Nelder-Mead algorithm optimization and Galerkin’s method 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. Also, modeling is assumed one-dimensional and the temperature changes only in the direction of the radius of the fin. Moreover, the thermal conductivity and heat transfer coefficient are a function of porosity and temperature, respectively. The governing equations are solved using the Galerkin method and the finite difference method and the use of the Gauss-Seidel algorithm. In this study, the effect of different parameters including relative humidity, Darcy number and Rayleigh number and porosity on temperature distribution, fin efficiency, and fin effectiveness was investigated. The results showed that the efficiency, effectiveness, and heat transfer rate to the base for the rectangular profile is higher than other profiles. In this research, the Nelder-Mead algorithm is 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.