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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.

Catheterization has an imperative rule in heat transfer investigations, which are frequently applied to analyze and deal with the heart transfer studies. Here, the entering of a catheter adjusts the flow of the blood and it affects the hemodynamic status in the artery region. In practical clinical cases, catheters cannot be precisely concentric with the artery. The impartial of this work is to investigate the behavior of a blood streaming characteristics, in the case of injecting the catheter eccentrically all the way through a stenotic overlapping artery. In this paper, we consider the heat transfer within the presence of blood corpuscle which has been characterized by a macroscopic two-phase model (i.e. a suspension of erythrocytes in plasma). The model here considers the blood fluid as a liquid fluid with adjourned particles in the gap bounded by the eccentric cylinder. The inside cylinder is identically rigid demonstrating the movable thin catheter and kept at constant temperature, where the outer cylinder is a taper cylinder demonstrating the artery that has overlapping stenosis and it is cooled and maintained at zero temperature. The coupled differential equations for both fluid (plasma) and particle (erythrocyte) phases have been solved. The expressions for the flow characteristics, namely, the flow rate, the impedance (resistance to flow), the wall shear stress and the temperature distribution, have been derived. The model is very useful in medicine, where the hemodynamic speed is higher for eccentric case than that of concentric one. Also, the temperature distribution and the entropy generation in the state of eccentric position are higher than in the case of the concentric position. A significant increase in the magnitude of the impedance and the wall shear stress occurs for an increase in the hematocrit, C for diseased blood.

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 rateQ¯, timet, azimuthal coordinate θ and eccentricity parameter ϵ (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.

The heat transfer characteristics of a couple-stress fluid (CSF) in a two-dimensional asymmetric channel is analyzed. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Mathematical modeling corresponding to the two-dimensional couple stress fluid is made. Analytical expressions for the axial velocity, stream function, heat transfer, and the axial pressure gradient are established using long wavelength assumption. Numerical computations have been carried out for the pressure rise per wavelength. The influence of various parameters of interest is seen through graphs on frictional forces, pumping and trapping phenomena, and temperatureproflle.