The ordinate weighting method for solving radiative heat transfer through a Fresnel interface

Refraction of electromagnetic waves at Fresnel interfaces, i.e. the boundaries between media with different refractive indices, is important not only in explaining many natural phenomena but also in radiation heat transfer in energy conversion and combustion systems, such as solar energy, spray cooling and combustion, and the evaporation of liquid fuels in pool fires. This paper presents a novel model for the efficient consideration of Fresnel interfaces in the Finite Volume Method-based solvers of thermal radiation. By conserving the transmitted radiative heat flux at the Fresnel interface, the new model accurately estimates the directional distribution of radiative intensities on the second side of the interface. To do so, a matrix of weighting coefficients is obtained, representing the transferred radiation energy from the control angles on the first side of the Fresnel interface into each control angle on the second side. To assess the accuracy of the novel ordinate weighting method (OWM), its predictions are compared with the analytical solutions that we obtained for one- and two-layer slabs with various combinations of absorption and scattering properties. The validations are shown for normalized heat flux and irradiation, reflectivity, transmissivity, and intensity. The predictions of the OWM show an excellent agreement with the results of the analytical solutions. Compared to Murthy's pixelation method, the OWM method provides better accuracy with lower computational cost. Finally, the sensitivity of the OWM method to uniform and non-uniform directional discretizations, used in the finite volume solution of the radiative heat transfer, is investigated.