Stokes' second problem with wall suction or blowing for UCM fluids

An analytical solution is derived for the time-dependent flow of an infinite pool of fluid described by the viscoelastic upper convected Maxwell (UCM) model driven by an oscillating porous plate in the presence of cross flow. Whereas for a Newtonian fluid there is a solution regardless of the amount of suction or blowing, for viscoelastic fluids the solution breaks down under certain conditions. When the suction velocity exceeds the elastic shear wave speed there is no solution. For sub-critical blowing through the plate the stream-wise velocity profiles are periodic, but when the blowing speed exceeds the elastic shear wave speed non-periodic chaotic-like waves appear under certain conditions, which are characterized. The flow characteristics are properly scaled by the reciprocal square root of the Reynolds number with and without cross flow. Generally speaking, the flow properties are controlled by the cross flow and by the fluid elasticity at low and high Deborah numbers, respectively.