Nelder-Mead Algorithm Optimization and Galerkin’s Method for Thermal Performance Analysis of Circular Porous Fins with Various Profiles in Fully Wet Conditions

The main objective of this research is to analyze optimization and the thermal performance of circular porous fins with four different profiles, rectangular, convex, triangular, and concave under fully wet conditions. In this research, a linear model was used for the relationship between humidity and temperature. Moreover, modeling was assumed one-dimensional and the temperature changed only in the direction of the radius of the fin. Moreover, the thermal conductivity and heat transfer coefficient were a function of porosity and temperature, respectively. The governing equations were solved using Galerkin’s method, the finite difference method, and the Gauss-Seidel algorithm. In this study, the effects of different parameters including relative humidity, Darcy number, Rayleigh number and porosity on temperature distribution, fin efficiency, and fin effectiveness were investigated. The results showed that the efficiency and effectiveness and heat transfer rate to the base for the rectangular profile were higher than those of other profiles. In this research, the Nelder-Mead algorithm was used for optimization. The results showed that to maintain optimal conditions, the ratio of thickness to fin length should be increased by increasing relative humidity or decreasing the Darcy number, Rayleigh number, and porosity.