differential approximation in the crucial limit of transparent gas and small inner sphere compared to outer. This is in contrast to both the conventional P2 and P4 moment approximations, which predict qualitatively incorrect results in this limit. Author