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Technical Brief

A New Stabilized Finite Element Formulation for Solving Radiative Transfer Equation

[+] Author and Article Information
L. Zhang

College of Mechanical and Electrical Engineering,
Northeast Forestry University,
26 Hexing Road,
Harbin 150040, China
e-mail: lzhang@nefu.edu.cn

J. M. Zhao

Mem. ASME
School of Energy Science and Engineering,
Harbin Institute of Technology,
92 West Dazhi Street,
Harbin 150001, China
e-mail: jmzhao@hit.edu.cn

L. H. Liu

School of Energy Science and Engineering,
Harbin Institute of Technology,
92 West Dazhi Street,
Harbin 150001, China
e-mail: lhliu@hit.edu.cn

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 12, 2015; final manuscript received February 19, 2016; published online March 22, 2016. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 138(6), 064502 (Mar 22, 2016) (5 pages) Paper No: HT-15-1338; doi: 10.1115/1.4032836 History: Received May 12, 2015; Revised February 19, 2016

A new stabilized finite element formulation for solving radiative transfer equation is presented. It owns the salient feature of least-squares finite element method (LSFEM), i.e., free of the tuning parameter that appears in the streamline upwind/Petrov–Galerkin (SUPG) finite element method. The new finite element formulation is based on a second-order form of the radiative transfer equation. The second-order term will provide essential diffusion as the artificial diffusion introduced in traditional stabilized schemes to ensure stability. The performance of the new method was evaluated using challenging test cases featuring strong medium inhomogeneity and large gradient of radiative intensity field. It is demonstrated to be computationally efficient and capable of solving radiative heat transfer in strongly inhomogeneous media with even better accuracy than the LSFEM, and hence a promising alternative finite element formulation for solving complex radiative transfer problems.

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Figures

Grahic Jump Location
Fig. 1

(a) Solved dimensionless heat flux distribution for slab optical thickness τd  = 0.1, 1, and 10. Inset: configuration of theemitting and absorbing slab surrounded by hot walls. (b) Spatial convergence characteristics of different FEMs for solving the case with τd  = 10.

Grahic Jump Location
Fig. 2

Spatial and angular radiative intensity distributions solved using different FEMs at τd  = 10: (a) exact result, (b) Galerkin FEM, (c) LSFEM, and (d) MSORTE-FEM

Grahic Jump Location
Fig. 3

(a) Configuration and definition of variables for the absorbing inhomogeneous medium. Radiative intensity distribution along the diagonal line of the square medium solved using different FEMs for (b) κ¯a  = 1, (c) κ¯a  = 5, and (d) κ¯a  = 10.

Grahic Jump Location
Fig. 4

The solved dimensionless radiative heat flux distributions along the bottom wall using different FEMs for Case 3. Inset: configuration of the hot enclosure with an emitting and scattering kernel.

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