Variable discrete ordinates method for radiation transfer in plane-parallel semi-transparent media with variable refractive index

•The discrete ordinate method is applied to solve the RTE in semitransparent media.•The number and direction of ordinates are changed locally to consider the curvature of ray paths.•The effects of diffuse-gray walls, optical thickness, and anisotropic scattering are examined.•The results show a good accuracy for arbitrary profiles of refractive index.

The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.