Chebyshev collocation approach to stability of blood flows in a large artery

Abstract

In this study, treating the large artery as a rigid channel with uniform width and the blood as an incompressible Newtonian fluid with variable viscosity due to transverse variation in hematocrit ratio, the basic flow structure and its temporal stability to small disturbances were studied. A fourth-order Eigenvalues problem which reduces to the well known Orr–Sommerfeld equation in some limiting cases was obtained and solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials implemented in MATLAB. Graphical results for the basic flow axial velocity, disturbance growth rate and marginal stability curve are presented and discussed. It is worth pointing out that a transverse increase in the blood hematocrit ratio towards the central region of the artery had a stabilizing effect on the flow.

Key words: Arterial blood flow, hematocrit ratio, variable viscosity, temporal stability, Chebyshev spectral collocation technique.