Variable discrete ordinates method for radiation transfer in concentric spherical variable index media. (June 2023) - Dehghani, S.; Hosseini Sarvari, S.M.
Highlights: The radiation transfer in concentric spherical media with variable refractive index is simulated. The variable discrete ordinates method is used for solving the radiative transfer equation. The performance of the method is shown by considering continuous-linear, non-linear, and discontinuous profiles of refractive index. The effects of radiative properties are examined for the media with specified temperature and in radiative equilibrium. Abstract: Radiation heat transfer in participating concentric spherical media with variable refractive index along the radial direction is solved by the variable discrete ordinates method. The radiative properties, including refractive index, are assumed to be constant in each volume element, such that a radiative ray travels along straight line in each volume element, and redirects by passing the interface of volume elements according to Snell's law of refraction, or specularly reflects back into the volume element. The radiative transfer equation in spherical coordinates system is solved for different number and direction of ordinates in each volume element. The performance of the present method is examined for two cases with medium's specified temperature and radiative equilibrium with continuous linear, continuous non-linear, and discontinuous profiles of refractive index. The accuracy of the present method is checked by comparing with benchmark solutions. For the cases where the exact solution is not available, the energy conservation criterion is used to validate the solution method. The effects of radiative properties, such as wall emissivities, optical thickness, single scattering albedo, and anisotropy factor are examined by some example problems.