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Technical Briefs

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

[+] Author and Article Information
Wei An1

College of Mechanical Engineering,  TongJi University, 200092 Shanghai, P.R. Chinaanweihit@gmail.com

Tong Zhu, NaiPing Gao

College of Mechanical Engineering,  TongJi University, 200092 Shanghai, P.R. Chinaanweihit@gmail.com

1

Corresponding author.

J. Heat Transfer 134(4), 044502 (Feb 16, 2012) (5 pages) doi:10.1115/1.4005165 History: Received January 26, 2011; Revised August 08, 2011; Published February 16, 2012; Online February 16, 2012

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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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The comparison of nondimensional radiative flux on the bottom wall for different emissivity of walls

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Figure 2

The comparison of nondimensional radiative flux on the top wall for different optical thickness of media

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Figure 3

Irregular enclosure and spatial mesh of FEM: (a) schematic diagram; (b) unstructured mesh; and (c) structured mesh

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Figure 4

The nondimensional radiative flux on the bottom wall of irregular enclosure

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