Abstract
The series solutions of unsteady flows of a viscous incompressible electrically conducting fluid caused by an impulsively rotating infinite disk are given by means of an analytic technique, namely the homotopy analysis method. Using a set of new similarity transformations, we transfer the Navier-Stokes equations into a pair of nonlinear partial differential equations. The convergent series solutions are obtained, which are uniformly valid for all dimensionless time 0 <= tau < infinity in the whole spatial region 0 <= eta < infinity. To the best of our knowledge, such kind of series solutions have never been reported. The effect of magnetic number on the velocity is investigated.