Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional Caputo derivatives

2018 ◽  
Vol 446 ◽  
pp. 28-36 ◽  
Author(s):  
M. Abdullah ◽  
Asma Rashid Butt ◽  
Nauman Raza ◽  
Ali Saleh Alshomrani ◽  
A.K. Alzahrani
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Circular Cylinder ◽  
Uniform Magnetic Field ◽  
Caputo Derivatives

The distortion of a magnetic field by the flow of a conducting fluid past a circular cylinder

1965 ◽  
Vol 22 (3) ◽  
pp. 561-578 ◽  
Author(s):  
R. Seebass ◽  
K. Tamada
Keyword(s):  
Magnetic Field ◽  
Integral Equation ◽  
Circular Cylinder ◽  
Potential Flow ◽  
Uniform Magnetic Field ◽  
The Body ◽  
Flow Potential ◽  
Field Lines ◽  
The Magnetic Field ◽  
Rear Stagnation Point

The distortion of a uniform magnetic field, aligned with the flow at infinity, by the potential flow of an inviscid conductor about a circular cylinder is determined. Potential flow of the fluid occurs when the interaction parameter is small; this is the case studied here. In the flow-potential and stream-function plane the problem may be formulated as a singular integral equation. Solutions of this equation show that for small fluid conductivities the magnetic field lines are distorted in the sense of being dragged along by the motion of the fluid. This process continues as the conductivity increases, with fewer and fewer of the magnetic field lines entering the body. For large conductivity this reduced flux of field lines enters over most of the body surface and exits in the neighbourhood of the rear stagnation point; behind the body there is a jet-like structure of magnetic field lines.

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 A Blood Flow Volume Linear Inversion Model Based on Electromagnetic Sensor for Predicting the Rate of Arterial Stenosis

Sensors ◽  
2019 ◽  
Vol 19 (13) ◽  
pp. 3006
Author(s):  
Dan Yang ◽  
Yan-jun Liu ◽  
Bin Xu ◽  
Yun-hui Duo
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Blood Flow ◽  
Uniform Magnetic Field ◽  
Geometric Model ◽  
Arterial Stenosis ◽  
Flow Volume ◽  
Linear Inversion ◽  
Inversion Model ◽  
Blood Flow Volume

This paper presents a mathematical model of measuring blood flow based on electromagnetic induction for predicting the rate of arterial stenosis. Firstly, an electrode sensor was used to collect the induced potential differences from human skin surface in a uniform magnetic field. Then, the inversion matrix was constructed by the weight function theory and finite element method. Next, the blood flow volume inversion model was constructed by combining the induction potential differences and inversion matrix. Finally, the rate of arterial stenosis was predicted based on mathematical relationship between blood flow and the area of arterial stenosis. To verify the accuracy of the model, a uniform magnetic field distribution of Helmholtz coil and a 3D geometric model of the ulnar artery of the forearm with different rates of stenosis were established in COMSOL, a finite element analysis software. Simulation results showed that the inversion model had high accuracy in the measurement of blood flow and the prediction of rate of stenosis, and is of great significance for the early diagnosis of arterial stenosis and other vessel diseases.

Analytical and numerical aspects of the electromagnetic stirring induced by alternating magnetic fields

1981 ◽  
Vol 102 ◽  
pp. 405-430 ◽  
Author(s):  
Y. R. Fautrelle
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Uniform Magnetic Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Case ◽  
Special Cases ◽  
Alternating Magnetic Fields

The dynamic effects of an alternating magnetic field on containers of conducting fluid are investigated in two special cases: (i) an infinitely long circular cylinder in a uniform magnetic field normal to the generators; (ii) a truncated circular cylinder in a uniform magnetic field parallel to the axis. Neglecting the motion effects in Maxwell's equations, the problem is conveniently decoupled into electromagnetic and dynamic parts. Using either analytical or numerical solutions of the electromagnetic equations, the electromagnetic forces are calculated and introduced in the motion equations. In the first case, asymptotic solutions of the Navier–Stokes equations valid for high frequencies are calculated and compared with numerical solutions obtained for the same geometry. The second case has been studied numerically, and the solutions are presented and interpreted.

scholarly journals On the Perturbation of the Three-Dimensional Stokes Flow of Micropolar Fluids by a Constant Uniform Magnetic Field in a Circular Cylinder

2011 ◽  
Vol 2011 ◽  
pp. 1-41 ◽  
Author(s):  
Panayiotis Vafeas ◽  
Polycarpos K. Papadopoulos ◽  
Pavlos M. Hatzikonstantinou
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Stokes Flow ◽  
Uniform Magnetic Field ◽  
Colloidal Suspension ◽  
Three Dimensional ◽  
Flow Fields ◽  
Creeping Flow ◽  
Spherical Particles ◽  
Circular Duct

Modern engineering technology involves the micropolar magnetohydrodynamic flow of magnetic fluids. Here, we consider a colloidal suspension of non-conductive ferromagnetic material, which consists of small spherical particles that behave as rigid magnetic dipoles, in a carrier liquid of approximately zero conductivity and low-Reynolds number properties. The interaction of a 3D constant uniform magnetic field with the three-dimensional steady creeping motion (Stokes flow) of a viscous incompressible micropolar fluid in a circular cylinder is investigated, where the magnetization of the ferrofluid has been taken into account and the magnetic Stokes partial differential equations have been presented. Our goal is to apply the proper boundary conditions, so as to obtain the flow fields in a closed analytical form via the potential representation theory, and to study several characteristics of the flow. In view of this aim, we make use of an improved new complete and unique differential representation of magnetic Stokes flow, valid for non-axisymmetric geometries, which provides the velocity and total pressure fields in terms of easy-to-find potentials. We use these results to simulate the creeping flow of a magnetic fluid inside a circular duct and to obtain the flow fields associated with this kind of flow.

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