Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 725196, 16 pages
Research Article

Some Effects of Side Walls on Unsteady Flow of a Viscous Fluid over a Plane Wall

İstanbul Teknik Üniversitesi, Makina Fakültesi, 34439 Gümüşsuyu, İstanbul, Turkey

Received 7 May 2009; Revised 9 July 2009; Accepted 7 August 2009

Academic Editor: Mehrdad Massoudi

Copyright © 2009 M. Emin Erdoğan and C. Erdem İmrak. 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.


Four types of unsteady flows of a viscous fluid over a plane wall bounded by two side walls are considered. They are flow caused by impulsive motion of a plate, flow due to oscillation of a plate, flow induced by constantly accelerating plate, and flow imposed by a plate that applies a constant tangential stress to the fluid. In order to solve these problems, the sine and cosine transformations are used, and exact solutions for the velocity distribution are found in terms of definite integrals. The cases for which the time goes to infinity and the distance between two side walls goes to infinity are compared with the cases for flows over a plane wall in the absence of the side walls. These provide to know the required time to attain the steady-state and what is the distance between the side walls for which the measured value of the velocity or the stress would be unaffected by the presence of the side walls.