International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 805-818
Influence of wall waviness on friction and pressure drop in channels
1Department of Mathematics, East Carolina University, Greenville 27834, North Carolina, USA
2Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg 24061, Virginia, USA
Received 7 November 1980
Copyright © 1981 K. Vajravelu and Ali H. Nayfeh. 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.
An attention has been given to investigate the flow behavior of an
incompressible viscous fluid confined in horizontal wavy channels and set in motion due to the movement of the upper wall and the pressure differences. The governing equations have been solved analytically as well as numerically subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and a disturbance or perturbed part. For small and moderate Reynolds numbers, the analytical solution for the perturbed part has been found to be in good agreement with the numerical one. The effects of Reynolds number, the pressure gradient parameter, and the undulation wavenumber on friction and pressure drop are found to be quite significant. In addition to the flow behavior for both long and short waves and for large Reynolds numbers, the effect of the wall waviness on friction and pressure drop has been examined for
any arbitrary amplitude of the wavy wall.