Exploration of peristaltic pumping of Casson fluid flow through a porous peripheral layer in a channel

Abstract

Abstract This article is aimed to investigate the peristaltic pumping of a two-layered model in a two-dimensional channel. The core region occupies Casson fluid, while the porous medium occupies the peripheral region. The fluid flow in a porous medium was described with a suitable model using the Brinkman-extended Darcy equation. In the interface between fluid and porous medium, a shear stress jump boundary condition was applied. Closed-form solutions were obtained in both regions (core and peripheral). The physical quantities of peristaltic flow, such as axial velocity, pumping and change in the interface, were derived and explained. The fluid flow was analyzed by different physical parameters such as viscosity, permeability, porosity, Casson parameter and Darcy number. It is observed that the peristalsis mechanism has greater pressure in a two-layered model containing a non-Newtonian fluid in contact with a porous medium compared to a viscous fluid in the peripheral layer. It was observed that pumping decreased with the increase in Darcy number and an increase in shear stress jump constant resulted in increasing the pumping. The outcomes of the pumping phenomenon may be helpful for understanding the fluid flow aspects of blood flow in capillaries.