The stepwise gray P-1 approximation for multi-dimensional radiative transfer in molecular-gas-particulate mixtures

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Binary Mixtures, Gas-Solid Interfaces, Molecular Gases, Particle Size Distribution, Radiative Transfer, Absorption Spectra, Emission Spectra, Gray Scale, Monte Carlo Method

Scientific paper

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 1D 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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