Slip effects on unsteady non-Newtonian blood flow through an inclined catheterized overlapping stenotic artery

Akbar Zaman,M Sajid,Nasir Ali

doi:10.1063/1.4941358

Abstract

Slip effects on unsteady non-Newtonian blood hydro-magnetic flow through an inclined catheterized overlapping stenotic artery are analyzed. The constitutive equation of power law model is employed to simulate the rheological characteristics of the blood. The governing equations giving the flow derived by assuming the flow to be unsteady and two-dimensional. Mild stenosis approximation is employed to obtain the reduced form of the governing equations. Finite difference method is employed to obtain the solution of the non-linear partial differential equation in the presence of slip at the surface. An extensive quantitative analysis is performed for the effects of slip parameter, Hartmann number, cathetered parameter and arterial geometrical parameters of stenosis on the quantities of interest such as axial velocity, flow rate, resistance impedance and wall shear stress. The streamlines for the blood flow through the artery are also included.

Highlights

A detail literature survey reveals that the cardiovascular disease is the most important factor in deaths
An extensive quantitative analysis is performed for the effects of slip parameter, Hartmann number, cathetered parameter and arterial geometrical parameters of stenosis on the quantities of interest such as axial velocity, flow rate, resistance impedance and wall shear stress
A mathematical model for magneto-hydrodynamic pulsatile flow of blood through overlapping stenotic artery incorporating the effects of inclination angle and slip is presented

Summary

INTRODUCTION

A detail literature survey reveals that the cardiovascular disease is the most important factor in deaths. Theoretical knowledge of the blood circulation, hemodynamics, offers significant help in diagnosis of the coronary disease. A glance of literature shows that several researcher have provided mathematical/theoretical studies for the blood circulation inside arteries subject to several problems. Motivated by above mentioned studies, the unsteady flow of blood flow through an inclined catheterized artery with overlapping stenosis in the presence of uniform magnetic field is considered in this paper. The present analysis generalizes the results in Ref. 9 by taking into account non-Newtonian rheology of the streaming blood, two dimensional blood flow and the overlapping stenotic nature of the artery. The unsteady oscillatory flow considered here is a variant of flow over an oscillatory stretching sheet studied by several other authors.[12,13,14,15,16,17] The structure of the paper is as follows: Section II illustrates mathematical formulation of the problem and development of flow equations.

MATHEMATICAL FORMULATION

NUMERICAL SOLUTION USING FINITE DIFFERENCE METHOD

RESULTS AND DISCUSSION

CONCLUSIONS