On Galerkin method for solving radiative heat transfer in finite slabs with spatially-variable refractive index

The problem of radiative heat transfer through a finite plane-parallel medium which possesses a continuous transverse spatial variation in refractive index has been solved. Galerkin method is used to have the analytical solution of the integral form of the radiative heat transfer equation, which gives the analytical forms of both the radiation energy density and the net radiant heat flux through the medium. Numerical results are obtained for the reflection and transmission coefficients at the medium boundaries. These results are carried out for isotropic scattering with different thicknesses and different ranges of refractive index. Some obtained results are compared with those calculated by using the Pomraning-Eddington approximation which was previously published, and gave good agreement.