Unsteady shear flow of fluids with pressure-dependent viscosity

We study the unsteady shear flow of fluids with pressure-dependent viscosity, situated between two parallel horizontal plates with the upper plate moving while the flow is subjected to an oscillating pressure gradient. The dimensionless form of the momentum equation is solved numerically using a central difference approximation for the spatial derivative terms and a forward difference approximation for the time derivative term. In addition to providing the velocity profiles at the midsection between the two plates, the values of shear stress at the lower (stationary) plate for various values of the dimensionless numbers are also plotted.