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In this article, the homotopy analysis method has been applied to solve a coupled nonlinear diffusion-reaction equations. The validity of this method has been successful by applying it for these nonlinear equations. The results obtained by this method have a good agreement with one obtained by other methods. This work illustrates the validity of the homotopy analysis method for the nonlinear differential equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems. © 2008 Springer Science+Business Media B.V  

This work studies the electrochemical growth behavior of cobalt nanowires in highly ordered aluminum oxide membrane. Considering the electrodeposition of metallic nanowires, cation concentration profile in each nano pore was calculated. With assumption of linear diffusion zone on the growing surface of nanowires, a modified Cottrell equation was evaluated. To confirm the model, the Co nanowires were electrodeposited into porous anodic aluminum oxide (AAO) templates and the mechanism of deposition was studied. Comparing the results of model and the experiments has proved the accuracy of the model. Also, it was observed that the growth of the Co nanowires was controlled mainly by diffusion... 

Diffusivity equation which can provide us with the pressure distribution, is a Partial Differential Equation (PDE) describing fluid flow in porous media. The quadratic pressure gradient term in the diffusivity equation is nearly neglected in hydrology and petroleum engineering problems such as well test analysis. When a compressible liquid is injected into a well at high pressure gradient or when the reservoir possess a small permeability value, the effect of ignoring this term increases. In such cases, neglecting this parameter can result in high errors. Previous models basically focused on numerical and semi-analytical methods for semi-infinite domain. To the best of our knowledge, no...