Mathematical modelling of pulsatile flow of Cassons fluid in arterial stenosis. Appl Math Comput
Department of Mathematics, Harcourt Butler Technological Institute, Kanpur 208 002, India Applied Mathematics and Computation
(Impact Factor: 1.55).
04/2009; 210(1):1-10. DOI: 10.1016/j.amc.2007.05.070
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.
Available from: Shubha Jain
- "It is now well established that blood is a suspension of corpuscles (cellular particles) in an aqueous saline solution of plasma which indicates that blood is having a non-Newtonian structure. Siddiqui et al.  have investigated the pulsatile nature of blood by modelling blood as a Casson fluid. They observed that the yield stress increases with a decrease in the mean and steady flow rates. "
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ABSTRACT: In this paper, we considered the pulsatile flow of blood through catheterized tapered artery in the presence of an -shaped stenosis. Blood flow is modelled as homogeneous incompressible couple stress fluid. Further the effects of velocity slip at the arterial wall are also examined. The analysis is carried out analytically and closed form solutions are obtained with the assumption of mild stenosis. In the present study, we analyze the effects of various fluid and geometric parameters on the physiological parameters such as resistance to flow and shear stress at the wall. The variation in the resistance to the flow and wall shear stress with respect to stenosis size ( ), radius of the catheter ( ), couple stress fluid parameters ( ), Reynolds number (Re) and pulsatile parameter ( ) has been studied. In particular shear stress at the wall is reckoned at both the locations corresponding to the maximum height of the stenosis. It has been observed that this physiological parameter is independent of the location of the maximum height in case of nontapered artery while these locations significantly impact the shear stress at the wall in case of tapered artery. The locations of the critical and maximum heights with corresponding annular radii are summarized in the form of Table 1. We also focussed our attention on the analysis of the wall shear stress over the entire stenosis region for various values of the geometric and fluid parameters. It is observed that the impedance and wall shear stress are increasing with increase in the radius of catheter and stenosis size while they are decreasing as the tapered parameter and the couple stress fluid parameters are increasing. It is observed that slip velocity and diverging tapered artery facilitate the fluid flow.
- "Pulsatile flow of blood through artery had been considered by Siddiqui et al. (2009) and Tu and Deville (1996) by implementing a sine function, whereas in both cases non-Newtonian characteristics of blood had been emphasised. Earlier, Rohlf and Tenti (2001) used perturbation theory for solving the same problem considering the pulsatile nature of blood flow as sine wave, giving emphasis on the role of Womersley number on the properties of flow behaviour using Casson model. "
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ABSTRACT: Hemodynamic transport in the stenosed blood vessel has been numerically investigated with five non-Newtonian rheological models. The results from Casson viscosity model, Carreau model, Cross model, power law viscosity model, and Quemada viscosity model as well as Newtonian model were compared to capture the physics at the arterial wall. At the inlet of a long artery, three different pulsating profiles are considered. Detailed flow statistics of the flow field were calculated by solving transient form of Navier-Stokes equation in an axi-symmetric domain. From the simulation data, wall shear stress and oscillatory shear index were calculated. The results show that among different rheological models, the predictions from Carreau model as well as Newtonian model differ significantly with other four models showing similar behaviour. The results demonstrate that the degree of stenoses have a significant effect on oscillatory shear index and recirculation length.
Available from: sciencedirect.com
- "Pulsatile flow of blood for a modified second-grade fluid model is presented by Massoudi and Phuoc . In another article Siddiqui et al.  discussed Casson fluid in arterial stenosis. Blood flow analysis for micropolar fluid model for axisymmetric but radially symmetric mild stenosis tapered artery is presented by Mekheimer and Kot . "
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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.
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