Adaptability analysis of radiative transport diffusion approximation in planar-graded-index media

To study the applicability of diffusion approximation method, the influence of the optical thickness, scattering albedo, and wall emissivity of the examined medium on the accuracy of the diffusion approximation is analyzed. The accuracy is determined by comparison with results obtained by using the Monte Carlo method. By calculating the dimensionless radiation heat flux distributions at the bottom of the medium for various parameter combinations, the influence of each optical parameter is analyzed. In addition, the adaptability of the diffusion approximation method to the case of a gradient-index medium is examined. The results show that in the homogeneous-refractive-index medium and the gradient-index medium, the accuracy of diffusion approximation method is improved by an increase in the optical thickness or the scattering albedo and by a decrease in the wall emissivity. Moreover, the maximum relative errors are primarily distributed at the medium boundary and center. In the case of increased optical thickness or decreased wall emissivity, the error of the diffusion approximation method becomes stable and remains at a small value.