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Estimation and Use of the Radiation Distribution Factor Median for Predicting Uncertainty in the Monte Carlo Ray-Trace Method

In a recent contribution, the authors show that the uncertainty in heat transfer results obtained using the Monte Carlo ray-trace (MCRT) method is related to the median of the radiation distribution factor probability density function (PDF). The value of this discovery would be significantly enhanced if the median could be known a priori without first computing the distribution factors. This would allow the user to determine the number of rays required to achieve the desired accuracy of a subsequent heat transfer analysis. The current contribution presents a correlation for the median of the distribution factor PDF as a function of emissivity and the number of surface elements defining an enclosure. The correlation involves a single parameter whose value is unique for a given enclosure geometry. We find that the radiation behavior of a given enclosure can be classified on a scale ranging from reflection-dominated to geometry-dominated. The correlation is shown to work well for reflection-dominated enclosures but less well for geometry-dominated enclosures.