Z. Naturforsch. **68a,** 515 – 523
(2013)

doi:10.5560/ZNA.2013-0033

Flow of a Giesekus Fluid in a Planar Channel due to Peristalsis

Nasir
Ali and
Tariq
Javed

Department of Mathematics & Statistics, International Islamic University, Islamabad, Pakistan

Received November 21, 2012 / revised March 7, 2013 / published online June 12, 2013

Reprint requests to: N. A.; nasirali_qau@yahoo.com

An attempt is made to investigate the peristaltic motion of a Giesekus fluid in a planar channel under long wavelength and low Reynolds number approximations. Under these assumptions, the flow problem is modelled as a second-order nonlinear ordinary differential equation. Both approximate and exact solution of this equation are presented. The validity of the approximate solution is examined by comparing it with the exact solution. A parametric study is performed to analyze the effects of non-dimensional parameters associated with the Giesekus fluid model (*α* and We) on flow velocity, pressure rise per wavelength, and trapping phenomenon. It is found that the behaviour of longitudinal velocity and pattern of streamlines for a Giesekus fluid deviate from their counterparts for a Newtonian fluid by changing the parameters *α* and We. In fact, the magnitude of the longitudinal
velocity at the center of the channel for a Giesekus fluid is less than that for a Newtonian fluid. It is also observed that the pressure rise per wavelength decreases in going form Newtonian to Giesekus fluid. Moreover, the size of trapped bolus is large and it circulates faster for a Newtonian fluid in comparison to a Giesekus fluid.

*Key words:* Peristalsis; Giesekus Fluid; Channel Flow; Exact Solution; Trapping.