Green Function Formulation and Finite Element Discretization for Solving the Heat Radiative Transfer in a Slab

The radiative transport problem involving the nonlinear coupling between temperature and radiative transfer poses several difficulties to be solved numerically. In this paper, we sought numerical solutions for the transient one-dimensional model by applying the Green Function Decomposition Method to the radiative transport equation and a finite element scheme to the energy balance equation. We apply this new numerical implementation to calculate the evolution of temperature in a slab of glass. The proposed scheme has been found computationally efficient and we have achieved better accuracy than the previous results from the literature.