Exact solution of the Navier–Stokes equations for the pulsating Dean flow in a channel with porous walls

Analytical solutions of the equations of motion of a Newtonian fluid for the fully developed laminar flow between two concentric cylinders are presented, when an oscillating circumferential pressure gradient is imposed (finite gap oscillating Dean flow). The walls of the cylinders are porous, so that a radial flow can be superimposed. The analytical solution is examined for a variety of values of the dimensionless parameters, which are the transverse radial Reynolds number, the Womersley number and the ratio of the radii of the cylinders.