Different methods for calculating a view factor in radiative applications: Strip to in-plane parallel semi-cylinder

Abstract

Determining the shape factor is essential for solving radiative heat transfer problems. An important case that has various applications in the heat power plant systems is calculation of the configuration factor between the fins and the in-plane parallel semi-cylinder. In the present work, Monte Carlo method, Cross string method, and analytical solutions were implemented for this problem. Several simulations were performed by varying semi-cylinders radius and different lengths of the fin. Also, the influence of the number of emitting rays and the number of strips was studied. Considering a fin between two tubes, it is found that calculating the view factor between one tube and a fin is sufficient due to axis symmetry. The results show that at the beginning of fin, analytical solution provides the answer, far from reality. Also, the Cross string solution had differences with Monte Carlo solution, especially for large semi-cylinders radius, but these differences were lower in comparison with the differences between Monte Carlo method and analytical solution. Therefore, the analytical solution for this configuration is almost wrong and is not suggested after this research. Monte Carlo solution had a good approximation for shape factor at all locations across the fin, based on the next discussions in the article. Although for smooth answer without any fluctuations Monte Carlo method needs high emitting rays, this solution has a suitable answer for all parts of the fin as the best solution.