Finite Element Solution of Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure With Gray Participating Media

1983 ◽  
Vol 105 (4) ◽  
pp. 933-936 ◽  
Author(s):  
M. M. Razzaque ◽  
D. E. Klein ◽  
J. R. Howell
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Finite Element Solution ◽  
Two Dimensional ◽  
Element Solution ◽  
Participating Media ◽  
Rectangular Enclosure

Accelerate Iteration of Least-Squares Finite Element Method for Radiative Heat Transfer in Participating Media With Diffusely Reflecting Walls

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Wei An ◽  
Tong Zhu ◽  
NaiPing Gao
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Radiative Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Present Model ◽  
Participating Media ◽  
Element Method

A high reflectivity of walls often leads to prohibitive computation time in the numerical simulation of radiative heat transfer. Such problem becomes very serious in many practical applications, for example, metal processing in high-temperature environment. The present work proposes a modified diffusion synthetic acceleration model to improve the convergence of radiative transfer calculation in participating media with diffusely reflecting boundary. This model adopts the P1 diffusion approximation to rectify the scattering source term of radiative transfer equation and the reflection term of the boundary condition. The corrected formulation for boundary condition is deduced and the algorithm is realized by finite element method. The accuracy of present model is verified by comparing the results with those of Monte Carlo method and finite element method without any accelerative technique. The effects of emissivity of walls and optical thickness on the convergence are investigated. The results indicate that the accuracy of present model is reliable and its accelerative effect is more obvious for the optically thick and scattering dominated media with intensive diffusely reflecting walls.

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