Abstract

The stepwise gray method is the simplest method for incorporating the effects of absorption-emission bands in radiative heat transfer calculations. The non-gray character of the mixture is replaced by an “equivalent” stepwise gray character. A method to obtain this equivalent gray character by utilizing the mean beam length is outlined. This method is coupled with the P-1 approximation, resulting in a simple model to deal with radiation from gas-particulate media in multi-dimensional geometries. To validate the accuracy of the method, it is applied to a few simple 1-D problems, i.e., to isothermal plane-parallel and spherical media as well as to plane-parallel media at radiative equilibrium. Absorption and scattering behavior are studied for both black and gray walls. Results are compared with those obtained from Monte Carlo calculations incorporating the exponential-wide-band model, indicating good accuracy for all conditions studied, within the limitations of the P-1 approximation.

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