Two-Dimensional Radiation in Absorbing-Emitting Media Using the P-N Approximation

[+] Author and Article Information
A. C. Ratzel

Sandia National Laboratories, Albuquerque, N. M. 87185

J. R. Howell

University of Texas at Austin

J. Heat Transfer 105(2), 333-340 (May 01, 1983) (8 pages) doi:10.1115/1.3245583 History: Received June 21, 1982; Online October 20, 2009


Radiative energy transfer in a gray absorbing and emitting medium is considered in a two-dimensional rectangular enclosure using the P-N differential approximation. The two-dimensional moment of intensity partial differential equations (PDE’s) are combined to yield a single second-order PDE for the P-1 approximation and four coupled second-order PDE’s for the P-3 approximation. P-1 approximation results are obtained from separation of variables solutions, and P-3 results are obtained numerically using successive-over-relaxation methods. The P-N approximation results are compared with numerical Hottel zone results and with results from an approximation method developed by Modest. The studies show that the P-3 approximation can be used to predict emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater. The P-1 approximation is identical to the diffusion solution and is thus applicable only if the medium is optically dense.

Copyright © 1983 by ASME
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