The effect of BRDF surface on radiative transfer within a two-dimensional graded index medium

Abstract

The traditional diffuse or specular surface assumption is insufficient to accurately characterize the reflection characteristics of a practical surface under some circumstances, which could cause distinct deviation in radiative heat transfer analysis and temperature measurements. The anisotropic reflection of a real surface can be well featured by the Bidirectional Reflectance Distribution Function (BRDF). This study aims to solve the radiative heat transfer in a two-dimensional non-uniform refractive index and anisotropic scattering medium coupled with the BRDF surface. The Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface (DRESOR) method is extended to deal with this issue. The effect of BRDF surface on the radiative heat flux and radiative intensity is investigated varying with optical thickness and scattering albedo of medium by compared to the corresponding diffuse surface. It is found that the more deviation from the diffuse characteristics the BRDF surface has, the larger difference of the radiative heat flux and intensity between the BRDF and diffuse surface there exits. The increased optical thickness and scattering albedo both decrease the difference of radiative flux on the wall between the BRDF and corresponding diffuse surface. And the influence of the reflection of the BRDF boundaries can be alleviated with thick optical thickness or large scattering capacity in the medium. The results demonstrate that the BRDF surface can impose remarkable impact on the radiative heat transfer, and an appropriate BRDF model should be introduced to be coupled with radiative transfer procedure in the accurate analysis of multi-dimensional radiative transfer problem if the boundary possesses the anisotropic reflection properties.