A four-layered model for flow of non-Newtonian fluid in an artery with mild stenosis

Abstract

The present article deals with a four-layered mathematical model for blood flow through an artery with mild stenosis. The four-layered model comprises a cell-rich core of suspension of all the erythrocytes described as a non-Newtonian (Jeffrey) fluid, a peripheral zone of cell-free plasma (Newtonian fluid) and the stenosed artery with porous wall consisting of a thin transition (Brinkman) layer followed by Darcy region. Analytical expressions have been obtained for velocity profiles in all the four regions, total volumetric flow rate, wall shear stress and flow impedance. MATLAB software is employed to compute numerical values of the pressure gradient. The influences of different parameters such as variable core fluid viscosity, hematocrit, thickness of the plasma layer, Brinkman and Darcy layer thickness, Darcy number, Jeffrey fluid parameter, and size and shape parameters of stenosis on the physiologically vital flow characteristics, specifically velocity profile, volume flow rate, wall shear stress and flow impedance, have been examined. It is observed that the wall shear stress and resistive impedance decrease with the increase of plasma layer thickness, Jeffrey fluid parameter, Darcy number and Darcy slip parameter, and increase with the rise of hematocrit. The results in the case of variable core viscosity and constant core viscosity are compared to investigate the impact of variable core viscosity in managing the flow of blood.