Flows induced by the surface motions of a cylindrical sheet

Fluid flows induced by the surface stretching or shearing motion of cylindrical sheets are investigated. Steady and unsteady exact solutions of the Navier–Stokes equations are found for periodic axial shearing of an impermeable sheet and for periodic azimuthal stretching of a permeable sheet. Steady Stokes-flow solutions induced by the periodic axial stretching and the periodic azimuthal stretching of impermeable cylindrical sheets are also reported. In each case flows interior and exterior to a cylinder are considered, as well as the flow in the annulus between concentric cylinders.