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Mathematical Problems in Engineering
Volume 2003, Issue 1, Pages 1-23
http://dx.doi.org/10.1155/S1024123X03308014

Peristaltic motion of a Johnson-Segalman fluid in a planar channel

1Mathematics Department, Quaid-i-Azam University, Islamabad 45320, Pakistan
2Fachbereich Mechanik, Technische Universität Darmstadt, Hochschulstraße 1, Darmstadt 64289, Germany
3Department of Mathematics, Pennsylvania State University, York, PA 17403, USA

Received 22 July 2002

Copyright © 2003 Hindawi Publishing Corporation. 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 publication of this article was funded by SCOAP3.

Abstract

This paper is devoted to the study of the two-dimensional flow of a Johnson-Segalman fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength. Both analytical and numerical solutions are presented. The analysis for the analytical solution is carried out for small Weissenberg numbers. (A Weissenberg number is the ratio of the relaxation time of the fluid to a characteristic time associated with the flow.) Analytical solutions have been obtained for the stream function from which the relations of the velocity and the longitudinal pressure gradient have been derived. The expression of the pressure rise over a wavelength has also been determined. Numerical computations are performed and compared to the perturbation analysis. Several limiting situations with their implications can be examined from the presented analysis.