Thermal performance analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation

In this study, thermal performance analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation is carried out using Galerkin's method of weighted residual. The developed symbolic heat transfer models are used to investigate the effects of various parameters on the thermal performance of the porous fin. It is found that increase in porosity parameter, Nusselt, Darcy and Rayleigh numbers and the thickness-length ratio of the fin increase the rate of heat transfer from the base of the fin and consequently improve the efficiency of the fin. Also, decreasing thermal conductivity parameter results in an increase in the rate of heat transfer from the base of the fin. However, an optimum value is reached beyond which further increase in porosity, Nusselt, Darcy and Rayleigh numbers, thermal conductivity ratio and thickness-length ratio has no significant influence on the rate of heat transfer. For the purpose of verification of the results, exact analytical solutions are developed. The results of the Galerkin's method for the second-order approximation function are found to be in excellent agreements with the results of the exact analytical solutions and also with that of the numerical methods and homotopy perturbation method.