An Exact Analytic Solution on Convective-Radiative Heat Transfer in Porous Fins by using HPM and VIM

摘要

One of the newest analytical methods to solve the nonlinear convection and radiation heat transfer equations arising in porous fin are using Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). To formulate the heat transfer equation, the energy balance and Darcy's model used. The calculations are done for three different types of the fin such as, the infinite fin, the finite-length fin with insulated tip and the finite-length fin with tip exposed to a known convection coefficient. The obtained solutions are compared with a type of numerical analysis as Boundary Value Problem (BVP) in solving this problem. All the examples show that the results of the present method are in excellent agreement with those obtained by the numerical solution. Also the HPM and VIM does not require small parameters in the equation, so that the limitations of the traditional perturbation methods can be eliminated, and also the calculations in the HPM and VIM are simple.