Laminar Flow in Rectangular Channels. Part I:Entry analysis. Part II:Numerical Solution for a Square Channel.

摘要

Laminar incompressible flow in rectangular channels is considered. The entry region is evaluated by a boundary layer/potential core analysis. It is shown that the three-dimensional displacement induced potential flow can be described with a pair of two-dimensional potential functions. Second-order boundary layer solutions, with and without surface mass transfer, are determined, an interesting secondary flow reversal is predicted. Numerical solutions are obtained for the viscous channel equations, which are derived from the asymptotic theory. A two stream function, velocity, vorticity systems, independent of the Reynolds number, is solved with a combined iterative ADI/point-relaxation numerical procedure. A single calculation applies for all Reynolds numbers, which appears only in the coordinate scaling.