Mathematical analysis of a non-newtonian model for blood flow considering shear rate dependent viscosity through a stenosed artery in presence of magnetic field

Abstract

The study of blood flow in the artery has some important aspects due to bio-medical engineering application. Many of the problems such as heart attacks and strokes are related to blood flow and also the physical characteristics of the artery wall. The abnormal and unnatural growth in the arterial wall thickness that develops at various locations of the cardiovascular system under diseased conditions is called arteriosclerosis or stenosis. The hemodynamic instability behavior of the blood flow is influenced by the presence of arterial stenosis. This study of magnetic field through blood flow is useful in the field of vascular surgery for proper circulation of blood by controlling blood flow. In this thesis, a mathematical model regarding non-Newtonian blood flow considering shear rate dependent viscosity through human artery in presence of magnetic field is developed. Three types of artery are considered: a regular, a stenosed and a grafting artery. Magnetic field of different magnitude and direction is applied to the artery. The governing equations are solved using finite element method. Comparison with previously published work is performed and the results are found to be in excellent agreement. Some results of numerical simulation are presented for the blood flow in terms of the velocity contours, pressure distribution and shear rate. Also velocity profile at different arterial location has been presented. The results show that the magnetic field perpendicular to the artery wall is most effective in reduction of flow.