A Method of “Separation of Variables” for the Solution of Laminar Boundary-Layer Equations of Narrow-Channel Flows

[+] Author and Article Information
F. Al-Bender, H. Van Brussel

Katholieke Universiteit Leuven, Division of Production Engineering, Machine Design and Automation (PMA), B-3001 Leuven (Heverlee), Balgium

J. Tribol 114(3), 623-629 (Jul 01, 1992) (7 pages) doi:10.1115/1.2920927 History: Received July 08, 1991; Revised December 13, 1991; Online June 05, 2008


A method of solution for laminar channel flow is established using the von Mises transformation followed by the “separation” of the main flow velocity into amplitude and profile functions. The known boundary conditions on the latter enable a generalized solution that yields, through a parametric relation between auxiliary parameters (the characteristics), a system of ordinary differential equations for the velocity amplitude and the pressure. The result is a powerful semi-analytical method which is very easy to implement for a variety of internal flow configurations. The method is, in essence, a downstream general solution which may be extended upstream to the singular limit of a uniform main flow velocity distribution at the channel entrance. The regular solution for uniform initial velocity distribution cannot thus be obtained. Comparisons with other solutions show only qualitative agreement, for reasons which are discussed, whereas agreement with experimental results, made in a separate publication, is remarkably good.

Copyright © 1992 by The American Society of Mechanical Engineers
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