D. S. Sankar

Two-Phase Non-Linear Model for the Flow Through Stenosed Blood Vessels

Pulsatile flow of a two-phase model for blood flow through arterial stenosis is analyzed through a mathematical analysis. The effects of pulsatility, stenosis, peripheral layer and non-Newtonian behavior of blood, assuming the blood in the core region as a Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid, are discussed. A perturbation method is used to solve the resulting system of non-linear quasi-steady differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. It is noticed that the plug core radius and resistance to flow increase as the stenosis size increases while all other parameters held constant The wall shear stress increases with the increase of yield stress while keeping other parameters as invariables. It is observed that the velocity increases with the axial distance in the stenosed region of the tube upto the maximum projection of the stenosis.

Two-Fluid Mathematical Models for Blood Flow in Stenosed Arteries: A Comparative Study

The pulsatile flow of blood through stenosed arteries is analyzed by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is assumed as a (i) Herschel-Bulkley fluid and (ii) Casson fluid. Perturbation method is used to solve the resulting system of non-linear partial differential equations. Expressions for various flow quantities are obtained for the two-fluid Casson model. Expressions of the flow quantities obtained by Sankar and Lee (2006) for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is found that the plug flow velocity and velocity distribution of the two-fluid Casson model are considerably higher than those of the two-fluid Herschel-Bulkley model. It is also observed that the pressure drop, plug core radius, wall shear stress and the resistance to flow are significantly very low for the two-fluid Casson model than those of the two-fluid Herschel-Bulkley model. Hence, the two-fluid Casson model would be more useful than the two-fluid Herschel-Bulkley model to analyze the blood flow through stenosed arteries.

Pulsatile Flow of Two-Fluid Nonlinear Models for Blood Flow through Catheterized Arteries: A Comparative Study

The pulsatile flow of blood through catheterized arteries is analyzed by treating the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is represented by (i) Casson fluid and (ii) Herschel-Bulkley fluid. The expressions for the flow quantities obtained by Sankar (2008) for the two-fluid Casson model and Sankar and Lee (2008) for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is noted that the plug-flow velocity, velocity distribution, and flow rate of the two-fluid H-B model are considerably higher than those of the two-fluid Casson model for a given set of values of the parameters. Further, it is found that the wall shear stress and longitudinal impedance are significantly lower for the two-fluid H-B model than those of the two-fluid Casson model.

Mathematical Analysis for MHD Flow of Blood in Constricted Arteries

Abstract The unsteady oscillatory magneto-hydrodynamic flow of blood in small diameter arteries with mild constriction is analyzed, blood being modelled as a Herschel-Bulkley fluid. Finite difference method is employed for solving the associated initial boundary value problem. Explicit finite difference schemes for velocity distribution, flow rate, skin friction and longitudinal impedance to the flow are obtained. The effects of pressure gradient, yield stress, magnetic field, power law index and maximum depth of the stenosis on the aforesaid flow quantities are discussed through appropriate graphs. It is found that the velocity and flow rate decrease and the skin friction and longitudinal impedance to flow increase with the increase of the magnetic field parameter. It was recorded that the flow rate increases and the skin friction decreases with the increase of the phase angle. It was also noted the skin friction and longitudinal impedance to flow that increase almost linearly with the increase of maximum depth of the stenosis. The estimates of the increase in the longitudinal impedance to flow and skin friction are increased considerably by the presence of the magnetic field.

Mathematical Analysis of Carreau Fluid Model for Blood Flow In Tapered Constricted Arteries

The pulsatile blood flow in tapered asymmetrically constricted narrow artery is investigated, treating the blood as Carreau fluid model. The expressions obtained by Sankar (2016) for various flow quantities are used to analyze the flow in different arterial geometry. It is found that the wall shear stress and longitudinal impedance to flow decrease with the increase of stenosis shape parameter, amplitude of the pulsatile pressure gradient, flow rate, power law index and Weissenberg number. The estimates of the percentage of increase in the wall shear stress and longitudinal impedance to flow increase with the increase of the angle tapering.