Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 479087, 18 pages
Research Article

Williamson Fluid Model for the Peristaltic Flow of Chyme in Small Intestine

1Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2Department of Mechanical Engineering, King Saud University, Riyadh 11451, Saudi Arabia

Received 21 September 2011; Revised 24 December 2011; Accepted 2 January 2012

Academic Editor: Angelo Luongo

Copyright © 2012 Sohail Nadeem et al. 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.


Mathematical model for the peristaltic flow of chyme in small intestine along with inserted endoscope is considered. Here, chyme is treated as Williamson fluid, and the flow is considered between the annular region formed by two concentric tubes (i.e., outer tube as small intestine and inner tube as endoscope). Flow is induced by two sinusoidal peristaltic waves of different wave lengths, traveling down the intestinal wall with the same speed. The governing equations of Williamson fluid in cylindrical coordinates have been modeled. The resulting nonlinear momentum equations are simplified using long wavelength and low Reynolds number approximations. The resulting problem is solved using regular perturbation method in terms of a variant of Weissenberg number 𝑊 𝑒 . The numerical solution of the problem is also computed by using shooting method, and comparison of results of both solutions for velocity field is presented. The expressions for axial velocity, frictional force, pressure rise, stream function, and axial pressure gradient are obtained, and the effects of various emerging parameters on the flow characteristics are illustrated graphically. Furthermore, the streamlines pattern is plotted, and it is observed that trapping occurs, and the size of the trapped bolus varies with varying embedded flow parameters.