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 A Physiologic Model for the Problem of Blood Flow through Diseased Blood Vessels

2016 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
Sapna Ratan Shah ◽  
S. U. Siddiqui
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Shape Parameter ◽  
Fluid Model ◽  
Porous Wall ◽  
Volumetric Flow Rate ◽  
Wall Model ◽  
Flow Through ◽  
Wall Shear

This study focuses on the behavior of blood flow through diseased artery in the presence of porous effects. The laminar, incompressible, fully developed, non-Newtonian in an artery having axially non-symmetric but radially symmetric stenosis is numerically studied. Here blood is represented as Herschel-Bulkley fluid model and flow model is shown by the Navier-Stokes and the continuity equations. Using appropriate boundary conditions, numerical expression for volumetric flow rate, pressure drop and wall shear stress have been derived. The expressions are computed numerically and results are presented graphically. The effects of porous parameter on wall shear stress, stenosis length, stenosis size and stenosis shape parameter are discussed. The wall shear stress increases as the porous parameter, stenosis size and stenosis length increases, but as the stenosis shape parameter increases, the wall shear stress decreases. The work shows that the results obtained from the porous wall model are significantly different from those obtained by the rigid wall model.

scholarly journals The Effect of Slip Velocity on Unsteady Peristalsis MHD Blood Flow through a Constricted Artery Experiencing Body Acceleration

2019 ◽  
Vol 24 (3) ◽  
pp. 645-659 ◽  
Author(s):  
J. Nandal ◽  
S. Kumari ◽  
R. Rathee
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Rate ◽  
Axial Velocity ◽  
Slip Velocity ◽  
Volumetric Flow Rate ◽  
Body Acceleration ◽  
Stenosed Artery ◽  
Flow Through

Abstract In this analysis, we present a theoretical study to examine the combined effect of both slip velocity and periodic body acceleration on an unsteady generalized non-Newtonian blood flow through a stenosed artery with permeable wall. A constant transverse magnetic field is applied on the peristaltic flow of blood, treating it as an elastico-viscous, electrically conducting and incompressible fluid. Appropriate transformation methods are adopted to solve the unsteady non-Newtonian axially symmetric momentum equation in the cylindrical polar coordinate system with suitably prescribed conditions. To validate the applicability of the proposed analysis, analytical expressions for the axial velocity, fluid acceleration, wall shear stress and volumetric flow rate are computed and for having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted with varying values of flow variables, to analyse the influence of the axial velocity, wall shear stress and volumetric flow rate of streaming blood.

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

2016 ◽  
Vol 09 (02) ◽  
pp. 1650027 ◽  
Author(s):  
Najma Saleem ◽  
Sufian Munawar
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
Pressure Drop ◽  
Mathematical Analysis ◽  
Uniform Magnetic Field ◽  
Symmetric Form ◽  
Regular Perturbation ◽  
Irregular Shapes

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.

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.

scholarly journals Effect of Externally Applied Transverse Magnetic Field on Unsteady Flow of Blood in Tapered Stenosed Artery

2019 ◽  
Vol 8 (6) ◽  
pp. 1398-1406
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Transverse Magnetic Field ◽  
Flow Rate ◽  
Flow Characteristics ◽  
Volumetric Flow Rate ◽  
Transverse Magnetic ◽  
Stenosed Artery

The role of flow parameters of blood is very important in maintaining proper functioning of heart and in turn health body. Herschel–Bulkley fluid model is used for the proposed one-fluid blood flow model. The behavior of important blood flow characteristics wall shear stress, volumetric flow rate and axial velocity of the flow in tapered mild stenosed artery in the presence of externally applied transverse magnetic field is studied. A combination of analytical and numerical methods is used to solve the mathematical model of the system. We report the importance constant/variable viscosity of blood on unsteady flow in the proposed artery. Numerical results are reported for different values of the physical parameters of interest. It is observed with the help of graphs, that the flow characteristics wall shear stress, volumetric flow rate and axial velocity are affected in tapered stenosed artery and flow can be regulated with the help externally applied transverse magnetic field.

INFLUENCE OF SLIP VELOCITY ON BLOOD FLOW THROUGH AN ARTERY WITH PERMEABLE WALL: A THEORETICAL STUDY

2012 ◽  
Vol 05 (05) ◽  
pp. 1250042 ◽  
Author(s):  
A. SINHA ◽  
J. C. MISRA
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Shear Stress ◽  
Slip Velocity ◽  
Flow Resistance ◽  
Theoretical Study ◽  
Perturbation Technique ◽  
Volumetric Flow Rate ◽  
Arterial Segment ◽  
Flow Through

A theoretical investigation concerning the influence of slip velocity on the flow of blood through an artery having its wall permeable has been carried out. Here blood is treated as a homogeneous Newtonian fluid. The flow is characterized by three parameters: β the ratio of radius to length of the arterial segment, Re the characteristic Reynolds number associated with the pressure outside the arterial segment and ϵ the filtration coefficient. The problem has been solved by the use of a perturbation technique. ϵ is considered to be very small, ensuring the validity of the perturbation method. The computed numerical results are presented graphically to depict the variations in velocity, volumetric flow rate, wall shear stress and flow resistance.

Computational Modeling of Non-Newtonian Blood Flow Through Stenosed Arteries in the Presence of Magnetic Field

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Aiman Alshare ◽  
Bourhan Tashtoush ◽  
Hossam H. El-Khalil
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Pressure Drop ◽  
Wall Shear Stress ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Stenosed Artery ◽  
Flow Through ◽  
Wall Shear

Steady flow simulations of blood flow in an axisymmetric stenosed artery, subjected to a static magnetic field, are performed to investigate the influence of artery size, magnetic field strength, and non-Newtonian behavior on artery wall shear stress and pressure drop in the stenosed section. It is found that wall shear stress and pressure drop increase by decreasing artery size, assuming non-Newtonian fluid, and increasing magnetic field strength. In the computations, the shear thinning behavior of blood is accounted for by the Carreau–Yasuda model. Computational results are compared and found to be inline with available experimental data.

scholarly journals Mathematical Model of the Process of Pallet Movement Along the Magnetic Type Centrifugal Brake Roller

2021 ◽  
Vol 346 ◽  
pp. 03009
Author(s):  
Ildar Sharifullin ◽  
Andrey Nosko ◽  
Yevgeniy Safronov
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Comparative Analysis ◽  
External Magnetic Field ◽  
Electromagnetic Induction ◽  
Eddy Currents ◽  
Disc Brake ◽  
Safe Operation ◽  
Magnetic Type ◽  
The Mathematical Model

One of the main elements of safe operation of gravity flow racks used in pallet racks is a brake roller. The most promising design is a centrifugal brake roller of magnetic (eddy current) type. The principle of operation of such rollers is based on the laws of electromagnetic induction and involves the deceleration of a conductor moving in a magnetic field, due to the interaction of eddy currents (or Foucault currents) arising in the volume of the conductor, with an external magnetic field. The mathematical model of the process of pallet movement along a centrifugal brake roller of magnetic type is developed in the article. The equation of the speed of movement of the pallet along the centrifugal brake roller of magnetic type is obtained. Comparative analysis of the speed of movement of a pallet along centrifugal and disc brake rollers of magnetic type is carried out.

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