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

Abstract

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.