Asymptotic Solution for Unsteady Viscous Flow in a Plane Channel

The method of matched asymptotic expansions is used in this paper to derive an approximate solution for unsteady flow of a viscous incompressible fluid in a plane channel. The unsteadiness of the flow is caused by a sudden reduction of flow rate to zero. The solution is valid for short time intervals immediately following the sudden blockage of the channel. The velocity profile prior to deceleration is assumed to be an arbitrary function of the transverse coordinate. A simple explicit formula for the shear at the wall is derived