Peristaltic pumping of a conducting fluid in a channel with a porousperipheral layer

TLDR: In this paper, a peristaltic transport of a conducting fluid in a composite region between two flexible walls is investigated under the assumptions of long wavelength and low Reynolds number, where a Brinkman extended Darcy equation is used to model the flow in the porous layer.

Abstract: Peristaltic transport of a conducting fluid in a composite region between two flexible walls is investigated under the assumptions of long wavelength and low Reynolds number. The composite region consists of core and peripheral layers. The core layer is a free flow region consisting of a conducting Newtonian fluid and the peripheral layer is a porous region filled with conducting fluid. An infinite train of peristaltic waves is moving on the walls of the channel. The fluid flow is investigated in the wave frame of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is used to model the flow in the porous layer. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pressure rise etc. are discussed for various parameters of interest governing the flow like viscosity ratio, magnetic parameter and amplitude ratio. The results found will have applications for understanding the physiological flows in small blood vessels which can modeled as channels bounded by finite permeable layers (Fung and Tang, [5]).