FDM analysis on pulsatile two-phase MHD rheology of blood in tapered stenotic blood vessels (original) (raw)
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Numerical Study of Magnetohydrodynamic Blood Flow through an Artery with Multiple Stenosis
IOP Conference Series: Materials Science and Engineering, 2020
The study theoretically accounts for the impact of Magnetohydrodynamics on streaming blood through an artery having multiple stenosis regions using the non-Newtonian Cross-rheological model. It is regarded that the streaming blood is unsteady and pulsative. The use of appropriate conditions is predicated on the assumption that the flow is laminar and axisymmetric which makes the problem two-dimensional. The geometry of stenosis was immobilized into a rectangular grid using the radial coordinate transformation. The finite difference scheme was employed for the numerical simulations. Specifically, magnetic field (Hartmann number), Reynolds number and severity of stenosis were varied over the entire arterial length. The results obtained predicted that increase in the Hartmann number and stenosis severity reduces the magnitude of the flow velocity, flow rate but the reverse is the case when the Reynolds number is increased. However, the wall shear stress and the resistance to flow are a...
FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries
Journal of Mechanical Science and Technology, 2011
A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.
International Journal for Computational Methods in Engineering Science and Mechanics, 2014
This paper introduces the impact of external magnetic field on blood flow patterns in a stenosis artery. Considering the fatty deposited lump, arterial walls as porous media, and pulsatile inflow base on human-heart-beating rate closes our model to the actual stenosis blood artery. In this study, by solving transient fluid dynamic equations in coupled porous and free media, the velocity, temperature, and shear stress distribution along the lump are investigated. The results show that applying 10 5 magnetic field intensity (Mn F ) creates two vortexes on the lumps' edges and 15X (16.6X) higher shear stress (temperature) in the stenosis region.
This paper introduces the impact of external magnetic field on blood flow patterns in a stenosis artery. Considering the fatty deposited lump, arterial walls as porous media, and pulsatile inflow base on human-heart-beating rate closes our model to the actual stenosis blood artery. In this study, by solving transient fluid dynamic equations in coupled porous and free media, the velocity, temperature, and shear stress distribution along the lump are investigated. The results show that applying 10 5 magnetic field intensity (Mn F ) creates two vortexes on the lumps' edges and 15X (16.6X) higher shear stress (temperature) in the stenosis region.
MHD Pulsatile Two-Phase Blood Flow Through a Stenosed Artery with Heat and Mass Transfer
arXiv: Fluid Dynamics, 2018
In this paper, effects of heat and mass transfer on two-phase pulsatile blood flow through a narrowed stenosed artery with radiation and the chemical reaction have been investigated. A vertical artery is assumed in which magnetic field is applied along the radial direction of the artery. The characteristics of blood in narrow arteries are analyzed by considering blood as Newtonian fluid in both core as well as in plasma regions. Exact solutions have been found for velocity, energy and concentration equations of the blood flow. To understand the behavior of blood flow, graphs of the velocity profile, wall shear stress, flow rate, flow impedance and concentration profile have been portrayed for different values of the magnetic and radiation parameter. In order to validate our result, a comparative study has been presented between the single-phase and two-phase model of the blood flow and it is observed that the two-phase model fits more accurately with the experimental data than the s...
2021
In this study, a tapered stenosed artery is considered to notice the effect of transverse magnetic field applied on blood flow to analyze the behavior of the flow with the help of significant flow attributes. The laminar, incompressible and fully developed flow of blood is studied taking into account the variable viscosity. To resemble the problem to real life situation, flow in core region is assumed to be non-Newtonian and flow in peripheral region is assumed to be Newtonian. The constitutive equation of blood is represented by Bingham plastic model in peripheral region and Herschel-Bulkley model in core region. The simulations are carried out for important flow characteristics such as wall shear stress, volumetric flow rate and axial velocity and the behavior is analyzed. We have reported numerical results for different values of physical parameters of interest. Biological implications of the present model are discussed. It has been observed that the important flow attributes are affected in tapered artery with stenosis and it is possible to stabilize the flow with the help of magnetic field applied externally. It is also noticed that the behaviour of flow attributes found by considering variable viscosity is in good agreement with the literature as compared to constant viscosity.
arXiv: Fluid Dynamics, 2017
In blood, the concentration of red blood cells varies with the arterial diameter. In the case of narrow arteries, red blood cells concentrate around the center of the artery and there exists a cell-free plasma layer near the arterial wall due to Fahraeus-Lindqvist effect. Due to non-uniformity of the fluid in the narrow arteries, it is preferable to consider the two-phase model of the blood flow. The present article analyzes the heat and mass transfer effects on the two-phase model of the unsteady pulsatile blood flow when it flows through the stenosed artery under the effects of radiation and chemical reaction. The direction of the artery is assumed to be vertical and the magnetic field is applied along the radial direction of the artery. We assume that the value of the shear stress is high enough so that nature of blood can be modeled as Newtonian in both erythrocytes suspended core region as well as RBC-depleted plasma region. We derive a mathematical model for the mixed convecti...
2018
A mathematical model for two-dimensional pulsatile blood flow through a constriction vessels under magnetic field and body acceleration is numerically simulated. The artery considered as an elastic cylindrical tube and the geometry of the constriction assumed to time-dependent with an aim to provide resemblance to the in-vivo situations. The blood flow considered nonlinear, incompressible and fully developed. The nonlinear momentum and the continuity equations under suitable initial and boundary conditions can be numerically solved using the Crank-Nicolson scheme. The blood flow specifications such as the velocity profile, the volumetric flow rate and the resistance to flow are obtained and effects of the magnetic field and the severity of the stenosis under these flow specifications are discussed. Besides the blood flow characteristics through elastic artery have been compared with the rigid ones.
Mathematical Analysis for MHD Flow of Blood in Constricted Arteries
Int. J. Nonlinear Sci. Numer. Simul., 2013
The unsteady oscillatory magneto-hydrodynamic flow of blood in small diameter arteries with mild constriction is analyzed, blood being modelled as a Herschel-Bulkley fluid. Finite difference method is employed for solving the associated initial boundary value problem. Explicit finite difference schemes for velocity distribution, flow rate, skin friction and longitudinal impedance to the flow are obtained. The effects of pressure gradient, yield stress, magnetic field, power law index and maximum depth of the stenosis on the aforesaid flow quantities are discussed through appropriate graphs. It is found that the velocity and flow rate decrease and the skin friction and longitudinal impedance to flow increase with the increase of the magnetic field parameter. It was recorded that the flow rate increases and the skin friction decreases with the increase of the phase angle. It was also noted the skin friction and longitudinal impedance to flow that increase almost linearly with the increase of maximum depth of the stenosis. The estimates of the increase in the longitudinal impedance to flow and skin friction are increased considerably by the presence of the magnetic field.
Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field
Journal of Computational and Applied Mathematics, 2009
Current theoretical investigation of atherosclerotic arteries deals with mathematical models that represent non-Newtonian flow of blood through a stenosed artery in the presence of a transverse magnetic field. Here, the rheology of the flowing blood is characterised by a generalised Power law model. The distensibility of an arterial wall has been accounted for based on local fluid mechanics. A radial coordinate transformation is initiated to map cosine geometry of the stenosis into a rectangular grid. An appropriate finite difference scheme has been adopted to solve the unsteady non-Newtonian momentum equations in cylindrical coordinate system. Exploiting suitably prescribed conditions based on the assumption of an axial symmetry under laminar flow condition rendered the problem effectively to two dimensions. An extensive quantitative analysis has been performed based on numerical computations in order to estimate the effects of Hartmann number (M), Power law index (n), generalised Reynolds number (Re G ), severity of the stenosis (δ) on various parameters such as flow velocity, flux and wall shear stress by means of their graphical representations so as to validate the applicability of the proposed mathematical model. The present results agree with some of the existing findings in the literature.