Boundary Value Problems
Volume 2010 (2010), Article ID 917067, 16 pages
Research Article

FDM Analysis for Blood Flow through Stenosed Tapered Arteries

School of Mathematical Sciences, Science University of Malaysia, 11800 Penang, Malaysia

Received 23 October 2009; Accepted 8 March 2010

Academic Editor: Salim Messaoudi

Copyright © 2010 D. S. Sankar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A computational model is developed to analyze the unsteady flow of blood through stenosed tapered narrow arteries, treating blood as a two-fluid model with the suspension of all the erythrocytes in the core region as Herschel-Bulkley fluid and the plasma in the peripheral layer as Newtonian fluid. The finite difference method is employed to solve the resulting system of nonlinear partial differential equations. The effects of stenosis height, peripheral layer thickness, yield stress, viscosity ratio, angle of tapering and power law index on the velocity, wall shear stress, flow rate and the longitudinal impedance are analyzed. It is found that the velocity and flow rate increase with the increase of the peripheral layer thickness and decrease with the increase of the angle of tapering and depth of the stenosis. It is observed that the flow rate decreases nonlinearly with the increase of the viscosity ratio and yield stress. The estimates of the increase in the longitudinal impedance to flow are considerably lower for the two-fluid Herschel-Bulkley model compared with those of the single-fluid Herschel-Bulkley model. Hence, it is concluded that the presence of the peripheral layer helps in the functioning of the diseased arterial system.