Open AccessAN UNSTEADY ANALYSIS OF NONLINEAR TWO‐LAYERED 2D MODEL OF PULSATILE FLOW THROUGH STENOSED ARTERIES
Author(s) -
Prashanta Kumar Mandal
Publication year - 2003
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2003.9637226
Subject(s) - pulsatile flow , newtonian fluid , mechanics , laminar flow , shear stress , microvessel , viscosity , generalized newtonian fluid , herschel–bulkley fluid , flow (mathematics) , reynolds number , nonlinear system , mathematics , classical mechanics , physics , thermodynamics , turbulence , shear rate , medicine , immunohistochemistry , quantum mechanics , cardiology
The effects of red cell concentration and peripheral layer viscosity on physiological characteristics of pulsatile flow in presence of mild stenosis are investigated. The flowing blood is represented by a two‐fluid model, consisting of a core region of suspension of all the erythrocytes assumed to be non‐Newtonian (inhomogeneous Newtonian) and a peripheral plasma layer free from cells of any kind as a Newtonian fluid. In the realm of the flow characteristics of blood the viscosity is taken to be a function of hematocrit in a manner that it varies radially only in the central core characterising its non‐Newtonian behaviour while it remains constant in the plasma region. The arterial wall motion and its effect on local fluid mechanics is also incorporated in the present theoretical study. Finite difference scheme has been used to solve the unsteady Navier‐Stokes equations in cylindrical coordinates assuming axial symmetry under laminar conditions, so that the problem effectively becomes two‐dimensional. The nonlinear terms appearing in the Navier‐Stokes equations governing blood flow are accounted for. Finally, the numerical illustration presented at the end of the paper provides an effective measure of the flux, the resistive impedance and the wall shear stress quantitatively in order to validate the applicability of the present model.