Analysis of Heat transfer in Porous Fin with Temperature-dependent Thermal Conductivity and Internal Heat Generation using Chebychev Spectral Collocation Method

Abstract

In this work, analysis of heat transfer in porous fin with temperature-dependent thermal conductivity and internal heat generation is carried out using Chebychev spectral collocation method. The numerical solutions are used to investigate the influence of various parameters on the thermal performance of the porous fin. The results show that increase in convective parameter, porosity parameter, Nusselt, Darcy and Rayleigh numbers and thickness-length ratio of the fin, the rate of heat transfer from the base of the fin increases and consequently improve the efficiency of the fin. However, the rate of heat transfer from the base of the fin increases with decrease in thermal conductivity material. Also, from the parametric studies, 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. It is established that the temperature predictions in the fin using the Chebychev spectral collocation method are in excellent agreement with the results of homotopy perturbation method and that of numerical methods using Runge-Kutta coupled with shooting method.