Choice of an Appropriate Mean Absorption Coefficient for Use in the General Grey Gas Equations

摘要

An approximate method for conveniently treating radiative transport in the intermediate regime in which a gas is neither optically thin nor optically thick is described. The method consists of using the general grey gas equations with the mean absorption coefficient chosen to be a function of optical thickness such that it decreases monotonically with increase in optical depth from the Planck mean absorption coefficient K sub P when the gas is very optically thin to the Rosseland mean absorption coefficient K sub R when the gas is very optically thick. Numerical results for the flux and the divergence of the flux obtained by this approximate method are compared with those obtained by an exact treatment for various optical thicknesses assuming free-free absorption and a linear temperature gradient. In this case where the frequency dependence of the absorption coefficient is strong enough that K sub P is approximately 30 K sub R, the results by our approximate method are nearly always within a factor of 2 of the correct values. (Author)