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An unsteady analysis of nonlinear two‐layered 2D model of pulsatile flow through stenosed arteries

    P. K. Mandal Affiliation

Abstract


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.


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Santrauka



Straipsnyje ištirti raudonuju kraujo kūneliu koncentracijos efektai ir periferinio sluoksnio klampumas priklausomai nuo pulsavimo fiziologiniu charakteristiku, esant nestipriai stenozei. Tekantis kraujas aprašomas dvieju skysčiu modeliu, vienas iš ju laikomas neniutoniniu skysčiu, kitas ‐ periferine plazma, laikoma niutoniniu skysčiu be jokiu lasteliu. Kraujo srauto klampumas yra hematokrito funkcija, kuri keičiasi pagal spinduli neniutoniniame skystyje, o plazmoje nekinta. I modelio tyrima itraukti arteriju sieneliu judejimas ir jo sukelti efektai lokaliajai skysčio mechanikai. Baigtiniu skirtumu schema naudojama spresti nestacionarias Navier‐Stokes lygtis cilindrinese koordinatese, kai laminarines salygos tenkina ašinio simetriškumo salyga, ir uždavinys yra faktiškai dvimatis. Pateiktas skaitinis eksperimentas patvirtina modelio tinkamuma.


First Published Online: 14 Oct 2010

Keyword : Hematocrit, Stenosis, Inhomogeneous Newtonian, Resistive impedance, Wall shear stress

How to Cite
Mandal, P. K. (2003). An unsteady analysis of nonlinear two‐layered 2D model of pulsatile flow through stenosed arteries. Mathematical Modelling and Analysis, 8(3), 229-246. https://doi.org/10.3846/13926292.2003.9637226
Published in Issue
Sep 30, 2003
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