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

• The BRDF surface is introduced into the radiative heat transfer within a graded index medium.
• The DRESOR method and the RMC method are extended to solve this problem and verify the accuracy.
• Compared with the diffuse surface, the BRDF surface has a great effect on radiative heat transfer.
• In a real radiative heat transfer analysis, the usage of an appropriate BRDF surface assumption is recommended.

The traditional diffuse or specular surface assumption, which is simple but provides limited information, is insufficient to fully characterize a real surface. The BRDF (Bidirectional Reflectance Distribution Function) surface, which is closer to the real surface, is introduced into the radiative heat transfer problem for the first time. A Minnaert model for the BRDF surface is applied and the genetic algorithm is used to obtain the parameters of the proposed model. The DRESOR (Distribution of Ratios of Energy Scattered by medium Or Reflected by surface) method and the RMC (Reverse Monte Carlo) method are extended to solve the radiative heat transfer within a 1-D absorbing, emitting and scattering graded index medium with BRDF surfaces. The temperature and radiative flux distributions under radiative equilibrium are analyzed under different kinds of graded indexes, optical thicknesses and scattering albedos. The results obtained by the DRESOR method and the RMC method coincide well with each other, which indicates the accuracy of the calculation. Compared with the corresponding diffuse surface, though the relative temperature difference of the BRDF surface is slightly within ±2%, the radiative flux increases significantly by 3.5–12%. And this influence is enhanced by the shortening of the optical thickness while varies little with the changes of graded index and scattering albedo.