An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move from r/R = 0 to r/R = 1 and it follows a concave pattern when we move from r/R = 0 to r/R = -1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

https://downloads.hindawi.com/journals/abb/2015/406195.pdf

Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation.

The present study deals with the flow of blood through a stenotic artery in the presence of a uniform magnetic field. Different flow situations are taken into account by considering the regular and irregular shapes of stenosis lying inside the walls of artery. Blood inside the artery is assumed to be Eyring–Powell fluid. A mathematical model is developed and simplified under the physical assumptions of stenosis. The regular perturbation method is adopted to find the solutions for axial velocity and pressure gradient. The variations in pressure drop across the stenosis length, the impedance and the shear stress at the walls of stenotic artery are discussed in detail through graphs. It is observed that the Eyring–Powell fluid is helpful in reducing the resistance to the flow in stenotic artery. Moreover, symmetric form of stenosis is more hazardous as compared to asymmetric stenosis.

A mathematical analysis of MHD blood flow of Eyring–Powell fluid through a constricted artery

A study about blood flow behaviour numerically and mathematically becomes invaluable tool in interpreting and analyzing the circulatory system. In this study, a mathematical model of fluid flow and mass transfer past through a stenoses artery is developed. The blood behaves as non-Newtonian fluid. The blood flow is considered to be unsteady, nonlinear, axisymmetric, two-dimensional and fully developed which is described by micropolar fluid. Meanwhile, the arterial wall is considered to be rigid. The geometry of stenosis is given by cosine-shaped plotted using MATLAB programme based on existing coding. The governing equations of the problem consist of continuity equation, momentum equation and convection-diffusion equation that govern mass transport to flow are formulated in cylindrical coordinate system. Then, all of the governing equations are written in dimensionless form by using dimensionless quantities in order to avoid difficulties. A radial coordinate transformation of the governing equation together with the set of initial and boundary are also needed in order to avoid interpolation error during discretization. A numerical technique has been performed in this study. Finite difference method in staggered grid known as Marker and Cell (MAC) method aid by existing MATLAB programme has been selected to solve all the governing equations involced. Successive over relaxive (SOR) method is also proposed in handling the poisson equation for pressure. Finally, two stability restriction which optimized the time step size at each calculation play an important role to limit the numerical computational. As a result, the value of wall shear stress and separation zone for micropolar fluid are lower than Newtonian fluid due to the presence of rotational viscosity. The values of wall shear stress and velocity were highest at around of critical stenotic region. While, the mass concentration were decrease and converge to zero at the arterial wall as the both wall shear stress and axial velocity decrease.

Numerical solution of mass transfer to micropolar fluid flow past a stenosed artery

dimensional, steady, Herschel-Bulkley fluid flow of blood through a stenosed artery under the effect of external magnetic field is studied. The blood is assumed as incompressible. The governing equations are solved analytically. This model has been used to study the influence of yield stress on blood flow through the stenosed artery. The effects of magnetic field on axial velocity, flow rate and wall shear rate has been shown graphically. The effects of all the parameters are quite significant on axial velocity, flow rate and wall shear rate as evidence from the results.

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Blood Flow through a Stenosed Artery with the Effect of Transverse Magnetic Field using a Non-Newtonian Model

This research work aims to provide Mathematical simulation of the flow of human blood through an arterial duct which has been narrowed by a cosine-shaped stenosis. This simulation provides a better understanding of this particular natural phenomena of blood flow. The flow has been taken similar to that of Newtonian flow and the Newtonian model is used. Regular perturbation method coupled with the Laplace transform is used for solving the model with appropriate initial and boundary conditions. Numerical technique-Stehfest’s algorithm is used for presenting the components of velocity, shear stress and temperature in graphs. The results conform to the observed theoretical descriptions.

Unsteady two-dimensional flow of pseudo-blood fluid in an arterial duct carrying stenosis

In this paper, one-dimensional Herschel-Bulkley fluid flow through a stenosed artery, has been studied. The problem is investigated by a joint effort of analytical and numerical techniques. Analytical expressions for several flow variables are obtained. This model has been used to study the influence of the fluid behaviour index n, shear-dependent non-linear viscosity k and the yield stress o H in blood flow through a stenosed artery. The variations of axial and plug velocities, flow rate, wall shear stress and pressure gradient with n, k and o H, have been shown graphically. It is observed that axial velocity and flow rate increase with slip but decrease with yield stress and, wall shear stress increases in Herschel-Bulkley fluid in comparison with corresponding Newtonian fluid. Biorheological implications of the present modelling for some arterial diseases, are included in brief.

Steady Flow of Blood through a Stenosed Artery: A Non-Newtonian Fluid Model

The present study deals with blood flow through a single constricted artery in presence of magnetic field and slip velocity. Blood is considered here as Newtonian incompressible fluid. Perturbation method is used to obtain the analytical expressions for velocity profile, wall shear stress, apparent viscosity, flow rate and resistance to flow of blood. Physical interpretation of obtained expressions is shown here for better understanding of the problem.

Rezia Begum Laskar

Papers

Steady Flow of Blood through a Stenosed Artery: A Non-Newtonian Fluid Model

Influence of magnetic field and slip velocity on pulsatile blood flow through a constricted artery