Chebyshev collocation spectral approach for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index. (English) Zbl 1183.80061
Summary: 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.
MSC:
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 78A40 | Waves and radiation in optics and electromagnetic theory |
| 80M22 | Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
Keywords:
combined radiation and conduction heat transfer; semitransparent medium; graded index; Chebyshev collocation spectral methodReferences:
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