A Similarity Solution for Flow in a Narrow Channel of Varying Gap

Abstract

A similarity solution may be obtained for the case of a narrow channel where the gap h varies, according to (a + bx) m . The lower surface may slide in either direction and there may be suction or injection at either surface which must vary as h −1 . Asymptotic solutions are found for large and small values of a modified Reynolds number which is based on the sliding velocity or the suction/injection rate. Boundary layer behavior may be exhibited at high Reynolds number. The present solution, being “exact” for all Reynolds numbers once the thin film assumptions have been invoked, may be of value to hydrodynamic lubrication workers to test approximations for the fluid inertia effect.