EFFECT OF INDUCED MAGNETIC FIELD ON BLOOD FLOW THROUGH A CONSTRICTED CHANNEL: AN ANALYTICAL APPROACH

2016 ◽  
Vol 16 (03) ◽  
pp. 1650030 ◽  
Author(s):  
G. C. SHIT ◽  
M. ROY
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Blood Flow ◽  
Pressure Gradient ◽  
Analytical Solutions ◽  
Axial Velocity ◽  
Induced Magnetic Field ◽  
Flow Through ◽  
Constricted Channel ◽  
Rotation Component

A nonlinear micropolar fluid model is considered with a view to examine the effect of induced magnetic field on blood flow through a constricted channel. We assume that the flow is unidirectional and flowing through a narrow channel, where the Reynolds number is less than unity such as in microvessels. Under the low Reynolds number approximation, the analytical expressions for axial velocity, micro-rotation component, axial pressure gradient, axial induced magnetic field, resistance to flow and wall shear stress have been obtained. The flow characteristic phenomena have been analyzed by taking valid numerical values of the parameters, which are applicable to blood rheology. The present analytical solutions have been compared with the analytical solutions of Hartmann (Hartmann J. Hg-Dynamics-I: Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field, Mathematisk-Fysiske Meddeleser XV:6, 1937) and found excellent agreement. The study shows that with the increasing values of the magnetic field strength decreases the axial velocity at the central line of the channel, while the flow is accelerating in the vicinity of the channel wall. The induced magnetic field has an increasing effect on the micro-rotation component, which in turn produces increasing pressure gradient. The electrical response of the microcirculation increases with the increase in the Hartmann number and the stenosis height. Thus, the resultant flow predictions presented here may be useful for the potential applications in cardiovascular engineering.

Induced magnetic field influences on blood flow through an anisotropically tapered elastic artery with overlapping stenosis in an annulus

2011 ◽  
Vol 89 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Kh. S. Mekheimer ◽  
Mohammed H. Haroun ◽  
M. A. El Kot
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Current Density ◽  
Axial Velocity ◽  
Mathematical Representation ◽  
Physical Parameters ◽  
Maximum Height ◽  
Induced Magnetic Field ◽  
Flow Through ◽  
Elastic Artery

A mathematical model for blood flow through an elastic artery with overlapping stenosis under the effect of induced magnetic field is presented. The present theoretical model may be considered as a mathematical representation to the movement of conductive physiological fluid through coaxial tubes such that the inner tube is uniform and rigid, representing a catheter tube, while the outer tube is an anisotropically tapered elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid, representing blood. The analysis is carried out for an artery with mild local narrowing in its lumen, forming a stenosis. Analytical expressions for the stream function, the magnetic force function, the axial velocity, the axial induced magnetic field, and the distribution of the current density are obtained. The results for the resistance impedance, the wall shear stress distribution, the axial velocity, the axial induced magnetic field, and distribution of the current density have been computed numerically, and the results were studied for various values of the physical parameters, such as the the Hartmann number Ha, the magnetic Reynolds number Rm, the taper angle ϕ, the maximum height of stenosis δ, the degree of anisotropy of the vessel wall n, and the contributions of the elastic constraints to the total tethering K.

scholarly journals CONVECTIVE HEAT TRANSFER ON STENOSED BLOOD FLOW THROUGH PERMEABLE MICROCIRCULATION IN THE PRESENCE OF A MAGNETIC FIELD

2020 ◽  
Author(s):  
Alana Sankar ◽  
Sreedhara Rao Gunakala ◽  
Donna Comissiong
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Reynolds Number ◽  
Blood Flow ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Hartmann Number ◽  
Darcy Number ◽  
Flow Through

Blood flow through permeable microcirculation in the presence of a composite stenosis, an external magnetic field and convective heat transfer was examined. A two-layered model for the blood consisting of a fluid-particle suspension in the core region with a peripheral cell-free plasma layer was used. The proposed system of equations was solved and plots were generated. In the presence of permeable walls, an external magnetic field and convective heat transfer, the temperature of the blood, friction-factor Reynolds number and Nusselt number were investigated. The temperature of the blood increased when the Hartmann number increased, Darcy number increased, haematocrit level increased or the peripheral layer thinned. The friction-factor Reynolds number product increased as the haematocrit, Hartmann number, stenosis height or Darcy number increased. The Nusselt number decreased as the Hartmann number, haematocrit, stenosis height or Darcy number increased. These results were interpreted in terms of the physical situation. This study aids in understanding the effects of wall permeability, a magnetic field and the presence of heat transfer on different diseased arterial systems in the future.

scholarly journals Mathematical Modelling of Blood Flow through a Tapered Overlapping Stenosed Artery with Variable Viscosity

2014 ◽  
Vol 11 (4) ◽  
pp. 185-195 ◽  
Author(s):  
G. C. Shit ◽  
M. Roy ◽  
A. Sinha
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Variable Viscosity ◽  
Stenosed Artery ◽  
Flow Through ◽  
Wall Shear ◽  
Analytical Expressions

This paper presents a theoretical study of blood flow through a tapered and overlapping stenosed artery under the action of an externally applied magnetic field. The fluid (blood) medium is assumed to be porous in nature. The variable viscosity of blood depending on hematocrit (percentage volume of erythrocytes) is taken into account in order to improve resemblance to the real situation. The governing equation for laminar, incompressible and Newtonian fluid subject to the boundary conditions is solved by using a well known Frobenius method. The analytical expressions for velocity component, volumetric flow rate, wall shear stress and pressure gradient are obtained. The numerical values are extracted from these analytical expressions and are presented graphically. It is observed that the influence of hematocrit, magnetic field and the shape of artery have important impact on the velocity profile, pressure gradient and wall shear stress. Moreover, the effect of primary stenosis on the secondary one has been significantly observed.

A MATHEMATICAL MODEL FOR BLOOD FLOW THROUGH INCLINED ARTERIES UNDER THE INFLUENCE OF INCLINED MAGNETIC FIELD

2012 ◽  
Vol 12 (03) ◽  
pp. 1250033 ◽  
Author(s):  
DHARMENDRA TRIPATHI
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Reynolds Number ◽  
Blood Flow ◽  
Couple Stress ◽  
Volume Flow Rate ◽  
Flow Characteristics ◽  
Physical Parameters ◽  
Inclined Magnetic Field ◽  
Flow Through

A mathematical model is developed to study the characteristics of blood flow through flexible inclined arteries under the influence of an inclined magnetic field. The blood is supposed to be couple stress fluid and the geometry of wall surface of inclined arteries is taken as peristaltic wave. The expressions for axial velocity, volume flow rate, pressure gradient and stream function are obtained under the assumptions of long wavelength and low Reynolds number. The effects of different physical parameters reflecting couple stress parameter, Hartmann number, Reynolds number, Froude number, inclination of channel and inclination of magnetic field on velocity profile, pressure and frictional force are discussed. The stream lines are drawn for various values of emerging parameters and the trapping phenomenon is discussed. The significant features of the blood flow characteristics are analyzed by plotting graphs and discussed numerically in detail.

Effects of magnetic field on blood flow with suspended copper nanoparticles through an artery with overlapping stenosis

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
C. Umadevi ◽  
G. Harpriya ◽  
M. Dhange ◽  
G. Nageswari
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Copper Nanoparticles ◽  
Analytical Solutions ◽  
Biomedical Applications ◽  
Flow Resistance ◽  
Cardiac Diseases ◽  
Stenosed Artery

The flow of blood mixed with copper nanoparticles in an overlapping stenosed artery is reported in the presence of a magnetic field. The presence of stenosis is known to impede blood flow and to be the cause of different cardiac diseases. The governing nonlinear equations are rendered dimensionless and attempted under the conditions of mild stenosis. The analytical solutions for velocity, resistance to the flow, wall shear stress, temperature, and streamlines are obtained and analyzed through graphs. The obtained outcomes show that the temperature variation in copper nanoparticles concentrated blood is more and flow resistance is less when compared to pure blood. The investigations reveal that copper nanoparticles are effective to reduce the hemodynamics of stenosis and could be helpful in biomedical applications.

scholarly journals Mathematical Modeling of Treatment Effect on Tumor Growth and Blood Flow through a Channel with Magnetic Field

2021 ◽  
pp. 66-79
Author(s):  
K. W. Bunonyo ◽  
C. U. Amadi
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Tumor Growth ◽  
Blood Velocity ◽  
Frequency Parameter ◽  
Womersley Number ◽  
Permeability Parameter ◽  
Flow Through

In this research, we investigated the effect of tumor growth on blood flow through a micro channel by formulated the governing model with the assumption that blood is an incompressible, eclectrially conducting fluid which flow is caused by the pumping action of the heart and suction. The governing model was scaled using some dimensionless variables and the region of the tumor was obtained from Dominguez [1] which was incorporated in our model. The model is further reduced to an ordinary differential equation using a perturbation condition. However, the ordinary differential equation was solved using method of undermined coefficients, and the constants coefficients obtained via matrix method. Furthermore, the simulation to study the effect of the pertinent parameters was done suing computation software called Mathematica. It is seen in our investigation that the entering parameters such as magnetic field parameter, the Reynolds number, womersley number, oscillatory frequency parameter, and permeability parameter affect the blood velocity profile in decreasing and increasing fashion.

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