Two infinite parallel plates are separated by a distance h. The space between them is filled with a Newtonian fluid: density (rho), viscosity (mu). The lower plate is fixed, but the upper plate executes a sinusoidal motion. (U=A*sin(omego*t). Calculate the velocity field between the plates, and plot some representative profiles.
coordinates x-dir along plate
y-dir normal to plate.
This full solution uses the only non-degenerated equation of motion p*(partial derivative u)/(partial derivative t) = u*(partial derivative^2*u)/(partial derivative y^2) and introducing non dimensional variables u' = u/A.