This paper analytically investigates the ow as well as the chemically reactive solute transfer problem in a viscous uid. The motion equations are reduced to a nonlinear ordinary di erential equations system using the similarity transformations. The obtained nonlinear di erential system is for the rst time approximately solved by means of the Optimal Homotopy Asymptotic Method (OHAM). The e ects of the partial slip and suction/blowing parameters are analytically analyzed. Some examples are given; the obtained results provides us with a good agreement with the numerical results and reveal that our procedure is e ective, accurate and easy to use.