Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate

In this paper, the unsteady magnetohydrodynamic viscous flows of non-Newtonian fluids caused by an impulsively stretching plate are studied by means of an analytic technique, namely the homotopy analysis method. We give the analytic series solutions which are accurate and uniformly valid for all dimensionless time in the whole spatial region 0≤η<∞. To the best of authors' knowledge, such kind of analytic solutions have been never reported. Besides, the effects of the integral power-law index (n=1, 2, 3) of the non-Newtonian fluids and the magnetic parameter M=0, 1, 2 on the flows are investigated.