Stokes flow induced by a sliding smooth plate over a finned plate

Abstract

Slow viscous flow between a sliding smooth plate and a finned plate is investigated in the Stokes limit. Theoretical solutions are obtained for unidirectional flow along the fin. An exact analogy is noted between the present Stokes flow and the heat conduction under the same geometry. Conformal mapping is displayed to secure closed-form solutions to the case of single fin. For periodically spaced fins the eigenfunction expansion technique is utilized to describe the flow details. The explicit effects of the fin height and of the fin spacing on global flow patterns are elucidated. To gauge the increase in drag and heat transfer caused by the fin spacing. the concepts of fin-interaction parameter and characteristic length scales are introduced. The theoretical predictions and full-dress numerical solutions are shown to be highly consistent. Criteria for enhanced conductive heat transfer in microsystems are suggested.