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: Pulsatile flow of blood in constricted narrow arteries under periodic body acceleration is analyzed, modeling blood as non-Newtonian fluid models with yield stress such as (i) Herschel-Bulkley fluid model and (ii) Casson fluid model. The expressions for various flow quantities obtained by Sankar and Ismail (2010) for Herschel-Bulkley fluid model and Nagarani and Sarojamma (2008), in an improved form, for Casson fluid model are used to compute the data for comparing these fluid models. It is found that the plug core radius and wall shear stress are lower for H-B fluid model than those of the Casson fluid model. It is also noted that the plug flow velocity and flow rate are considerably higher for H-B fluid than those of the Casson fluid model. The estimates of the mean velocity and mean flow rate are considerably higher for H-B fluid model than those of the Casson fluid model.Journal of Applied Mathematics 01/2012; 2012, Special Issue. · 0.83 Impact Factor
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ABSTRACT: In the present article we have discussed the blood flow analysis of Prandtl fluid model in tapered stenosed arteries. The governing equations for considered model are presented in cylindrical coordinates. Perturbation solutions are constructed for the velocity, impedance resistance, wall shear stress and shearing stress at the stenosis throat. Attention has been mainly focused to the analysis of embedded parameters in converging, diverging and non-tapered situations. Streamlines have been plotted at the end of the article for considered arteries. It is observed that due to increase in Prandtl fluid parameters, the stenosis shape and maximum height of the stenosis the velocity profile decreases.Ain Shams Engineering Journal. 08/2014;
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ABSTRACT: Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence of periodic body acceleration is analyzed mathematically, treating it as two-fluid model with the suspension of all the erythrocytes in the core region as non-Newtonian fluid with yield stress and the plasma in the peripheral layer region as Newtonian. The non-Newtonian fluid with yield stress in the core region is assumed as (i) Herschel-Bulkley fluid and (ii) Casson fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius, and longitudinal impedance to flow obtained by Sankar (2010) for two-fluid Herschel-Bulkley model and Sankar and Lee (2011) for two-fluid Casson model are used to compute the data for comparing these fluid models. It is observed that the plug core radius, wall shear stress, and longitudinal impedance to flow are lower for the two-fluid H-B model compared to the corresponding flow quantities of the two-fluid Casson model. It is noted that the plug core radius and longitudinal impedance to flow increases with the increase of the maximum depth of the stenosis. The mean velocity and mean flow rate of two-fluid H-B model are higher than those of the two-fluid Casson model.Abstract and Applied Analysis 01/2012; 2012. · 1.10 Impact Factor