Mathematical models of blood flow in stenosed arteries involving non-newtonian fluids

Abstract

The objective of present thesis is to explore the flow of blood in the stenotic blood vessels with and without considering the properties of the tapering angle. The consequences of magnetic field and periodic body acceleration have been explored. Various shapes of the stenosis are chosen to highlight the impact of the mechanical structure of the blood vessel. The Herschel-Bulkley, Bingham plastic, power law and Sutterby fluid models are utilized to capture the non-Newtonian rheological behaviour of the blood in the stenosed blood vessels under diseased conditions. The dynamic response to the heat and mass concentration to the blood streaming in the stenotic blood vessel has been incorporated. The flow equations involving continuity, momentum, energy and mass concentration accomplished with appropriate boundary conditions are nondimensionalized. The mild stenosis assumption is utilized to simplify the flow equations of the flow. The resultant equations are solved analytically using regular perturbation method and numerically by using the explicit finite difference scheme. The physical implication of various emerging parameters on the velocity, wall shear stress, volumetric flux, longitudinal resistance to the flow, temperature and mass concentration are displayed through graphs and are discussed in detail. A comprehensive comparison between different flow geometries and different fluid models is also presented. It is concluded that increase in the yield stress enhances the resistance to the flow. The radius of the plug flow region is expressively altered by the change in the tapering parameter and the severity of the stenosis. The higher values of body acceleration and the inclination angle give rise to the velocity of the blood. The converging diverging and non-tapering structure of the arterial blood vessel bears a potential to bring out significant changes in temperature and mass concentration within the fluid.