Heat Transfer Performance on Longitudinal Porous Fins with Temperature-Dependent Heat Generation, Heat Transfer Coefficient and Surface Emissivity

Analytical and numerical analyses have been performed to study the problem of the porous fin with temperature-dependent heat generation, heat transfer coefficient and thermal emissivity. This study is performed using Darcy’s model to formulate the heat transfer equation. The partial differential equations have been transformed into an ordinary differential equation using a similarity transformation. The powerful analytical methods called collocation method, the least square method and homotopy analysis method have been used to solve nonlinear differential equations. It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem. Also, temperature fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of natural convection parameter Nc, radiation parameter Nr and porosity Sh parameter on the heat transfer rate. As an important outcome, these proposed methods are able to solve a large class of nonlinear problems effectively, more easily and accurately; and thus, it has been widely applicable in engineering and physics.