A study on two-layered (K.L-Newtonian) model of blood flow in an artery with six types of mild stenoses

摘要

A mathematical model of the steady flow of blood in arteries with six different types of mild stenoses (symmetric, triangular, trapezoidal, elliptical, bell-shaped and composite) is analyzed. The model comprises a core (suspension of cells) surrounded by a layer of plasma near the wall. The rheology of blood in the core region is characterized by a K-L (non-Newtonian) fluid model and the peripheral plasma layer as a Newtonian fluid. An attempt has been made to obtain analytical expressions for the velocity of blood flow in the stenotic arterial region, radius of the plug-core region, the velocity of the fluid in the plug-flow region, flow flux, shear stress at wall and resistance to flow, using the suitable boundary conditions. The computational results were presented graphically for several values of the parameters involved in the present analysis, and also several comparisons have been made with the existing models to endorse the applicability of the present model. The study revealed that the velocity of blood decreases by increasing values of the yield stress of the blood and K-L fluid parameters and an opposite nature is observed for wall shear stress and resistive impedance to flow. It is found that the shape of the plug flow region is purely dependent on the shape of the stenosis present in the cardiovascular system. It is also recovered that the wall shear stress and flow resistance are significantly reduced for the two-layered model (K.L-Newtonian) than those of the one-layered model (K-L) irrespective of the type of geometries of stenosis. Also, the axial variation of wall shear stress and resistive impedance are lowest for the bell-shaped stenosis than those of the other stenoses considered in the present study, and they found to be highest for the trapezoidal stenosis. A comparison of the velocity profiles obtained from the present study with the experimental data is made, and a good agreement between them is found. Further, the relevant physiological applications of the present mathematical model have been analyzed.