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Research Papers: Radiative Heat Transfer

Uncertainty Analysis and Experimental Design in the Monte Carlo Ray-Trace Environment

[+] Author and Article Information
Mehran Yarahmadi, J. Robert Mahan

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

Kory J. Priestley

Climate Science Branch,
NASA Langley Research Center
Hampton, VA 23682

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 18, 2018; final manuscript received November 5, 2018; published online January 14, 2019. Assoc. Editor: Yuwen Zhang. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Heat Transfer 141(3), 032701 (Jan 14, 2019) (9 pages) Paper No: HT-18-1451; doi: 10.1115/1.4042365 History: Received July 18, 2018; Revised November 05, 2018

Despite the dominant role of the Monte Carlo ray-trace (MCRT) method in modern radiation heat transfer analysis, the contemporary literature remains surprisingly reticent on the uncertainty of results obtained using it. After first identifying the radiation distribution factor as a population proportion, standard statistical procedures are used to estimate its mean uncertainty, to a stated level of confidence, as a function of the number of surface elements making up the enclosure and the number of rays traced per surface element. This a priori statistical uncertainty is then shown to compare favorably with the observed variability in the distribution factors obtained in an actual MCRT-based analysis. Finally, a formal approach is demonstrated for estimating, to a prescribed level of confidence, the uncertainty in predicted heat transfer. This approach provides a basis for determining the minimum number of rays per surface element required to obtain the desired accuracy.

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References

Mahan, J. R. , 2002, Radiation Heat Transfer: A Statistical Approach, Wiley, New York.
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Figures

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Fig. 1

Exploded view of the cubic enclosure for example problem 1. The three interior surfaces comprising the upper-right section are maintained at 500 K (hot surfaces), and the three interior surfaces comprising the lower-left section are maintained at 300 K (cold surfaces).

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Fig. 2

Average net heat flux distribution for the cold and hot surfaces for example problem 1

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Fig. 3

Comparison for each of the 50 experiments of the observed mean uncertainty (filled symbols) and the observed relative error (open symbols) with the predicted mean uncertainty in the distribution factors (continuous line) for example problem 1

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Fig. 4

Isometric view of oven in example problem 2

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Fig. 5

Net heat flux distributions for the oven and product surfaces for example problem 2

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Fig. 6

Comparison for each of the 50 experiments of the observed mean uncertainty (filled symbols) and the observed relative error (open symbols) with the predicted mean uncertainty in the distribution factors (continuous line) for example problem 2

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Fig. 7

Probability density functions for radiation distribution factors in (a) example problem 1 and (b) example problem 2

Tables

Errata

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