Peristaltic Flow of a Compressible Non-Newtonian Maxwellian Fluid Through Porous Medium in a Tube

Abstract

This work is concerned with the peristaltic transport of a Newtonian and non-Newtonian Maxwellian fluid in an axisymetric cylindrical tube filled with a homogenous porous medium, in which the flow is induced by traveling transversal waves on the tube wall. Like in peristaltic pumping, the traveling transversal waves induce a net flow of the liquid inside the tube. The viscosity as well as the compressibility of the liquid is taken into account. Modified Darcy's law has been used to model the governing equation. The present theoretical model may be considered as mathematical representation to the case of gall bladder and bile duct with stones and dynamics of blood flow in living creatures. The Navier–Stokes equations for an axisymmetric cylindrical tube are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the tube is small parameter. In the second order approximation, a net flow induced by the traveling wave is calculated for various values of the compressibility of the liquid, relaxation time and the permeability parameter of porous medium. The calculations disclose that the compressibility of the liquid, the permeability parameter of porous medium and non-Newtonian effects in presence of peristaltic transport have a strong influence of the net flow rate. Finally, the graphical results are reported and discussed for various values of the physical parameters of interest.

Unsteady MHD Pulsatile Blood Flow through Porous Medium in a Stenotic Channel with Slip at the Permeable Walls Subjected to Time Dependent Velocity (Injection/Suction)

“…From Figs. 8,9,11, it is seen that the volumetric flow rate decreases with increasing the height of the stenosis  , the magnetic parameter M and the Reynolds number Re while the volumetric flow rate increases with increasing the Darcian linear drag parameter  as shown in Fig. 10.…”

Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method

“…In these investigations, many authors have used a no-slip boundary condition. Recently, some researchers have investigated boundary layer ow assuming a slip condition at the boundary [29][30][31][32][33][34][35].…”

Peristaltic transport of a Maxwell fluid in a porous asymmetric channel through a porous medium

“…Since, the first investigation done by Latham (1966) a large amount of literature is available on peristaltic motion of Newtonian and non-Newtonian fluid with different flow geometries Akram, Nadeem, & Hanif, 2013;Ali, Hayat, & Asghar, 2009;Eldesoky, 2012Eldesoky, , 2013Eldesoky & Mousa, 2010;El-Shehawey, El-Dabe, & El-Desoky, 2006;Mittra & Prasad, 1973;Nadeem & Akram, 2010;Nadeem, Akram, & Akbar, 2013;Shapiro, Jaffrin, & Weinberg, 1969). Peristaltic mechanism is a fluid transport induced by a progressive wave of area contraction or expansion along the walls of a distensible tube containing fluid.…”