Homotopy analysis solution of three dimensional diffusion equations

In this paper, the Homotopy Analysis Method (HAM) is employed to find a suitable solution for parabolic equations. This method is a strong and easytouse analytic tool for investigating linear and nonlinear problems, which do not need small parameters. Homotopy analysis method contains the auxiliary parameter ?, which provides us with a simple way to adjust and control the convergence region of solution series.By suitable choice of the auxiliary parameter ?, we can obtain reasonable solutions for large modulus. In this study, we compare obtained results through (HAM) with the exact solutions. This type of equations governs on numerous scientific and engineering experimentations.