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Second Thermal and Fluids Engineering  Conference

ISSN: 2379-1748
ISBN: 978-1-56700-430-4

CHEBYSHEV COLLOCATION SPETRAL METHOD FOR RADIATIVE HEAT TRANSFER IN ONE-DIMENSIONAL CYLINDRICAL MEDIUM

Rui-Rui Zhou
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy & Power Engineering, Dalian University of Technology, Dalian 116024, China

Ben-Wen Li
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy & Power Engineering, Dalian University of Technology, Dalian 116024, China

Abstract

A Chebyshev collocation spectral method (CCSM) is developed for solving the radiative transfer equation (RTE) in an infinitely long, axisymmetric cylindrical medium. Both the spatial and angular domains of the RTE are discretized by the CCSM. In order to avoid the singularity on the origin, the Chebyshev Gauss-Lobatto (CGL) grids are adopted along the diameter. An even number of grids are used to exclude the origin. Comparing with the discrete ordinates method (DOM), which has the second order convergence, the CCSM has an exponential convergence in both the spatial and angular directions. To investigate the effect of spatial grid number on the numerical accuracy, the angular grid number is adopted as large as possible. Excellent results can be obtained by the CCSM even using few spatial grid points. For the optical thickness τ0 = 1 , the results of an O(1E-5) accuracy can be obtained by using 12 spatial points. Increasing the grid points by a very small amount is enough for significant improving the quality of the result. When the original spatial number is in the scale of 8 to 14, increasing 3-4 points can improve the accuracy by almost one order. The DOM needs about 100 spatial points to receive an O(1E-4) accuracy, and about triple points to improve the accuracy by one order. The proposed CCSM performs much better than the DOM to obtain accurate results. Moreover, effects of the optical thickness, scattering albedo, degree of anisotropy and wall emissivity on numerical accuracy are investigated.

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