Generalized power-law model of magnetohydrodynamic blood flow in an inclined stenosed artery with body acceleration

Abstract

This thesis focuses on the development of a mathematical model to investigate the effect of magnetic field and body acceleration on blood flow characteristics, heat and mass transfer from a stenosed artery, a condition due to the abnormal narrowing of a blood vessel. The arterial segment is assumed to be a cylindrical tube in an inclined position with oscillating boundary condition and the stenosis taking the shape of a cosine function. The momentum equation is based on the generalized power law model which is expected to handle the variations in blood rheology as blood flows through a different-sized vessel, with the index n < 1, n > 1 and n = 0 describing the shear-thinning, shear-thickening and Newtonian fluid respectively. The full governing equations comprising the generalized power-law equation, heat and mass equations are non-linear partial differential equations whose numerical procedure involves the discretization of the equations using the Marker and Cell (MAC) method, where pressure along the tube is calculated iteratively using the Successive-Over-Relaxation (SOR) technique. The results have been compared and validated with existing results in certain limiting cases. New results in terms of pressure, streamlines, heat and mass distribution are obtained for various parameter values of each of the external body forces. Specifically, for a stenosis with 48% occlusion, separation is seen to occur for Newtonian fluids at Re = 1000 and this region can be seen to increase in the case of shear thickening fluids, while the shear-thinning fluid is shown to be free of separation region. Moreover, blood velocity, wall shear stress and pressure drop decrease with increase n, while heat and mass transfer increase. It is also demonstrated through the simulations that under the influence of magnetic field, the velocity in the centre of the artery and the separation region are reduced with a sufficient strength of magnetic field, depending on the severity of stenosis. For a 75% and 84% occlusion, the separation zones entirely disappear with magnetic strength 8 and 12 Tesla respectively, while the pressure drop, wall shear stress, heat and mass transfer increase. On the other hand, increasing periodic body acceleration leads to increase velocity and the pressure drop while reducing heat and mass transfer. Inclination angle increases the velocity and wall shear stress but decreases the pressure drop and heat and mass transfer. Based on the results, patients with blood vessel disease are advised not to do a high-intensity exercise; it can put extra strain on the heart leading to a risk in chest pain or even cardiac arrest. Regular exercise and suitable intensity of magnetic field could enhance vascular health.