A SUBSTITUTE-KERNEL APPROXIMATION FOR RADIATIVE TRANSFER IN A NONGREY GAS NEAR EQUILIBRIUM WITH APPLICATION TO RADIATIVE ACOUSTICS

The equations for radiative transfer in plane-parallel geometries are studied for a nongrey gas near equilibrium. Local thermodynamic equilibrium is assumed in the molecular processes. On the supposition that deviations from a reference state of radiative equilibrium are small, the equation of radiative transfer is linearized. This allows the required integrations over space and spectral frequency to be carried out independently. In analogy to the grey-gas procedures, a nongrey substitute-kernel (or exponential) approximation is then made for certain frequency-integrated transmission functions that occur in the expressions for the heat fluxes. This leads to a purely differential equation for the net radiative flux. The spectral properties appear in the formulation in two functions, which are introduced by the approximation and which depend on the reference state of the gas. These functions are found by analytical matching procedures, which define linearized Planck- and Rosseland-like mean absorption coefficients that are physically meaningful for a general nongrey gas. For use in radiative acoustics, the differential equation for the heat flux is coupled with the linearized equations of gas dynamics. The resulting nongrey equations have the same mathematical structure as the grey equations, which are now contained as a special case. The results of existing grey-gas solutions can therefore be reinterpreted in terms of a nongrey gas by an appropriate normalization. © 1969.