Mathematical modeling of electro hydrodynamic non-Newtonian fluid flow through tapered arterial stenosis with periodic body acceleration and applied magnetic field

Abstract

A mathematical model is proposed to the pulsatile flow of blood in a tapered artery with mild constriction. This study considers blood as an electrically conducting, non-Newtonian fluid (Jeffrey fluid) which contains magnetic nanoparticles. As blood conducts electricity, it exerts an electric force along the flow direction due to the induced magnetic force by an applied magnetic field which produces Lorentz force and influences the fluidity. Assuming that the pulsatile fluid flow is accelerated by a body force that has in slip velocity at the wall, a set of coupled nonlinear Navier–Stokes equation governing the flow networks is obtained. By employing Laplace and Hankel transforms on the partial equations, we obtain an exact solution for the velocity of flow pattern. Further, the evaluated axial velocity of both fluid and particle are used to find the physiological quantities such as shear stress, flow resistivity and volume of fluid flow. Their dependency on the Womersley parameter, Hartmann number, shape parameter, Jeffrey number and electrokinetic number are calculated numerically and explained graphically. Furthermore, the results are compared with in slip and no slip velocities.