Computational study to predict the thermal performance and optimal design parameters of a T-shaped fin subjected to natural convection

The present paper aims to predict the optimal design parameters of a T-shaped fin subjected to natural convection using constructal theory. Both analytical and computational investigations are performed to determine its thermal performance for a wide range of thermo-physical and geometric parameters. Power law type temperature-dependent heat transfer coefficient is assumed for natural convection. For analytical solution Adomian decomposition method is adopted to evaluate the temperature distribution in both the stem and flange part of the fin. A numerical scheme called finite difference method is implemented to validate the analytical results. The temperature distribution obtained from the computational analysis using ANSYS FLUENT 14.0 is lower than that obtained from the analytical calculations. Moreover, the actual heat transfer rate is also compared between the two methods which reveal that the computational analysis gives higher value as compared to the analytical results. Further, optimization study has also been carried out in a generalized way so that either the fin volume or the heat transfer rate can be taken as a constraint. It is found that with the increase in length ratio, the optimum effectiveness is obtained at a higher value of aspect ratio whereas the optimum efficiency is obtained at a lower value of it. Though, a decrease in thickness ratio predicts a higher value of actual dimensionless heat transfer rate.