Kh. S. Mekheimer

SUSPENSION MODEL FOR BLOOD FLOW THROUGH ARTERIAL CATHETERIZATION

This article is concerned with the analysis of a dusty model for the axi-symmetric flow of blood through coaxial tubes such that the outer tube with an axially nonsymmetreic but radially symmetric mild stenosis and the inner tube have a balloon (assumed that is axi-symmetric in nature). The mild stenosis approximation is used to solve the problem. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also employed to study the effect of the volume fraction density of the particles C, the maximum height attained by the balloon δ2, the radius of the inner tube, which keeps the balloon in position κ, and the axial displacement of the balloon x d . Flow parameters such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed numerically for different shape parameters n, C, δ2, κ, and x d . It is shown that the resistance to flow decreases with increasing values of the parameter determining the stenosis shape n and the axial displacement of the balloon x d , while the resistance to flow increases with the volume fraction density of the particles C, the radius of the inner tube, which keeps the balloon in position κ, and the maximum height attained by the balloon δ2. The magnitudes of the resistance to flow are higher in the case of a dusty fluid model than in the case of a Newtonian fluid model. The wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis possess a character similar to the resistance to flow with respect to C, δ2, κ, and x d . Finally, the effect of the volume fraction density of the particles C, δ2, and x d on the velocity profile are discussed.

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.

Effect of lateral walls on peristaltic flow through an asymmetric rectangular duct

Peristaltic transport of an incompressible viscous fluid due to an asymmetric waves propagating on the horizontal sidewalls of a rectangular duct is studied under long-wavelength and low-Reynolds number assumptions. The peristaltic wave train on the walls have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with velocity of the wave. The effect of aspect ratio, phase difference, varying channel width and wave amplitudes on the pumping characteristics and trapping phenomena are discussed in detail. The results are compared to with those corresponding to Poiseuille flow.

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.

Peristaltic transport through eccentric cylinders: Mathematical model

This paper discusses the effect of peristaltic transport on the fluid flow in the gap between two eccentric tubes eccentric-annulus flows. The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow analysis has been developed for low Reynolds number and long wave length approximation. The velocity and the pressure gradient have been obtained in terms of the dimensionless flow rate

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

\overline{Q}

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

, time t, azimuthal coordinate θ and eccentricity parameter e the parameter that controls of the eccentricity of the inner tube position. The results show that there is a significant deference between eccentric and concentric annulus flows.

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

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.