Mathematical modeling of electro-magnetohydrodynamic pulsatile flow of an elastico-viscous fluid through an inclined porous tapered arterial stenosis

Abstract

The pulsatile and electro-osmotic motion of blood through a porous medium in an artery with multiple stenoses in the presence of a magnetic field has been studied considering blood as an incompressible electrically conducting and non-Newtonian fluid. The flow network is controlled by a system of coupled nonlinear partial differential equations. By means of small Reynolds number and mild stenoses assumptions, the system is simplified and solved by applying the Laplace and Hankel transforms. The Poisson-Boltzmann equation for electrical potential distribution is presumed to accommodate the electrical double layer. The closed-form explicit expressions of axial velocity, volume flow rate, wall shear stress, and flow resistance are given. The effects of physiologically pertinent parameters like tapering, electro-osmotic, angle of inclination, elastico-viscous parameter, Hartmann number, and Darcy number on the flow characteristics are discussed through graphs. It is found that a sophisticated combination of magnetic and electric fields can significantly control the motion of blood in diseased arteries. Further, the present mathematical model also generalizes the previous studies from the existing literature, which can be retrieved as particular cases.