Asymptotic solution for unsteady flow in expanding or contracting channels with large suction Reynolds

An incompressible laminar flow in a semi-infinite porous channel with expanding or contracting wails is considered. Following the self-similarity transformation, the Navier-Stokes equations are reduced to a fourth-order non-linear differential equation. The resulting equation is then solved asymptotically for large suction Reynolds number. The influences of expansion rate and Reynolds number on the fluid are obtained. When the wall contracts, the boundary layer becomes thinner; and when the wall expands, the boundary layer becomes thicker. It appears that flow reversal begins when the ratio of expansion rate to suction Reynolds number exceeds 1.