Unsteady Couette flow in a rotating system

We have studied the unsteady Couette flow of a viscous incompressible fluid confined between parallel plates, rotating with an uniform angular velocity about an axis normal to the plates. The flow is induced by the motion of the upper plate and the fluid and plates rotate in unison with the same constant angular velocity. An exact solution of the governing equations have been obtained for small and large time ττ by applying Laplace transform technique. It is found that the primary velocity decreases with increase in rotation parameter for small as well as large time. It is interesting to note that a back flow occurs in the region 0.0⩽η⩽0.70.0⩽η⩽0.7 for large time with increase in K   when K=4K=4 and 5. The secondary velocity increases in magnitude for small time with increase in rotation parameter. It is observed that the secondary velocity increases in magnitude for small values of rotation parameter. On the other hand, for large values of rotation parameter K2K2, it decreases near the stationary plate and increases near the moving plate. The shear stress due to primary flow decreases with increase in rotation parameter K2K2. On the other hand, it increases due to secondary flow with increase in rotation parameter for small time. It is noticed that for large time there exists separation in the primary and secondary flows due to high rotation.