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RESEARCH PAPERS: Radiative Heat Transfer

A New Numerical Procedure for Coupling Radiation in Participating Media With Other Modes of Heat Transfer

[+] Author and Article Information
Sandip Mazumder

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43202mazumder.2@osu.edu

J. Heat Transfer 127(9), 1037-1045 (Apr 01, 2005) (9 pages) doi:10.1115/1.1929780 History: Received December 27, 2004; Revised April 01, 2005

Traditionally, radiation in participating media is coupled to other modes of heat transfer using an iterative procedure in which the overall energy equation (EE) and the radiative transfer equation (RTE) are solved sequentially and repeatedly until both equations converge. Although this explicit coupling approach is convenient from the point of view of computer code development, it is not necessarily the best approach for stability and convergence. A new numerical procedure is presented in which the EE and RTE are implicitly coupled and solved simultaneously, rather than as segregated equations. Depending on the average optical thickness of the medium, it is found that the coupled solution approach results in convergence that is between 2–100 times faster than the segregated solution approach. Several examples in one- and two-dimensional media, both gray and nongray, are presented to corroborate this claim.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Solution procedure used to date to solve combined mode heat transfer problems involving radiation in participating media

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Figure 2

Nondimensional temperature profiles for combined gray radiation conduction in a one-dimensional slab. ε0=εL=1 and τL=κL=1 were used for these calculations

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Figure 3

Comparison of nondimensional temperature profiles computed using the gray and nongray formulations

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Figure 4

Geometry and boundary conditions for the two-dimensional example problem

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Figure 5

Temperature distributions for various cases computed using a 51×51 mesh. Note that the figures have been stretched by a factor of two in the radial direction to enhance clarity. The lower boundary represents the axis of symmetry: (a) nongray radiation with three stepwise boxes and κB=1m−1, (b) nongray radiation with three stepwise boxes and κB=10m−1, and (c) nongray radiation with three stepwise boxes and κB=100m−1.

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