Exact solution for the pulsating finite gap Dean flow

Analytical solutions of the Navier–Stokes equations for the fully developed laminar flow in a cylindrical annulus, when an oscillating circumferential pressure gradient is imposed (finite gap oscillating Dean flow), are presented. The solution for the case of steady flow, which has been given by Goldstein, is obtained as a limit case of the oscillating flow when the frequency of the oscillating pressure gradient tends to zero. The pulsating flow solution is obtained by the superposition of the constant and oscillating pressure gradient solutions.