A NONLINEAR UNSTEADY RESPONSE OF NON-NEWTONIAN BLOOD FLOW PAST AN OVERLAPPING ARTERIAL CONSTRICTION

Abstract

The present study deals with an appropriate mathematical model describing blood flow through a constricted artery that is used to analyze the physiological flow field. The time-variant geometry of the arterial segment having an overlapping type of constriction in the arterial lumen — which frequently occurs in diseased arteries, causing flow disorder and leading to malfunction of the cardiovascular system — is framed mathematically. Blood flow contained in the stenosed artery is treated as non-Newtonian (having shear-dependent viscosity) and is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics are not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow field can be obtained by first transforming radial coordinates with the use of appropriate boundary conditions, and then adopting a suitable finite difference scheme numerically. The unsteady response of the system and the influence of the arterial wall distensibility, the non-Newtonian rheology of blood, and the presence of stenosis on the important aspects of the physiological flow phenomena are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby validate the applicability of the present theoretical model.