Finite element method for radiation heat transfer in multi-dimensional graded index medium

2006 ◽  
Vol 97 (3) ◽  
pp. 436-445 ◽  
Author(s):  
L.H. Liu ◽  
L. Zhang ◽  
H.P. Tan
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Graded Index ◽  
Element Method

Numerical Simulation of Radiation Heat Transfer in a One-Dimensional Graded Index Sphere

2012 ◽  
Vol 430-432 ◽  
pp. 2017-2020
Author(s):  
Lin Zhang ◽  
Shu Yang Wang ◽  
Guo Ling Niu
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Problem ◽  
Radiative Transfer Problem ◽  
Fermat Principle ◽  
One Dimensional ◽  
Graded Index ◽  
Element Method

The rays will propagate along a curved path determined by the Fermat principle in medium with inhomogeneous refractive index distribution. To avoid the complicated computation of ray trajectories, a finite element method is extended to solve the radiative transfer problem in a one-dimensional absorbing-emitting semitransparent spherical graded index medium. A problem of radiative transfer inside a semitransparent spherical graded index medium is taken as an example to verify the method. The predicted temperature distributions are determined by the proposed method, and are compared with the results available in references. The results show that finite element method can predict the radiative heat transfer in one-dimensional absorbing-emitting semitransparent spherical graded index medium accurately.

Discontinuous Galerkin Method for Internal Thermal Radiation Problems

2003 ◽  
Author(s):  
X. Cui ◽  
B. Q. Li
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Integral Differential Equation

The internal thermal radiation phenomena are described by a first-order integral-differential equation, which poses an intrinsic problem for the popular diffusion-based Galerkin finite element method. By allowing for discontinuity across the internal inter-element boundaries, the finite element procedure can be adapted to solve the integral-differential equation. This paper discusses a numerical procedure based on the discontinuous Galerkin method for the solution of radiation heat transfer involving participating media. Detailed formulation using the discontinuous Galerkin method for internal radiation heat transfer calculations is given. The coupling of the method with the conventional finite element method for mixed heat transfer calculations is also presented.

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