Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method

In this paper, the homotopy analysis method (HAM), one of the most effective method, is applied to obtain the approximate solution of the nonlinear model of diffusion and reaction in catalyst pellets for the case of n  th-order reactions. The approximate analytical solution obtained by HAM logically contains the solution obtained with Adomian decomposition method. The homotopy analysis method contains the auxiliary parameter ℏℏ, which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter ℏℏ, we can obtain reasonable solution for large Thiele modulus.