Unsteady motion of a viscous liquid between rotating parallel walls in the presence of a crossflow

The paper considers the unsteady flow of a viscous incompressible fluid inside an infinitely long slot with uniform injection or suction of the fluid through the porous walls of the slot. The plates with the fluid are rotated rigidly with constant angular velocity. The unsteady flow is induced by nontorsional vibrations of the upper plate. The flow-velocity field and the tangential stress vectors exerted by the fluid on the upper and lower walls of the slot are determined. In this case, one can find an exact solution of the three-dimensional nonstationary Navier–Stokes equations. No restrictions are imposed on the motion pattern of the plate.