Asymmetrical suction and injection in laminar channels with porous walls: a fixed point approach

Abstract

The problem of laminar flow in a rectangular channel with a pair of porous walls is considered. The porous walls allow fluid to be injected into or sucked out of the channel at constant velocities normal to the walls; the velocities at each wall are not necessarily of equal magnitude nor symmetrical in direction. In this article, a unique solution to this problem is shown to exist for sufficiently low Reynolds numbers through the application of Banach's fixed point theorem. This serves to further the discussion about the uniqueness of solutions for this problem, whilst also demonstrating the suitability of a fixed point approach to this family of fluid dynamics problems.