Biomagnetic flow in a curved square duct under the influence of an applied magnetic field

Papadopoulos, Polycarpos K.; Tzirtzilakis, E. E.

doi:10.1063/1.1764509

Cited by 43 publications

(24 citation statements)

References 31 publications

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“…The authors found that for different locations of the permanent magnet and different strengths of the imposed magnetic field, different locations of the reattachment point downstream the orifice were observed. Haik's model was applied again in Papadopoulos and Tzirtzilakis (2004) where a blood flow in a curved square duct under the influence of an applied magnetic field was studied by a finite-difference numerical method.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of blood flow in realistic arteries subjected to strong non-uniform magnetic fields

Kenjereš¹

2008

International Journal of Heat and Fluid Flow

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The paper reports on a comprehensive mathematical model for simulations of blood-flow under the presence of strong non-uniform magnetic fields. The model consists of a set of Navier-Stokes equations accounting for the Lorentz and magnetisation forces, and a simplified set of Maxwell's equations (Biot-Savart/Ampere's law) for treating the imposed magnetic fields. The relevant hydrodynamic and electro-magnetic properties of human blood were taken from the literature.The model is then validated for different test cases ranging from a simple cylindrical geometry to real-life right-coronary arteries in humans. The time-dependency of the wall-shear-stress for different stenosis growth rates and the effects of the imposed strong non-uniform magnetic fields on the blood flow pattern are presented and analysed. It is concluded that an imposed nonuniform magnetic field can create significant changes in the secondary flow patterns, thus making it possible to use this technique for optimisations of targeted drug delivery.

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Section: Introductionmentioning

confidence: 99%

Numerical analysis of blood flow in realistic arteries subjected to strong non-uniform magnetic fields

Kenjereš¹

2008

International Journal of Heat and Fluid Flow

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“…We find that the value of the magnetic parameter M is approximately 500, when the fluid (blood) is under the influence of a sufficiently strong magnetic field of strength B 0 = 8T(tesla); the blood density is ρ = 1,050 kg/m 3 and the electrical conductivity of blood, σ = 0.8 s/m. As in [17,21,22], we consider M = 0-600 and K = 0.0, 0.005, 0.05, 0.1, 0.5 and for a human body temperature, T = 310 • K, the value of Pr = 21 is considered for blood. In order to study the effect of the Prandtl number on the flow characteristics, we have also examined the cases where Pr = 1, 7, 14.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…For this purpose, we first solve numerically the system of nonlinear differential equations (12), (13) and (20) subject to the boundary conditions (14), (15), (21) and (22). While the analysis presented here is applicable to a variety of fluids, as an illustrative example we consider here the case of blood.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow

et al. 2010

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The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic electrically conducting fluid. The partial differential equations that govern the flow are solved by developing a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are found to be in good agreement with those of earlier investigations.

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“…Our aim is initially to eliminate the internal angular momentum S given by (9) and the magnetization M given by (10) from the momentum equation (3) and afterwards to rearrange the terms to obtain the effective viscosity and the magnetic pressure. Our work is based on the minimum of the simplifications that have to be taken in order to make the analytical process feasible.…”

Section: General Effect Of Magnetic Fields To Viscosity and Pressurementioning

confidence: 99%

A general theoretical model for the magnetohydrodynamic flow of micropolar magnetic fluids. Application to Stokes flow

Hatzikonstantinou

Vafeas

2009

Math. Meth. Appl. Sci.

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Many practical applications, which have an inherent interest of physical and mathematical nature, involve the hydrodynamic flow in the presence of a magnetic field. Magnetic fluids comprise a novel class of engineering materials, where the coexistence of liquid and magnetic properties provides us with the opportunity to solve problems with high mathematical and technical complexity. Here, our purpose is to examine the micropolar magnetohydrodynamic flow of magnetic fluids by considering a colloidal suspension of ferromagnetic material (usually non-conductive) in a carrier magnetic liquid, which is in general electrically conductive. In this case, the ferromagnetic particles behave as rigid magnetic dipoles. Thus, the application of an external magnetic field, apart from the creation of an induced magnetic field of minor significance, will prevent the rotation of each particle, increasing the effective viscosity of the fluid and will cause the appearance of an additional magnetic pressure. Despite the fact that the general consideration consists of rigid particles of arbitrary shape, the assumption of spherical geometry is a very good approximation as a consequence of their small size. Our goal is to develop a general three-dimensional theoretical model that conforms to physical reality and at the same time permits the analytical investigation of the partial differential equations, which govern the micropolar hydrodynamic flow in such magnetic liquids. Furthermore, in the aim of establishing the consistency of our proposed model with the principles of both ferrohydrodynamics and magnetohydrodynamics, we take into account both magnetization and electrical conductivity of the fluid, respectively. Under this consideration, we perform an analytical treatment of these equations in order to obtain the three-dimensional effective viscosity and total pressure in terms of the velocity field, the total (applied and induced) magnetic field and the hydrodynamic and magnetic properties of the fluid, independently of the geometry of the flow. Moreover, we demonstrate the usefulness of our analytical approach by assuming a degenerate case of the aforementioned method, which is based on the reduction of the partial differential equations to a simpler shape that is similar to Stokes flow for the creeping motion of magnetic fluids. In view of this aim, we use the potential representation theory to construct a 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, via an analytical fashion.

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Biomagnetic flow in a curved square duct under the influence of an applied magnetic field

Cited by 43 publications

References 31 publications

Numerical analysis of blood flow in realistic arteries subjected to strong non-uniform magnetic fields

Numerical analysis of blood flow in realistic arteries subjected to strong non-uniform magnetic fields

Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow

A general theoretical model for the magnetohydrodynamic flow of micropolar magnetic fluids. Application to Stokes flow

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