An Approximation of the Analytic Solution of Some Nonlinear Heat Transfer Equations: A Survey by using Homotopy Analysis Method

In this letter, the approximate solution of nonlinear heat diffusion and heat transfer and also the energy balance for a differential fin element are developed via Homotopy Analysis Method HAM. This method is a strong and easy–to–use analytic tool for investigating nonlinear problems, which does not need small parameters. Homotopy analysis method contains the auxiliary parameter h , which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter h , we can obtain reasonable solutions for large modulus. In this study, we compare obtained results through HAM results, with those of homotopy perturbation method and the exact solutions. The first differential equation to be solved is a straight fin with a temperature–dependent thermal conductivity and the second one is the modeling equation of a cooling Lumped system with variable specific heat.