Analysis of transport of radiative transfer in an inhomogeneous two-layered slab with graded refractive indices and bounded by Fresnel's reflecting walls is carried out using the lattice Boltzmann method. The radiative intensity in each layer is found as a superposition of two radiative waves, which undergo multiple reflections and refractions at the boundaries and interface. The accuracy and efficiency of the methodology is first tested for steady-state problems with constant or variable refractive indices and for time-resolved reflectance and transmittance in a single layer with graded-index. The effect of the governing parameters is examined and the results show that these parameters significantly influence radiative transfer. Especially, the curvature of the incoming beam due to refractive index variation changes when considering the increasing or decreasing variation of the refractive index. The smaller refractive index gap at the interface induces smaller reflection and radiative intensity discontinuity at the interface, while increasing the scattering albedo has no significant effect on the transmittance signal but corresponds to increasing the reflectance signal which takes more time to show the steady state profile. Moreover, the developed LBM is an efficient, powerful, and accurate solver for radiative transport in inhomogeneous layered media with graded-index.
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