Numerical and Galerkin?s methods for thermal performance analysis of circular porous fins with various profiles when the surface temperature is higher/lower than the air temperature

The main objective of this research is to analyze the optimization and the thermal performance of circular porous fins with three different profiles: rectangular, convex, and triangular under dry surface conditions. In this research, when the surface temperature of fin is higher or lower than the air temperature was studied. 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 finite difference method and the Galerkin?s method. In this study, the effect of different parameters including porous parameter (S-H) and porosity, fin efficiency, and fin effectiveness on temperature distribution were investigated. In both cases, the results showed that the fin temperature distribution should be decreased by increasing the porous parameter (S-H) and porosity. In addition, in both cases, the results demonstrated that the efficiency and effectiveness for the rectangular profile are higher than other profiles. In this study, the total average absolute deviation percentage was calculated and its magnitude was 1 to 2.35%.