Combination of spherical harmonics and spectral method for radiative heat transfer in one-dimensional anisotropic scattering medium with graded index

In this paper, the combination of spherical harmonics and spectral method is developed to solve radiative heat transfer in anisotropic scattering medium with graded index. The decomposition of the radiative transfer equation with graded index is deduced to deal with the angular distribution using spherical harmonics method. Then spectral method is employed to implement the spatial discretization. Radiation combined conduction heat transfer model and diffuse irradiation model are considered. The results show that the combination of spherical harmonics and spectral method has a good accuracy, compared with other methods in literatures. It can be seen that refractive index distribution and scattering phase function have important effects on the temperature, radiative heat flux, reflectance and transmittance.