Further Study on Thermal Performance of Porous Fin with Temperature-Dependent Thermal Conductivity and Internal Heat Generation using Galerkin’s method of Weighted Residual

This work is presented as a further study to our previous work, “Thermal performance analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat" published in "Thermal Science and Engineering Progress. 1 (2017) 39–52”, where it was assumed that the surface convection is negligible and heat is transferred only by natural convection in the porous fin. In this present study, such an assumption has been relaxed. Also, effects of surface convective heat transfer on the thermal performance of porous fin with temperature-dependent thermal conductivity and internal heat generation have been investigated using Galerkin’s method of weighted residual. The results of the Galerkin’s method of weighted residual show excellent agreement with the results of numerical method using shooting method coupled with Runge-Kutta method and also with the results of homotopy perturbation method. Thereafter, the developed analytical solutions are used to investigate the influences of the thermal model parameters on the thermal performance of the porous fin. It is found as the with the other model parameters that as the convective parameter increases, the rate of heat transfer from the base of the fin increases and consequently, the porous fin efficiency improves. However, increase in the nonlinear thermal conductivity parameter decreases the temperature distribution in the fin. Based on the high accuracy of the Galerkin’s method of weighted residual as displayed in this work, it is hoped that the simple analytical solutions given by the approximate analytical method will enhance the analysis of extended surfaces and also assist the designers.