E.F. Elshehawey

Peristaltic Motion of an Incompressible Generalized Newtonian Fluid in a Planar Channel

Peristaltic flow in a two-dimensional channel with a sinusoidal wave is analyzed. Under the assumption of creeping motion, the problem is formulated using a perturbation expansion in terms of a variant of the Weissenberg number. To determine the characteristics of the peristaltic motion of shear thinning non-Newtonian fluids, the motion of a Carreau fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and neglecting wave number. We found the pumping rate of a Carreau fluid is less than that for a Newtonian having a shear viscosity the same as zero-shear-rate viscosity of the non-Newtonian fluid. The peristaltic pumping and the augmented pumping are discussed for various values of the physical parameters of interest.

Peristaltic Motion of a Generalized Newtonian Fluid Through a Porous Medium

In this paper, peristaltic motion of an incompressible non-Newtonian fluid through a porous medium is studied in a two-dimensional uniform channel with a sinusoidal wave using long wave approximation. The problem is formulated and analyzed using a perturbation expansion in terms of a variant of the Weissenberg number. Carreau flow is considered in this study to investigate the influence of porous medium. An analytic forms for axial velocity component and pressure gradient have been obtained. Moreover, the pressure rise and friction force were computed numerically. It has been shown that the pressure rise increases as the permeability decreases. Further, it is noted that both pressure rise and friction force does not depend on permeability parameter at a certain value of flow rate. The results were studied for various values of the physical parameters of interest.

Peristaltic transport of a magneto-fluid with porous boundaries

Peristaltic pumping by a sinusoidal traveling wave in the porous walls of a two-dimensional channel filled with a viscous incompressible conducting fluid under the effect of transverse magnetic field is investigated theoretically and graphically. It has been considered that the fluid entering the flow region through one plate at the same rate as it is leaving through the other plate. This rate called the porosity of the boundaries and denoted by V. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio is small. It has been noticed that the mean axial velocity and the reversal flow decrease by increasing the magnetic parameter. The mean axial velocity and the reversal flow decrease by increasing V until the upper quarter of the channel they increase by increasing V. Also the fluid motion is non-symmetric. Numerical results are reported for various of the physical parameters of interest.

Chebyshev finite difference method for MHD flow of a micropolar fluid past a stretching sheet with heat transfer

In this paper, the problem of heat transfer to MHD flow of a micropolar fluid from a stretching sheet with suction and blowing through a porous medium is studied numerically by using Chebyshev finite difference method (ChFD). A similarity solution to governing momentum, angular momentum and energy equations is derived. The effects of surface mass transfer, Prandtl number, magnetic field and porous medium on the velocities and temperature profiles have been studied. The numerical results indicate that, the velocity and the angular velocity increase as the permeability parameter increases but they decrease as the magnetic field increases. Also, the temperature decreases as the permeability parameter increases but it increases as the magnetic field increases.

MHD flow of an elastico-viscous fluid under periodic body acceleration.

Magnetohydrodynamic (MHD) flow of blood has been studied under the influ- ence of body acceleration. With the help of Laplace and finite Hankel transforms, an exact solution is obtained for the unsteady flow of blood as an electrical conducting, incompress- ible and elastico-viscous fluid in the presence of a magnetic field acting along the radius of the pipe. Analytical expressions for axial velocity, fluid acceleration and flow rate has been obtained.

Pulsatile Flow of Blood through a Porous Mediumunder Periodic Body Acceleration

Pulsatile flow of blood through a porous medium has been studied studied underthe influence of body acceleration. With the help of Laplace and finite Hankeltransforms, analytic expressions for axial velocity, fluid acceleration, flow rate,and shear stress have been obtained.

Peristaltic transport of three-layered flow with variable viscosity

This paper is an analytical study of peristaltic motion of an incompressible newtonian fluid through a channel in the presence of three layers flow with different viscosities. We use a small Reynolds number and long wavelengths approximations to solve the system of the governing equations. The interfaces shapes are described by a system of non-linear fourth-order algebraic equations. We solve this system numerically. We present a detailed analysis of the effects of both peripheral and intermediate layers on the fluid motion. The effect of the variation of the two viscosities on the mechanical efficiency has been studied. The trapping limits are found. Also, the variation of trapping width with the variation of the volume flow rate has been investigated. It has been noticed that the shape of interfaces, the pumping performance and the mechanical efficiency affect by the variation of the viscosity of the peripheral layer more than the variation of the viscosity of the intermediate layer.

Peristaltic viscoelastic fluid motion in a tube.

Peristaltic motion of viscoelastic incompressible fluid in an axisymmetric tube with a sinusoidal wave is studied theoretically in the case that the radius of the tube is small relative to the wavelength. Oldroyd flow has been considered in this study and the problem is formulated and analyzed using a perturbation expansion in terms of the variation of the wave number. This analysis can model the chyme movement in the small intestine by considering the chyme as an Oldroyd fluid. We found out that the pumping rate of Oldroyd fluid is less than that for a Newtonian fluid. Further, the effects of Reynolds number, Weissenberg number, amplitude ratioand wave number on the pressure rise and friction force have been discussed. It is found that the pressure rise does not depend on Weissenberg number at a certain value of flow rate. The results are studied for various values of the physical parameters of interest.

Effect of inclined magnetic field on magneto fluid flow through a porous medium between two inclined wavy porous plates (numerical study)

In this paper, the problem of an incompressible viscous fluid moving through a porous medium (Brinkmain model) between two inclined wavy porous plates under the effects of a constant inclined magnetic field that makes an angle with the vertical axis and constant suction (or injection) is studied numerically by a method related to that of Takabatake-Ayukawa in 1982. The present approach is not restricted by any of the parameters appearing in the problem such as Reynolds number, Froude number, magnetic parameter, suction (or injection) parameter, permeability parameter, wave number and amplitude ratio. The effects of the above variable parameters on the velocity, stream function and pressure gradient profiles have been studied. Moreover, the effect of varying the Froude number and the inclined angle on the pressure gradient and pressure rise is studied.

Peristaltic Motion of Generalized Newtonian Fluid in a Non-Uniform Channel

The problem of peristaltic transport of a non-Newtonian (Carreau) fluid in a non-uniform channel has been investigated under zero Reynolds number with long wavelength approximation. The problem is formulated using a perturbation expansion in terms of a variant of Weissenberg number. It is assumed that chyme in the male small intestine behave like Carreau fluid since most of the physiological fluid behave like a non-Newtonian fluid. Pressure rise and friction force, in the case of non-uniform geometry, are found much smaller than the corresponding values in the case of uniform geometry. Furthermore, the pressure rise and the friction force are smaller in the case of Carreau fluid than Newtonian fluid. A comparison between Carreau fluid, couple-stress fluid and Casson fluid is given. The pressure rise and friction force are discussed for various of the physical parameters of interest.