Chebyshev collocation spectral approach for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index

The Chebyshev collocation spectral method for discrete ordinates equation is presented to solve combined radiation and conduction heat transfer problem in semitransparent graded index media. The angular dependence of the problem is discretized by discrete ordinates method, and the space dependence is expressed by Chebyshev polynomial and discretized by collocation spectral method. The exponential convergence characteristic of the spectral methods is studied. The comparisons between the present results and those available in references indicate that, the Chebyshev collocation spectral-discrete ordinates method (SP-DOM so called) for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index is accurate and efficient.