Laminar flow in symmetrical channels with slightly curved walls, I. On the Jeffery-Hamel solutions for flow between plane walls

Abstract

The Jeffery-Hamel solutions for plane, viscous, source or sink flow between straight walls are not unique. In this paper these solutions are regarded as providing the leading term of a series solution for a class of channels with walls that are nearly straight in a certain sense, but are such that the fluid is not required to emerge from, or converge on, a point. This approach suggests a further condition which the appropriate solution must satisfy, and hence leads to uniqueness in a limited domain of the physical parameters. The resulting velocity profiles include, at one extreme, the parabolic one of Poiseuille flow, and, at the other, profiles with a single region of flow reversal at each wall. The way is thus opened to an asymptotic series solution of the Navier-Stokes equations which shows laminar separation.