Unsteady Flow in a Porous Medium Between Two Infinite Parallel Plates in Relative Motion

An approximate solution to the unsteady flow of a viscous incompressible fluid through a porous medium bounded by two infinite parallel plates, the lower one stationary and the upper one oscillating in its own plane, is presented here. Expressions for the transient velocity, the amplitude, the phase angle α and the skin-friction are derived and numerically calculated. It is observed that the amplitude increases with increasing σ, the permeability parameter, and ω, the frequency. Also, there is always a phase lead, and the phase angle α decreases with increasing σ.