Analytical investigation of non-linear model arising in heat transfer through the porous fin

Abstract

In this paper simple analytical methods called homotopy perturbation method, variation iteration method, and perturbation method are employed to approach temperature distribution of porous fins. Also energy balance and Darcy's model used to formulate the heat transfer equation. To study the thermal performance, a type case considered is finite-length fin with insulated tip. The obtained results from variation iteration method are compared with other analytical techniques proposed before. These methods are homotopy perturbation method and perturbation method. Also boundary value problem is applied as a numerical method for validation. The obtained results shows that the variational iteration method is more accurate, stable, and more appropriate than other techniques. Also it is found that this method is powerful mathematical tools and can be applied to a large class of linear and non-linear problems arising in different fields of science and engineering specially some heat transfer equations.