An analytical solution of the navier-stokes equation for flow over a moving plate bounded by two side walls

An exact solution of the Naiver-Stokes equation for unsteady flow over a moving plate between two side walls is given. This solution solves the problem that arises calculating shear stress at the bottom wall when the expression of velocity presented in literature is used. The variation of the shear stress at the bottom wall with the distance between two side walls for various values of the non-dimensional time is illustrated and it is shown that when the value of non-dimensional time is equal to unity, the shear stress approaches the asymptotic value. Furthermore, the volume flux across a plane normal to the flow is calculated and it is found that when the value of the non-dimensional time is equal to unity, the volume flux approaches the asymptotic value.