Mathematical modelling of blood flow through a tapered overlapping stenosed artery with variable viscosity

TL;DR

This study develops an analytical model for blood flow in a tapered, stenosed artery considering variable viscosity, magnetic field effects, and porous medium assumptions, providing insights into flow characteristics and wall shear stress.

Contribution

It introduces a comprehensive analytical approach incorporating variable blood viscosity, magnetic field influence, and artery shape effects on blood flow in stenosed arteries.

Findings

Hematocrit and magnetic field significantly affect velocity profiles.

Artery shape influences pressure gradient and shear stress.

Primary stenosis impacts secondary stenosis behavior.

Abstract

This paper presents a theoretical study of blood flow through a tapered and overlapping stenosed artery under the action of an externally applied magnetic field. The fluid (blood) medium is assumed to be porous in nature. The variable viscosity of blood depending on hematocrit (percentage volume of erythrocytes) is taken into account in order to improve resemblance to the real situation. The governing equation for laminar, incompressible and Newtonian fluid subject to the boundary conditions is solved by using a well known Frobenius method. The analytical expressions for velocity component, volumetric flow rate, wall shear stress and pressure gradient are obtained. The numerical values are extracted from these analytical expressions and are presented graphically. It is observed that the influence of hematocrit, magnetic field and the shape of artery have important impact on the velocity profile, pressure gradient and wall shear stress. Moreover, the effect of primary stenosis on the secondary one has been significantly observed.