An approximation of the analytic solution of some nonlinear heat transfer in fin and 3D diffusion equations using HAM

In this article, the approximate solution of nonlinear heat diffusion and heat transfer equation 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. HAM 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 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 two- and three-dimensional unsteady diffusion problems.