Spectral Element Approach for Coupled Radiative and Conductive Heat Transfer in Semitransparent Medium

A spectral element method is presented to solve coupled radiative and conductive heat transfer problems in multidimensional semitransparent medium. The solution of radiative energy source is based on a second order radiative transfer equation. Both the second order radiative transfer equation and the heat diffusion equation are discretized by spectral element approach. Four various test problems are taken as examples to verify the performance of the spectral element method. The $h$-and the $p$-convergence characteristics of the spectral element method are studied. The convergence rate of $p$ refinement for different values of Planck number follows the exponential law and is superior to that of $h$ refinement. The spectral element method has good property to tolerate skewed meshes. The predicted dimensionless temperature distributions determined by the spectral element method agree well with the results in references. The presented method is very effective to solve coupled radiative and conductive heat transfer in semitransparent medium with complex configurations and demands little on the quality of mesh.