Analysis of radiative heat transfer in two-dimensional semitransparent medium with piece-wise constant refractive index

Abstract

In this work, radiative heat transfer in a medium with piece-wise constant refractive index is considered. The interfaces between two different materials are smooth, thus can be treated as Fresnel surfaces. Based on the Fresnel's equations and Snell's law, the interfacial intensity formulas for the whole solid angle space considering Fresnel reflection and refraction phenomena are introduced. To solve the radiative transfer equation, the angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by natural element method. Radiative heat transfer problems in rectangular medium with a circle or rectangular inclusion are studied. The results show that, due to the existence of the Fresnel interface, the radiative heat transfer with piece-wise constant refractive index is much more complicate than the case with uniform refractive index, and obvious discontinuous characteristics are observed on the interface. The refractive index distributions and optical parameters greatly influence the radiative heat transfer. Several interesting phenomenon is observed and analyzed.