Free and forced convectional heat transfer analysis of rectangular porous fin with Differential transformation method

In this article, the free and forced convectional heat transfer in a rectangular porous fin with considering pressure loss across the fin length is investigated analytically. A well-known Differential transformation method is employed to obtain the solution of energy balance equation. Convergence of obtained solution is examined by previous works and they are found to be in a good agreement. In order to simulate heat transfer through porous media, Darcy model is applied. Also convective heat transfer coefficient is assumed to be constant. Dimensionless temperature distribution is defined as a function of convection and porosity parameters. Also the effects of pressure loss across the fin length on the temperature distribution, rate of heat transfer, fin efficiency and effectiveness of fin are studied. A comparative study is also made between the porous and solid fins for an equal mass of fins. It is highlighted that the porous fin transfer always more heat at specific condition compared to the solid fin. Results show that all of thermal parameters are influenced by pressure loss parameter. So in order to reach to high fin efficiency, pressure loss across the fin length should be controlled.