A study on the bifurcation of stagnation points for a peristaltic transport of micropolar fluids with slip condition

Abstract

The objective of present work is to investigate the impacts of embedded parameters on various flow phenomena and the bifurcations of stagnation points. This analysis is made for peristaltic transports of micropolar fluids through symmetric channel with slip condition. Exact analytic expressions for velocity profile and stream function are obtained under the constraints of long wavelength and vanishing Reynolds number. Three various flow phenomena (backward, trapping and augmented flow) and two bifurcation conditions due to their transitions are encountered in the flow by employing the dynamical system theory. The local bifurcation diagrams are used to explore the influences of micropolar parameter, coupling number and slip parameter on these bifurcations. The backward region experiences contraction by enlarging the micropolar parameter up to a critical value and after that an opposite trend is observed. The augmented flow and trapping regions expand by increasing the coupling number, while slip parameter shows an opposite behavior. At the end, the results of this analysis are summarized by using global bifurcation diagrams.