International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 1, Pages 21-34

Peristaltic viscoelastic fluid motion in a tube

Elsayed F. Elshehawey1 and Ayman M. F. Sobh2

1Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt
2Department of Mathematics, College of Education, P.O. Box 4051, Gaza Strip, Gaza, Palestinian Authority

Received 24 June 1999

Copyright © 2001 Elsayed F. Elshehawey and Ayman M. F. Sobh. 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.


Peristaltic motion of viscoelastic incompressible fluid in an axisymmetric tube with a sinusoidal wave is studied theoretically in the case that the radius of the tube is small relative to the wavelength. Oldroyd flow has been considered in this study and the problem is formulated and analyzed using a perturbation expansion in terms of the variation of the wave number. This analysis can model the chyme movement in the small intestine by considering the chyme as an Oldroyd fluid. We found out that the pumping rate of Oldroyd fluid is less than that for a Newtonian fluid. Further, the effects of Reynolds number, Weissenberg number, amplitude ratio and wave number on the pressure rise and friction force have been discussed. It is found that the pressure rise does not depend on Weissenberg number at a certain value of flow rate. The results are studied for various values of the physical parameters of interest.