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.

Influence of an inclined magnetic field on the Poiseuille flow of immiscible micropolar–Newtonian fluids in a porous medium

2018 ◽  
Vol 96 (9) ◽  
pp. 1016-1028 ◽  
Author(s):  
Pramod Kumar Yadav ◽  
Sneha Jaiswal
Keyword(s):  
Magnetic Field ◽  
Rotational Velocity ◽  
Immiscible Fluids ◽  
Newtonian Fluids ◽  
Porous Channel ◽  
Physical Parameters ◽  
Inclined Magnetic Field ◽  
Two Phase ◽  
Flow Through ◽  
Newtonian Viscous Fluid

The present problem is concerned with two-phase fluid flow through a horizontal porous channel in the presence of uniform inclined magnetic field. The micropolar fluid or Eringen fluid and Newtonian viscous fluid are flowing in the upper and lower regions of the horizontal porous channel, respectively. In this paper, the permeability of each region of the horizontal porous channel has been taken to be different. The effects of various physical parameters like angles of inclination of magnetic field, viscosity ratio, micropolarity parameter, etc., on the velocities, micro-rotational velocity of two immiscible fluids in horizontal porous channel, wall-shear stress, and flow rate have been discussed. The result obtained for immiscible micropolar–Newtonian fluids are compared with the results of two immiscible Newtonian fluids. The obtained result may be used in production of oil from oil reservoirs, purification of contaminated ground water, etc.

Pulsatile Blood Flow Through a Constricted Porous Artery

2020 ◽  
Vol 17 (2) ◽  
pp. 743-749
Author(s):  
Salah Uddin ◽  
Obaid Ullah Mehmood ◽  
Mahathir Mohamad ◽  
Mahmod Abd Hakim Mohmad ◽  
D. F. Jamil ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Flow Velocity ◽  
Nonlinear Differential Equations ◽  
Fluid Velocity ◽  
Volumetric Flow Rate ◽  
Physical Parameters ◽  
Porosity Parameter ◽  
Arterial Blood ◽  
Flow Through

In this paper a speculative study of an incompressible Newtonian blood flow through a constricted porous channel and pulsatile nature is inspected. Porosity parameter λ is incorporated in the momentum equation. Governing nonlinear differential equations are numerically evaluated by employing the perturbation method technique for a very small perturbation parameter ε 1 such that ε ≠ 0 and with conformable boundary conditions. Numerical results of the flow velocity profile and volumetric flow rate have been derived numerically and detailed graphical analysis for different physical parameters porosity, Reynolds number and stenosis has been presented. It is found that arterial blood velocity is dependent upon all of these factors and that the relationship of fluid velocity and flow is more complex and nonlinear than heretofore generally believe. Furthermore the flow velocity enhanced with Reynolds number, porosity parameter and at maximum position of the stenosis/constriction.

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.

MATHEMATICAL MODELING OF BLOOD FLOW IN A POROUS VESSEL HAVING DOUBLE STENOSES IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

2011 ◽  
Vol 04 (02) ◽  
pp. 207-225 ◽  
Author(s):  
J. C. MISRA ◽  
A. SINHA ◽  
G. C. SHIT
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
External Magnetic Field ◽  
Volumetric Flow Rate ◽  
Hematocrit Level ◽  
Flow Through ◽  
The Mathematical Model

In this paper, a mathematical model has been developed for studying blood flow through a porous vessel with a pair of stenoses under the action of an externally applied magnetic field. Blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics. Expressions for the velocity profile, volumetric flow rate, wall shear stress and pressure gradient have been derived analytically under the purview of the model. The above said quantities are computed for a specific set of values of the different parameters involved in the model analysis. This serves as an illustration of the validity of the mathematical model developed here. The results estimated on the basis of the computation are presented graphically. The obtained results for different values of the parameters involved in the problem under consideration, show that the flow is appreciably influenced by the presence of magnetic field and the rise in the hematocrit level.

scholarly journals Analysis of Flow Characteristics of the Blood Flowing through an Inclined Tapered Porous Artery with Mild Stenosis under the Influence of an Inclined Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Neetu Srivastava
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Rate ◽  
Flow Characteristics ◽  
Volumetric Flow Rate ◽  
Mhd Equations ◽  
Inclined Magnetic Field ◽  
Wall Shear

Analytical investigation of MHD blood flow in a porous inclined stenotic artery under the influence of the inclined magnetic field has been done. Blood is considered as an electrically conducting Newtonian fluid. The physics of the problem is described by the usual MHD equations along with appropriate boundary conditions. The flow governing equations are finally transformed to nonhomogeneous second-order ordinary differential equations. This model is consistent with the principles of magnetohydrodynamics. Analytical expressions for the velocity profile, volumetric flow rate, wall shear stress, and pressure gradient have been derived. Blood flow characteristics are computed for a specific set of values of the different parameters involved in the model analysis and are presented graphically. Some of the obtained results show that the flow patterns in converging region (ξ<0), diverging region (ξ>0), and nontapered region (ξ=0) are effectively influenced by the presence of magnetic field and change in inclination of artery as well as magnetic field. There is also a significant effect of permeability on the wall shear stress as well as volumetric flow rate.

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.

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.

scholarly journals Influence of an Inclined Magnetic Field and Rotation on the Peristaltic Flow of a Micropolar Fluid in an Inclined Channel

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Ajaz Ahmad Dar ◽  
K. Elangovan
Keyword(s):  
Magnetic Field ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Volume Flow Rate ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Physical Parameters ◽  
Inclined Magnetic Field ◽  
Symmetric Channel ◽  
Highly Nonlinear

This present article deals with the interaction of both rotation and inclined magnetic field on peristaltic flow of a micropolar fluid in an inclined symmetric channel with sinusoidal waves roving down its walls. The highly nonlinear equations are simplified by adopting low Reynolds number and long wavelength approach. The analytical and numerical solutions for axial velocity, spin velocity, volume flow rate, pressure gradient, pressure rise per wavelength, and stream function have been computed and analyzed. The quantitative effects of various embedded physical parameters are inspected and displayed graphically with fussy prominence. Pressure rise, frictional forces, and pumping phenomenon are portrayed and characterized graphically.

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