Radiative Heat Transfer in Two-Dimensional Cylindrical Medium Coupled with BRDF Surface

Abstract

For radiative heat transfer analysis and temperature measurements, the surface is usually assumed to be blackbody, diffuse, or specular, which may cause obvious errors under actual working conditions. The bidirectional reflectance distribution function (BRDF), which is considered as a relatively strict approach for characterizing a real surface, has been adopted in heat transfer analysis. In this study, two BRDF models—the Minnaert model and the Torrance and Sparrow model—are applied to investigate the effects of different boundary conditions on the radiative heat transfer. Additionally, the distribution of ratios of energy scattered by the medium or reflected by the boundary surface method is extended to solve the radiative transfer in a two-dimensional graded-index medium coupled with BRDF surfaces in a cylindrical coordinate system. The results show that greater deviation of the BRDF surface from the diffuse characteristics yields a larger difference of the radiative heat flux and intensity distributions between the BRDF and the diffuse surface. The radiative heat flux deviation reaches 12.78%, and more significant differences exist in the radiative intensity along some directions under different boundary conditions. The specular reflection plays a leading role at high reflection angles. However, the increased scattering ability can weaken the influence of the reflection of the BRDF on the radiative intensity distributions.