The S-N discrete ordinates method is applied to analyze radiative heat transfer in nongray gases. Spectral correlation between the terms in the equation of transfer is considered for black or nearly nonreflecting walls. Formulations to apply the S-N method using a narrow-band or the exponential wide-band model are presented. The net radiative wall heat fluxes and the radiative source distributions are obtained for uniform, parabolic, and boundary layer type temperature profiles, as well as for a parabolic concentration profile. The narrow- and wide-band nongray solutions are compared with gray-band approximations using the same band models. The computational speed of the gray-band approximation is obtained at the expense of accuracy in the internal fluxes and radiative source distributions. The wall radiative flux predictions by the gray-band approximation are satisfactory.

The full anisotropic scattering solutions of the radiative equation of transfer are compared with the scaled isotropic scattering solutions. Square enclosures with a collimated incidence, a diffuse incidence, or an isothermal emission are considered for comparison. The isotropic scaling approximation is found to predict accurately the radiative flux and the average incident radiation for the isothermal emission problem and for most diffuse incidence problems. For the collimated incidence problem, the isotropic scaling solutions are acceptable only for weakly scattering media. For large scattering albedo the error in the isotropic scaling is appreciable for the diffuse incidence problem and unacceptably large for the collimated incidence problem. The largest error in the y-direction net flux is found at the side wall regions when the medium is purely scattering. The isothermal emission problem or problems with symmetric boundary conditions can be accurately modeled by a scaled isotropic phase function, since the effect of the phase function anisotropy is negligible in such problems.

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A modified δ-M scaling method, which adjusts the δ-M scaled phase functions to be always positive, is applied to radiative transfer problems in two-dimensional square enclosures. The scaled anisotropic results are compared with the results obtained from an accurate model of the full anisotropic scattering problems using the S-N discrete ordinates method. The modified δ-M anisotropic scaling is shown to improve the isotropic scaled results of a collimated incidence problem, but the required number of terms increases as the phase function complexity and the asymmetry factor increase. For the diffuse incidence problems, even a low-order modified δ-M phase function significantly improves the accuracy of scaled solutions over the isotropic scaling. Significant savings in the computer times are observed when the modified δ-M method is applied.

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