The DRESOR method for one-dimensional transient radiative transfer in graded index medium coupled with BRDF surface

Most research on transient radiative transfer is coupled with blackbody, specular or diffuse surface, which may only provide limited or inefficient information to analyze transient radiation transfer problems under particular circumstances. This study aims to extend the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to solve the transient radiative heat transfer in a one-dimensional, non-emitting, absorbing and isotropically scattering medium with a linear graded index coupled with the BRDF (Bidirectional Reflectance Distribution Function) surface, which is closer to a real surface and can offer more accurate information. Here, a Minnaert model for the BRDF surface is applied. Numerically computed results of the time-resolved reflectance and transmittance are compared with those obtained by DOM and DFEM with blackbody surfaces, which verifies the DRESOR method. Meanwhile, the comparison between BRDF surface and diffuse surface has also been carried out. With the increase of optical thickness, the time-resolved reflectance and transmittance profiles change from a single peak, to a double-peak, and finally to a single peak with a relatively large scattering albedo, especially under the graded index. The scattering albedo has a significant influence on the peak values of the reflectance and transmittance. With the increase of parameter k of Minnaert model, the difference between BRDF surface and diffuse surface enlarges significantly. Furthermore, compared with the corresponding diffuse surface, the relative time-resolved reflectance difference of the BRDF surface can reach 16.7% and the transmittance can reach 7.4% at some dimensionless time. The intensities with the change of time in some directions show an evident difference between BRDF and diffuse surface. These discrepancies imply that the BRDF surface has an important influence on the transient radiative transfer.