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RESEARCH PAPERS: Radiative Heat Transfer

Smoothing Monte Carlo Exchange Factors through Constrained Maximum Likelihood Estimation

[+] Author and Article Information
K. J. Daun1

Department of Mechanical Engineering,The University of Texas at Austin

D. P. Morton, J. R. Howell

Department of Mechanical Engineering,The University of Texas at Austin

1

Present Address: National Research Council, Ottawa, Canada, K1A OR6.

J. Heat Transfer 127(10), 1124-1128 (Apr 20, 2005) (5 pages) doi:10.1115/1.2035111 History: Received November 05, 2004; Revised April 20, 2005

Complex radiant enclosure problems are often best treated by calculating exchange factors through Monte Carlo simulation. Because of its inherent statistical nature, however, these exchange factor estimations contain random errors that cause violations of the reciprocity rule of exchange factors, and consequently the second law of thermodynamics. Heuristically adjusting a set of exchange factors to satisfy reciprocity usually results in a violation of the summation rule of exchange factors and the first law of thermodynamics. This paper presents a method for smoothing exchange factors based on constrained maximum likelihood estimation. This method works by finding the set of exchange factors that maximizes the probability that the observed bundle emissions and absorptions would occur subject to the reciprocity and summation rules of exchange factors as well as a nonnegativity constraint. The technique is validated by using it to smooth the sets of exchange factors corresponding to two three-dimensional radiant enclosure problems.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Enclosure geometry for the first test problem (7). (Surface numbers are circled.)

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Figure 2

RMS error in exchange factor sets for the first test problem

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Figure 3

(a) Enclosure geometry, and (b) computational domain for the second test problem. (Perfectly specular reflecting surfaces are shaded.)

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Figure 4

RMS error in exchange factor sets for the second test problem

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