Slow Motion in a Two-Dimensional Semi-Infinite Channel with Moving Walls

Abstract

Investigations are made of the two-dimensional flow of a viscous incompressible fluid due to slow and steady motion of a plane piston in a channel. Three methods are adopted: analytical, numerical and composite ones. Numerical errors of the velocity distribution on the walls derived by Dean’s technique are found to be less than 1.1%. Vorticity distributions on the walls obtained by the three methods are compared. The vorticity becomes infinite as r⁻¹ when the distance r from a corner tends to zero, where the wall velocity is discontinuous and the numerical solution becomes invalid. It is found that the composite method gives the most accurate and uniform approximation.