The main theme of this work is to apply the Adomian decomposition method (ADM) to solve the non-linear differential equations which arise in fluid mechanics. we study some steady unidirectional magnetohydrodynamics (MHD) flow problems namely, Couette flow, Poiseuille flow and Generalized-Couette flow of a third grade non Newtonian fluid between two horizontal infinite parallel plates in the presence of a transversal magnetic field. Moreover, the MHD solutions for a Newtonian fluid, as well as those corresponding to a third grade fluid are obtained by the limiting cases of our solutions. Finally, the influence of the pertinent parameters on the velocity of fluids is also analyzed by graphical illustrations.
