Finite element solution of radiative transfer across a slab with variable spatial refractive index

To avoid the complicated computation of ray trajectories, a finite element formulation is developed to solve the radiative transfer problem in a one-dimensional absorbing–emitting–scattering semitransparent slab with variable spatial refractive index. A problem of radiative equilibrium is taken as an example to verify this finite element formulation. The predicted temperature distributions are determined by the proposed method and compared with the data in references. The results show that the finite element formulation presented in this paper has good accuracy in solving the radiative transfer in one-dimensional absorbing–emitting–scattering semitransparent medium with variable spatial refractive index.