Blood Flow Behaviour in a Straight Vein under the Influence of a Magnetic Field (original) (raw)
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A mathematical model for blood flow in magnetic field
In the present study a mathematical model of biomagnetic fluid dynamics (BFD), suitable for the description of the Newtonian blood flow under the action of an applied magnetic field, is proposed. This model is consistent with the principles of ferrohydrodynamics and magnetohydrodynamics and takes into account both magnetization and electrical conductivity of blood. As a representative application the laminar, incompressible, three-dimensional, fully developed viscous flow of a Newtonian biomagnetic fluid (blood) in a straight rectangular duct is numerically studied under the action of a uniform or a spatially varying magnetic field. The numerical results are obtained using a finite differences numerical technique based on a pressure-linked pseudotransient method on a collocated grid. The flow is appreciably influenced by the application of the magnetic field and in particularly by the strength and the magnetic field gradient. A comparison of the derived results is also made with those obtained using the existing BFD model indicating the necessity of taking into account the electrical conductivity of blood.
MATHEMATICAL MODELS FOR BIOMAGNETIC FLUID FLOW AND APPLICATIONS
1. SUMMARY In this work a mathematical model governing the biomagnetic fluid flow is presented. Expressions describing the variation of the saturation magnetization of the fluid with temperature or the magnetic field intensity are also given. After proper simplifications of the above-mentioned mathematical model the flow in a rectangular channel of a biomagnetic fluid (blood) under the action of an applied magnetic field is studied. The results obtained from the numerical solution of this problem, showed that the fluid flow is appreciably influenced by the applied magnetic field.
Biofluid flow in a channel under the action of a uniform localized magnetic field
Computational Mechanics, 2005
In this work the fundamental problem of the biomagnetic (blood) fluid flow in a channel under the influence of a steady localized magnetic field is studied. For the mathematical formulation of the problem both magnetization and electrical conductivity of blood are taken into account and blood is considered as a homogeneous Newtonian fluid. For the numerical solution of the problem, which is described by a coupled, non linear system of PDEs, with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by the development of an efficient numerical technique based on finite differences. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the magnetic field influences considerably the flow field. It is also obtained that the electrical conductivity of blood should be taken into account at the area of the uniform magnetic field.
Mathematical Model of Blood Flow in Small Blood Vessel in the Presence of Magnetic Field
Applied Mathematics, 2011
A mathematical model for blood flow in the small blood vessel in the presence of magnetic field is presented in this paper. We have modeled the two phase model for the blood flow consists of a central core of suspended erythrocytes and cell-free layer surrounding the core. The system of differential equations has been solved analytically. We have obtained the result for velocity, flow rate and effective viscosity in presence of peripheral layer and magnetic field .All the result has been obtained and discussed through graphs.
Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016
A meshless numerical scheme is developed in order to simulate the magnetically mediated separation of biological mixture used in lab-on-chip devices as solid carriers for capturing, transporting and detecting biological magnetic labeled entities, as well as for drug delivering, magnetic hyperthermia treatment, magnetic resonance imaging, magnetofection, etc. Due to the imposed magnetic field stagnation regions are developed, leading to the accumulation of the magnetic labeled species and finally to their collection from the heterogeneous mixture. The role of (i) the intensity of magnetic field and its gradient, (ii) the position of magnetic field, (iii) the magnetic susceptibility of magnetic particles, (iv) the volume concentration of magnetic particles and their size, (v) the flow velocity in the magnetic fluidic interactions and interplay between the magnetophoretic mass transfer and molecular diffusion are thoroughly investigated. Both Newtonian and non-Newtonian blood flow models are considered.
In this paper, the behavior of a two-dimensional tube with an elastic segment containing ferrofluid (blood and 3 vol% Fe 3 O 4), in presence of non-uniform magnetic field is reported. Two cases of magnetic field including constant gradient (both positive and negative) and field of a wire, carrying electric current were examined. Surface tension of the membrane is considered to be fixed and constant along the elastic wall. Numerical solution of governing equations of the flow field has been obtained using the two-phase mixture model and control volume technique. Also, the membrane equation has been used to iterate and access the membrane position. Based on the obtained results, applying positive gradient magnetic field makes the tube narrower, but the negative one and magnetic field of electric wire opens the tube up.
Biomagnetic flow in a curved square duct under the influence of an applied magnetic field
Physics of Fluids, 2004
The laminar incompressible fully developed biomagnetic (blood) flow in a curved square duct under the influence of an applied magnetic field is studied. The mathematical formulation is based on the model of BFD which is consistent with the principles of ferrohydrodynamics. According to this formulation blood is considered as an electrically non-conducting, homogeneous and Newtonian magnetic fluid. For the numerical solution of the problem, which is described by a coupled, non-linear system of PDEs, with their appropriate boundary conditions, the SIMPLE method is used. The results indicate that the axial velocity, as well as the secondary flow at the transverse plane are appreciably influenced and indicate that the magnetic field could be used for controlling the blood flow by magnetic means.
Numerical simulation of biomagnetic fluid in a channel with thrombus
Journal of Visualization, 2002
Biomagnetic fluid dynamics is the study of the interaction of biological fluids with an applied steady magnetic field. Recently, several medical applications begin to utilize magnetic labeling of specific cells and targeted drug delivery using magnets. The magnetically labeled cells and the drug encapsulates are usually loaded in the blood stream and are directed toward a specific site by use of a magnet. In this paper, numerical simulation of biomagnetic fluid in the presence of a thrombus when exposed to magnetic field is presented. The finite analytic method is used to obtain the numerical simulation. It is found that the magnetic force causes a drastic change in the fluid behavior and the friction coefficient increases as the magnetic field strength increases.
Numerical simulation of biomagnetic fluid flow in a stenosed bifurcated artery
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation, 2019
Biomagnetic fluid dynamics (BFD) is an important application in medical sciences and bioengineering research. Due to this, biomagnetic fluid flow through a stenosed bifurcated artery is numerically studied. A biomagnetic fluid can be found in a living creature and its flow is influenced by the present of a magnetic field. Blood is a typical biomagnetic fluid due to the interaction of intercellular protein, cell membrane and the haemoglobin. This study considered the flow to be incompressible, laminar, two-dimensional (2D), fully developed viscous flow of a Newtonian biomagnetic fluid (blood) in a stenosed bifurcated artery under the effect of a spatially varying magnetic field. A simplified mathematical model of BFD was developed only for isothermal case. Numerical results are obtained using COMSOL Multiphysics 5.2 based on finite element method (FEM). Results concerning the different values of magnetic field intensity produce a considerable effect on the blood flow characteristics such as the velocity profiles and the streamlines patterns. It is shown that the vortex at lower wall extends vertically while vortex at upper wall becomes shrink as the magnetic field strength increases. The location of the magnetic source also can affect the velocity at the daughter artery where the velocity at the lower wall of daughter artery is lower than the upper wall.