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Journal of Heat Transfer | Volume 129 | Issue 8 | TECHNICAL PAPERS
TECHNICAL PAPERS: Radiative Heat Transfer

Discontinuous Finite Element Approach for Transient Radiative Transfer Equation

[+] Author and Article Information
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

L. J. Liu

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

1

Corresponding author.

J. Heat Transfer 129(8), 1069-1074 (Jan 17, 2007) (6 pages) doi:10.1115/1.2737477 History: Received September 03, 2006; Revised January 17, 2007
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A discontinuous finite element method based on the discrete ordinates equation is extended to solve transient radiative transfer problems in absorbing, emitting, and scattering media. The fully implicit scheme is used to discretize the transient term. Three numerical examples are studied to illustrate the performance of this discontinuous finite element method. The numerical results are compared to the other benchmark approximate solutions. By comparison, the results show that the discontinuous finite element method is efficient, accurate, and stable, and can be used for solving transient radiative transfer problems in participating media. Because the continuity at interelement boundaries is relaxed in discontinuous finite element discretization so that field variable is considered discontinuous across the element boundaries. This feature makes the discontinuous finite element method able to predict the correct propagation speed within medium and accurately capture the sharp drop in the incident radiation and the radiative heat flux at the penetration front.
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Copyright © 2007 by American Society of Mechanical Engineers
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+Element boundary, its unit outward normal vectors, and the neighboring elements
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Element boundary, its unit outward normal vectors, and the neighboring elements
Figure 1

Element boundary, its unit outward normal vectors, and the neighboring elements

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+Relationship of node, boundary, and upwind radiative intensity in one-dimensional linear elements
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Relationship of node, boundary, and upwind radiative intensity in one-dimensional linear elements
Figure 2

Relationship of node, boundary, and upwind radiative intensity in one-dimensional linear elements

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+Dimensionless incident radiation distributions at different dimensionless times
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Dimensionless incident radiation distributions at different dimensionless times
Figure 3

Dimensionless incident radiation distributions at different dimensionless times

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+Dimensionless radiation heat flux distributions at different dimensionless times
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Dimensionless radiation heat flux distributions at different dimensionless times
Figure 4

Dimensionless radiation heat flux distributions at different dimensionless times

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+Effects of dimensionless time step on the solution accuracy for incident radiation
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Effects of dimensionless time step on the solution accuracy for incident radiation
Figure 5

Effects of dimensionless time step on the solution accuracy for incident radiation

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+Dimensionless incident radiation distributions in medium with collimated irradiation at boundary
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Dimensionless incident radiation distributions in medium with collimated irradiation at boundary
Figure 6

Dimensionless incident radiation distributions in medium with collimated irradiation at boundary

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+Dimensionless radiative heat flux distributions in medium with collimated irradiation at boundary
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Dimensionless radiative heat flux distributions in medium with collimated irradiation at boundary
Figure 7

Dimensionless radiative heat flux distributions in medium with collimated irradiation at boundary

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+Schematic and grid system of an irregular quadrilateral enclosure (dimensions in meters)
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Schematic and grid system of an irregular quadrilateral enclosure (dimensions in meters)
Figure 8

Schematic and grid system of an irregular quadrilateral enclosure (dimensions in meters)

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+Relationship of node, boundary, and upwind radiative intensity in triangular elements
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Relationship of node, boundary, and upwind radiative intensity in triangular elements
Figure 9

Relationship of node, boundary, and upwind radiative intensity in triangular elements

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+Transient evolution of dimensionless radiative heat fluxes on the bottom wall
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Transient evolution of dimensionless radiative heat fluxes on the bottom wall
Figure 10

Transient evolution of dimensionless radiative heat fluxes on the bottom wall

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