Mathematical modelling of pulsatile flow of Casson’s fluid in arterial stenosis
ABSTRACT The effects of non-Newtonian nature of blood and pulsatility on flow through a stenosed artery have been investigated. It is of interest to note that the thickness of the viscous flow region changes with axial distance. An important result is that the mean and steady flow rates decrease as the yield stress increases. The critical value of the yield stress at which the flow rate behaviour changes from one type to another has been determined. Another important result of pulsatility is the mean resistance to flow is greater than its steady flow value, whereas the mean value of the wall shear for pulsatile blood flow is equal to steady wall shear stress. The velocity profiles and associated physiological characteristics involved in the analysis have been determined. Many standard results regarding Casson and Newtonian fluids flow, uniform and steady flow in an artery can be obtained in the present analysis as the special cases.
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ABSTRACT: A computational model is developed to analyze the unsteady flow of blood through stenosed tapered narrow arteries, treating blood as a two-fluid model with the suspension of all the erythrocytes in the core region as Herschel-Bulkley fluid and the plasma in the peripheral layer as Newtonian fluid. The finite difference method is employed to solve the resulting system of nonlinear partial differential equations. The effects of stenosis height, peripheral layer thickness, yield stress, viscosity ratio, angle of tapering and power law index on the velocity, wall shear stress, flow rate and the longitudinal impedance are analyzed. It is found that the velocity and flow rate increase with the increase of the peripheral layer thickness and decrease with the increase of the angle of tapering and depth of the stenosis. It is observed that the flow rate decreases nonlinearly with the increase of the viscosity ratio and yield stress. The estimates of the increase in the longitudinal impedance to flow are considerably lower for the two-fluid Herschel-Bulkley model compared with those of the single-fluid Herschel-Bulkley model. Hence, it is concluded that the presence of the peripheral layer helps in the functioning of the diseased arterial system.Boundary Value Problems 01/2010; · 0.92 Impact Factor
- Mathematical Modelling and Analysis. 12/2008; 13:401-412.
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ABSTRACT: A theoretical investigation concerning the influence of externally imposed periodic body acceleration on the flow of blood through a time-dependent stenosed arterial segment by taking into account the slip velocity at the wall of the artery has been carried out. A mathematical model is developed by treating blood as a non-Newtonian fluid obeying the Casson fluid model. The pulsatile flow is analyzed by considering a periodic pressure gradient and the inertial effects as negligibly small. A suitable generalized geometry for time-dependent stenosis is taken into account. Perturbation method is used to solve the coupled implicit system of nonlinear differential equations that govern the flow of blood. Analytical expressions for the velocity profile, volumetric flow rate, and wall shear stress are obtained. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in this study. The computational results are presented graphically. The results for different values of the parameters involved in the problem under consideration presented here show that the flow is appreciably influenced by slip velocity in the presence of periodic body acceleration.ISRN Biomedical Engineering. 08/2013; 2013:1-10.