International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 783-797

Further studies of fully developed flow through ducts of arbitrary section by the contour line-conformal mapping technique

J. Mazumdar and D. Hopkins

Department of Applied Mathematics, University of Adelaide, 5005, Australia

Received 19 December 1995

Copyright © 1997 J. Mazumdar and D. Hopkins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper discusses fully developed flow of viscous fluid through ducts of arbitrary cross-section. The method uses a constant velocity contour line in a typical cross-section of the duch as an independent variable. The amplitude of the oscillatory velocity is then obtained from an ordinary integro-differential equation. Several examples of a practical nature are given, with some that have not yet been discussed in the literature. All details are explained by graphs.