Laminar flow in symmetrical channels with slightly curved walls II. An asymptotic series for the stream function

Abstract

A class of two-dimensional channels, with walls whose radius of curvature is uniformly large relative to local channel width, is described, and the velocity field of laminar flow through these channels is obtained as a power series in the small curvature parameter. The leading term is the Jeffery-Hamel solution considered in part I, and it is shown here how the higher-order terms are found. Terms of the third approximation have been computed. The theory is applied to two examples, for one of which experimental results are available and confirm the theoretical values with fair accuracy.