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# Mathematical modelling of pulsatile flow of Casson’s fluid in arterial stenosis

Department of Mathematics, Harcourt Butler Technological Institute, Kanpur 208 002, India; Department of Mathematics, K.N.I.T., Sultanpur, India

Applied Mathematics and Computation (Impact Factor: 1.35). 01/2009; DOI: 10.1016/j.amc.2007.05.070 Source: DBLP

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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 -
##### Article: Mathematical Analysis of blood flow through an arterial segment with time dependent stenosis

Mathematical Modelling and Analysis. 12/2008; 13:401-412. - [Show abstract] [Hide abstract]

**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.

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