Galerkin method for solving combined radiative and conductive heat transfer

This article deals with a numerical solution for combined radiation and conduction heat transfer in a gray absorbing and emitting medium applied to a two-dimensional domain using triangular meshes. The radiative transfer equation was solved using the high order Discontinuous Galerkin method with an upwind numerical flux. The energy equation was discretized using a high order finite element method. Stability and error analysis were performed for the Discontinuous Galerkin method to solve radiative transfer equation. A new algorithm to solve the nonlinear radiative–conductive heat transfer systems was introduced and different types of boundary conditions were considered in numerical simulations. The proposed technique's high performance levels in terms of accuracy and stability are discussed in this paper with numerical examples given.