This paper applies Homotopy Analysis Method (HAM) to obtain analytical solutions of system of non-linear partial differential equations. Numerical results clearly reflect complete compatibility of the proposed algorithm and discussed problems. Moreover, the validity of the present solution and suggested scheme is presented and the limiting case of presented findings is in excellent agreement with the available literature. The computed solution of the physical variables against the influential

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... rameters is presented through graphs. Several examples are presented to show the efficiency and simplicity of the method.