Laminar flow in rectangular channels. Part I: Entry analysis. Part II: Numerical solution for a square channel?

Laminar incompressible flow in rectangular channels is considered. In Part I, 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. In Part II, numerical solutions are obtained for the viscous channel equations, which are derived from the asymptotic theory of Part I. A two stream function, velocity, vorticity system, independent of the Reynolds Number, is solved with a combined iterative ADI/point-relaxation numerical procedure. A single calculation applied for all Reynolds numbers, which appears only in the coordinate scaling. The axial flow behavior of Parts I and II are in good agreement in the asymptotic entry region where both analysis apply. Secondary flow reversal is calculated; however, the grid is too crude for quantitative comparisons. Numerical solutions are obtained until fully developed conditions are achieved. Agreement with experimental data is good.