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TECHNICAL PAPERS: Radiative Heat Transfer

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

[+] Author and Article Information
J. M. Zhao

School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, P.R. China

L. H. Liu1

School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, P.R. Chinalhliu@hit.edu.cn

1

Corresponding author.

J. Heat Transfer 129(10), 1417-1424 (Feb 05, 2007) (8 pages) doi:10.1115/1.2755061 History: Received October 12, 2006; Revised February 05, 2007

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.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of boundary conditions prescription for the SORTE

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Figure 2

The p-convergence characteristics of the SEM for different values of Planck number

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Figure 3

The h-convergence characteristics of the SEM for different values of Planck number

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Figure 4

The h and the p-convergence rate of the SEM according to total number of solution nodes

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Figure 5

Dimensionless temperature distributions for different scattering conditions and different values of Planck number

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Figure 6

The h- and the p-convergence characteristics of the SEM according to total number of solution nodes for different values of anisotropy factor a1

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Figure 7

Dimensionless temperature distribution along the symmetry line (y∕L=0.5) of the square enclosure

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Figure 8

Skewed meshes with increasing degree of skewness from (a) to (d)

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Figure 9

Relative deviation of the solution from the skewed meshes obtained with different orders of polynomial

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Figure 10

Configuration and two different mesh decomposition of the circular ring (the dots denotes the spectral nodes of fourth order Chebyshev polynomial expansion): (a) good quality mesh (b) poor quality mesh

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Figure 11

Dimensionless temperature distributions along the symmetry line of the circular ring for different values of scattering albedo

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