Magnetohydrodynamic plane Couette flow of an elasto-viscous fluid

Using the Laplace transform, an analytical solution of the Navier-Stokes equation is obtained for a two-dimensional incompressible elasto-viscous fluid past between two infinite parallel walls. It is assumed that the lower wall is moving with velocity which is a function of any given free stream velocity. As an application of the solution, two cases for the stream velocity are studied.