Bifurcation of streamlines in channel and tube flow of FENE-P fluid due to peristaltic activity

Abstract

In this paper, we have analyzed the bifurcation of stagnation points in the non-Newtonian flow of the FENE-P fluid through a channel induced by peristalsis. The stream function for the flow under consideration is developed under negligible inertia and streamline curvature effects. A nonlinear autonomous system is developed for scrutiny of the critical points. A dynamical system approach is used to examine the stability of bifurcation points. Streamline patterns, and local and global bifurcation diagrams are plotted for analysis of the backward flow, trapping, and augmented flow regions. The impacts of important embedded parameters, i.e., extensibility parameter and Deborah number on local and global bifurcation diagrams, are also examined. The whole analysis reveals that two critical conditions appear in the flow field that are actually responsible for the conversion of backward flow to trapping and trapping to augmented flow. It is further seen that bifurcations occur at lower flow rates for increasing Deborah’s number while an opposite trend prevails for increasing the extensibility parameter. A comparison of bifurcations between planar and axisymmetric flows is also performed. It is observed that a greater area of the trapping region is encountered for axisymmetric flow than that for planar flow.