An Analysis of Peristaltic Flow of Finitely Extendable Nonlinear Elastic- Peterlin Fluid in Two-Dimensional Planar Channel and Axisymmetric Tube

Abstract

We have investigated the peristaltic motion of a non-Newtonian fluid characterized by the finitely extendable nonlinear elastic-Peterlin (FENE-P) fluid model. A background for the development of the differential constitutive equation of this model has been provided. The flow analysis is carried out both for two-dimensional planar channel and axisymmetric tube. The governing equations have been simplified under the widely used assumptions of long wavelength and low Reynolds number in a frame of reference that moves with constant wave speed. An exact solution is obtained for the stream function and longitudinal pressure gradient with no slip condition. We have portrayed the effects of Deborah number and extensibility parameter on velocity profile, trapping phenomenon, and normal stress. It is observed that normal stress is an increasing function of Deborah number and extensibility parameter. As far as the velocity at the channel (tube) center is concerned, it decreases (increases) by increasing Deborah number (extensibility parameter). The non-Newtonian rheology also affect the size of trapped bolus in a sense that it decreases (increases) by increasing Deborah number (extensibility parameter). Further, it is observed through numerical integration that both Deborah number and extensibility parameter have opposite effects on pressure rise per wavelength and frictional forces at the wall. Moreover, it is shown that the results for the Newtonian model can be deduced as a special case of the FENE-P model