A mathematical modeling of pulsatile blood flow through a stenosed artery under effect of a magnetic field (original) (raw)
Related papers
2012
Blood flow in stenosed tube has been modeled in the present investigation. The model is aimed at studying the effect of stenosis on flow rate and shear stress distribution on time dependent (pulsatile) flow of blood in the arteries. The model has been compared with the time independent model and shown that the time dependent has significant effect on the flow situation. The model accounts for the anomalies of blood flow such as; blunted velocity profile, and Fahraeus - Lindquist effect (FLE). The model also has been studied for various of parametric effects such as magnetic, body acceleration, size of Blood cells (Couple Stress)frequency, amplitude, phase difference, percentage stenosis(constriction), and length of stenosis .One of the most important aspect of the present model is that the model has been studied for different blood diseases and compared with the case of normal blood.
Pulsatile flow of blood under the influence of externally imposed magnetic field and periodic body acceleration through a multistenosed artery is studied. In this problem a Mathematical model is developed by treating blood as a non Newtonian fluid characterized by the Casson fluid. The pulsatile is analyzed by considering a periodic pressure gradient which is a function of time. In this analysis we try to find the computational result by using the Perturbution analysis, assuming that the Womersely frequency parameter is very small. The effect of pulsatility and body acceleration have been discussed with the help of graphs.
One-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.
International Journal of Heat and Technology
In the present study, a two-dimensional pulsatile blood flow model is created and the related heat transfer characteristics through a stenosed artery are investigated in the presence of a defined magnetic field with the body acceleration. The blood domain is assumed as a nonlinear, time-dependent, incompressible and laminar flow. The blood flow is considered with the unsteady characteristics because the pulsatile pressure gradient is arising due to the systematic reactions between the heart and the body acceleration. The non-linear momentum and continuity equations are solved with suitable initial and boundary conditions using the Crank-Nicolson scheme. In this study, the blood flow characteristics (velocity profiles, temperature, volumetric flow rate and flow resistance) are evaluated, also effects of the defined stenosis severity, the heat transfer factors and the considered magnetic field on the effective flow properties are discussed. Besides, the blood flow characteristics have been analyzed in a comparison form for two rigid and elastic arteries. Finally, it should be said that the present outputs are in good agreement with some available and validated results.
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.
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.
Journal of Biorheology, 2011
A proper understanding of the interactions of body acceleration and a magnetic field with blood flow could be useful in the diagnosis and treatment of some health problems. In the work reported in this paper we studied the pulsatile flow of blood through stenosed arteries, including the effects of body acceleration and a magnetic field. Blood is regarded as an electrically conducting, incompressible, couple-stress fluid in the presence of a magnetic field along the radius of the tube. The effects of the body acceleration and the magnetic field on the axial velocity, flow rate, and fluid acceleration were obtained analytically by use of the Hankel transform and the Laplace transform. Velocity variations under different conditions are shown graphically. The results have been compared with those from other theoretical models, and are in good agreement. Finally, our mathematical model gives a simple velocity expression for blood flow so it will help not only in the field of physiological fluid dynamics but will also help medical practitioners with elementary knowledge of mathematics. Keywords Blood flow Á Couple-stress fluid Á Non-Newtonian fluid Á Magnetohydrodynamics List of symbols op oz Pressure gradient A 0 Steady-state part of the pressure gradient A 1 Amplitude of the oscillatory part x 1 2pf 1 , where f 1 is the heart pulse frequency z Axial distance t Time a 0 Amplitude of body acceleration x 2 2pf 2 , where f 2 is the body force acceleration frequency / Phase difference u Velocity in the axial direction q Density of blood l Dynamic coefficient of viscosity of blood g Couple-stress viscosity r Electrical conductivity B 0 Applied magnetic field r Radial coordinate R(z) Radius of the tube in the stenotic region " a 2 ¼ R 2 l g Couple-stress parameter a 2 ¼ R 2 xq l Womersley parameter H ¼ B 0 R r l 1=2 Hartmann number k n Roots/zeros of Bessel functions J 0 (n) = 0
Herschel-Bulkley Magnetized Blood Flow Model for an Inclined Tapered Artery for an Accelerated Body
Journal of Science and Technology
Analytical investigation of Herschel-Bulkley model for axisymmetric pulsatile blood flow through an inclined stenosed artery of a periodically accelerated body under the influence of a magnetic field has been done. Invoking suitable transformations, the flow governing partial differential equations are non-dimensionalized. For these non-dimensionalized equations, an exact solution representing the different flow characteristic has been derived by employing the perturbation method. Flow rate and impedance analysis of the Herschel-Bulkley fluid has been done graphically by varying the yield stress, pressure gradient. Some important results are obtained pertaining to the medical interest.
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.