Y. Abd Elmaboud

PARTICULATE SUSPENSION FLOW INDUCED BY SINUSOIDAL PERISTALTIC WAVES THROUGH ECCENTRIC CYLINDERS: THREAD ANNULAR

This paper describes a new model for obtaining analytical solutions of peristaltic flow through eccentric annuli. A mathematical model of peristaltic pumping of a fluid mixture (as blood model) in a circular eccentric cylinders is presented and it is motivated due to the fact that thread injection is a promising method for placing medical implants within the human body with minimum surgical trauma. For the eccentric annuli, the inner cylinder is rigid and moving with a constant velocity V, and the outer one is hollow flexible cylinder that has a sinusoidal wave traveling down its wall. The coupled differential equations for both the fluid and the particle phases have been solved by using two methods and the expressions for the velocity distribution of fluid and particle phase, flow rate, pressure drop, friction forces at the inner and outer cylinders have been derived. The results obtained are discussed in brief. The significance of the particle concentration and the eccentricity parameter as well as the nature of the basic flow has been well explained.

Thermal Properties of Couple-Stress Fluid Flow in an Asymmetric Channel With Peristalsis

The heat transfer characteristics of a couple-stress fluid (CSF) ina two-dimensional asymmetric channel is analyzed. The channelasymmetry is produced by choosing the peristaltic wave train onthe walls to have different amplitudes and phase. Mathematicalmodeling corresponding to the two-dimensional couple stress fluidis made. Analytical expressions for the axial velocity, stream func-tion, heat transfer, and the axial pressure gradient are establishedusing long wavelength assumption. Numerical computations havebeen carried out for the pressure rise per wavelength. The influ-ence of various parameters of interest is seen through graphs onfrictional forces, pumping and trapping phenomena, and tempera-ture profile. [DOI: 10.1115/1.4023127]Keywords: peristaltic flow, heat transfer, couple-stress fluid,frictional force

Series solution of a natural convection flow for a Carreau fluid in a vertical channel with peristalsis

An analysis has been achieved to study the natural convection of a non-Newtonian fluid (namely a Carreau fluid) in a vertical channel with rhythmically contracting walls. The Navier-Stokes and the energy equations are reduced to a system of non- linear PDE by using the long wavelength approximation. The optimal homotopy analysis method (OHAM) is introduced to obtain the exact solutions for velocity and temperature fields. The convergence of the obtained OHAM solution is discussed explicitly. Numerical calculations are carried out for the pressure rise and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail.

Peristaltic transport of a particle--fluid suspension through a uniform and non-uniform annulus

This study looks at the influence of an endoscope on the peristaltic flow of a particle--fluid suspension as blood model through tubes. A long wavelength approximation through a uniform and non-uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V0, whereas the outer non-uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase uf, particulate phase up and the pressure gradients have been obtained in terms of the dimensionless flow rate \bar{Q}, the amplitude ratio φ, particle concentration C, the velocity constant V0 and the radius ratio ∈ the ratio between the radius of the inner tube and the radius of the outer one at the inlet. Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes.

The influence of a micropolar fluid on peristaltic transport in an annulus: application of the clot model

A serious pathological condition is encountered when some blood constituents deposited on the blood vessels get detached from the wall, join the blood stream again and form a clot. Study of the peristaltic transport of a micropolar fluid in an annular region is investigated under low Reynolds number and long wavelength approximations. We model a small artery as a tube having a sinusoidal wave travelling down its wall and a clot model inside it. Closed form solutions are obtained for the velocity and the microrotation components, as well as the stream function, and they contain new additional parameters, namely, δ, the height of the clot, N, the coupling number and m, the micropolar parameter. The pressure rise and friction force on the inner and the outer tubes have been discussed for various values of the physical parameters of interest.

The Flow Separation of Peristaltic Transport for Maxwell Fluid between Two Coaxial Tubes

We study the peristaltic mechanism of an incompressible non-Newtonian biofluid (namely, Maxwell model) in the annular region between two coaxial tubes. The inner tube represents the endoscope tube. The system of the governing nonlinear PDE is solved by using the perturbation method to the first order in dimensionless wavenumber. The modified Newton-Raphson method is used to predict the flow separation points along the peristaltic wall and the endoscope tube. The results show that the presence of the endoscope (catheter) tube in the artery increases the pressure gradient and shear stress. Such a result seems too reasonable from the physical and medical point of view.

A Study of Nonlinear Variable Viscosity in Finite-Length Tube with Peristalsis

Peristaltic motion of an incompressible Newtonian fluid with variable viscosity induced by periodic sinusoidal traveling wave propagating along the walls of a finite-length tube has been investigated. A perturbation method of solution is sought. The viscosity parameter α (α << 1) is chosen as a perturbation parameter and the governing equations are developed up to the first-order in the viscosity parameter (α). The analytical solution has been derived for the radial velocity at the tube wall, the axial pressure gradient across the length of the tube, and the wall shear stress under the assumption of low Reynolds number and long wavelength approximation. The impacts of physical parameters such as the viscosity and the parameter determining the shape of the constriction on the pressure distribution and on the wall shear stress for integral and non-integral number of waves are illustrated. The main conclusion that can be drawn out of this study is that the peaks of pressure fluctuate with time and attain different values with non-integral numbers of peristaltic waves. The considered problem is very applicable in study of biological flow and industrial flow.

Unsteady Flow of Magneto Thermomicropolar Fluid in a Porous Channel With Peristalsis: Unsteady Separation

The magneto thermodynamic aspects of micropolar fluid (blood model) through an isotropic porous medium in a nonuniform channel with rhythmically contracting walls have been investigated. The flow analysis has been discussed under long wavelength and low Reynolds number approximations. The closed form solutions are obtained for velocity components, microrotation, heat transfer, as well as the wall vorticity. The modified Newton–Raphson method is used to predict the unsteady flow separation points along the peristaltic wall. Numerical computations have been carried out for the pressure rise per wavelength. The study shows that peristaltic transport, fluid velocity, microrotation velocity, and wall shear stress are significantly affected by the nonuniform geometry of the blood vessels. Moreover, the amplitude ratio, the coupling number, the micropolar parameter, and the magnetic parameter are important parameters that affect the flow behavior.