Exact solution for the problem of a two-dimensional Couette flow between two parallel infinite plates is obtained when the lower plate is stationary and the upper plate is moving with an arbitrary time-dependent velocity. In this investigation the transpiration flow which is with constant velocity and pressure gradient is normal to the plates. For selected upper plate timedependent velocities and different boundary conditions the Navier-Stocks equations are solved. The Laplace Transform technique is used to solve the governing equations and the effect of different parameters on flow velocity and flow shearstress are presented in order to discuss the interesting aspects of the problem.

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