Bifurcation analysis for a two-dimensional peristaltic driven flow of power-law fluid in asymmetric channel
Nasir Ali, Kaleem Ullah, Husnain Rasool
Abstract
In the present article, the bifurcations of equilibrium points and their streamlined patterns for the peristaltic transport of shear-thinning and shear-thickening fluids through an asymmetric channel are studied by incorporating a power-law model. An exact solution in the wave frame of reference is obtained under the vanishing Reynolds number and long wavelength approximations. A system of non-linear autonomous differential equations is developed to locate the equilibrium points in the flow. The qualitative nature of equilibrium points and their bifurcations are investigated through the dynamical system method. There exist three distinct flow conditions (backward flow, trapping, and augmented flow). It is observed that the shifting of these flow phenomena corresponds to bifurcations where non-hyperbolic degenerate points are conceived. The impacts of various embedded parameters on flow phenomena and their bifurcations are demonstrated through graphical representations. It is found that the trapping phenomenon manifests at a high flow rate for shear-thinning fluids. That is, the backward flow region shrinks for large values of the power-law index. Trapping in mechanical devices can be diminished by enlarging the phase difference of channel walls, while an opposite trend is observed for amplitude ratios. The obtained results are concluded through global bifurcation diagrams. At the end, findings of this analysis are verified by making a comparison with the existing literature.