Peristaltic Pumping of a Fluid of Variable Viscosity in a Non Uniform Tube/Channel with Permeable Wall

摘要

In this paper, the peristaltic flow of a fluid of variable viscosity in a non uniform tube or channel lined with porous material is studied. This model is suitable for the pumps whose inner surface of the tube is rough, the roughness that arises due to corrugations plays an important role in pumping and in the biological systems such as blood vessels containing tissue region. The flow in the free flow of the tube is governed by Navier-Stokes equation and the flow in the permeable boundary is described by Darcy law. It is observed that the magnitude of peak pressure rise decreases with increase in flow rate and increases with increasing amplitude ratio and increasing Darcy number. It shows that the larger the permeability of porous medium, the greater the pressure rise against which the pump works. It is also observed that as the viscosity decreases the pressure rise increases and for different values of mean flow rate the frictional force exhibits opposite behavior to that of pressure rise. The trough in the frictional force increases with decreasing amplitude ratio and decreases with increasing Darcy number which shows that the increase in permeability of wall causes less frictional forces. The decrease in viscosity makes the peristaltic pump to work under less frictional force.