Biomagnetic channel flow in spatially varying magnetic field

Loukopoulos, V. C.; Tzirtzilakis, E. E.

doi:10.1016/j.ijengsci.2003.07.007

Cited by 115 publications

(93 citation statements)

References 20 publications

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“…Second, the construction of a boundary condition for the vorticity equation on the solid walls and third, the development of a semi-implicit numerical technique for the estimation of the solution at the next time step (iteration). In order to investigate the efficiency of the developed numerical methodology, a comparison is made with the obtained results in [5]. Moreover, new results are presented concerning high values of the magnetic number, for which the method used in [5] fails to converge.…”

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confidence: 99%

A simple numerical methodology for BFD problems using stream function vorticity formulation

Tzirtzilakis

2007

Commun. Numer. Meth. Engng.

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SUMMARYThe fundamental problem of biomagnetic fluid dynamics (BFD) in a 2D rectangular channel is numerically studied. The physical problem is described by a coupled, non-linear system of partial differential equations, with appropriate boundary conditions. For the mathematical formulation, the stream function-vorticity formulation is used and the numerical solution is obtained by developing a pseudotransient numerical technique. A boundary condition for the vorticity is also constructed and grid stretching is used. The efficiency of the method is verified by comparison with other results documented in the literature. New results are also obtained for high values of the magnetic number which is the dominant factor for the determination of the flow field in biomagnetic fluid flow problems.

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mentioning

confidence: 99%

A simple numerical methodology for BFD problems using stream function vorticity formulation

Tzirtzilakis

2007

Commun. Numer. Meth. Engng.

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“…Numerical solution for magnetic fluid is verified with [12]. The dimensionless axial velocity component is shown in Fig.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The mathematical model on a rectangular domain had been employ and solved using SIMPLE algorithm. In addition, spatially varying magnetic field had been studied using FDM and pressure-linked psuedotransient method on grid method [11][12][13]. As a result, dominant flow form was observed nearby the magnetic source with no evidence of secondary flow effect.…”

Section: Introductionmentioning

confidence: 99%

Mixed Finite Element Formulation for Magnetic Fluid Oil Flow in Electromagnetic Field

Tan

Yassin

2017

MATEC Web Conf.

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Abstract. Pressure depletion and high viscosity of crude oil in oil reservoir are the main challenges in oil recovery process. A potential solution is to employ electromagnetic heating coupled with magnetic fluid injection. The present work delivers a fundamental study on the interaction between magnetic fluid flow with electromagnetic field. The two-dimensional, incompressible flow is solved numerically using mixed finite element method. The velocity fields, temperature and pressure are the variables of interest, to be obtained by solving mass, momentum and energy equations coupled with Maxwell' equations. The fluid stress arises simultaneously with the external magnetic force which mobilises and increases the temperature of the oil flow. Verification is made against available data obtained from different numerical method reported in literature. The results justify feasibility of the mixed finite element formulation as an alternative for the modelling of the magnetic fluid flow.

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“…In addition to this, a secondary flow was found to be present and strengthen due to the increase of the magnetic field intensity. Loukopoulos and Tzirtzilakis [5] investigated a laminar, viscous incompressible flow of a Newtonian biomagnetic fluid in a two-dimensional channel under the action of spatially varying magnetic field at a low Reynolds number (Re = 250). In this numerical study, the magnetic field was located on the lower wall of the planar channel by taking into account FHD effects with a magnetization linearly dependent on the temperature and magnetic field intensity.…”

Section: Introductionmentioning

confidence: 99%

Validation of a Magneto- And Ferro-Hydrodynamic Model for Non-Isothermal Flows in Conjunction With Newtonian and Non-Newtonian Fluids

Könözsy¹,

Scienza²,

Drikakis³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. This work focuses on the validation of a magnetohydrodynamic (MHD) and ferrohydrodynamic (FHD) model for non-isothermal flows in conjunction with Newtonian and nonNewtonian fluids. The importance of this research field is to gain insight into the interaction of non-linear viscous behaviour of blood flow in the presence of MHD and FHD effects, because its biomedical application such as magneto resonance imaging (MRI) is in the centre of research interest. For incompressible flows coupled with MHD and FHD models, the Lorentz force and a Joule heating term appear due to the MHD effects and the magnetization and magnetocaloric terms appear due to the FHD effects in the non-linear momentum and temperature equations, respectively. Tzirtzilakis and Loukopoulos [1] investigated the effects of MHD and FHD for incompressible non-isothermal flows in conjunction with Newtonian fluids in a small rectangular channel. Their model excluded the non-linear viscous behaviour of blood flows considering blood as a Newtonian biofluid. Tzirakis et al. [2,3] modelled the effects of MHD and FHD for incompressible isothermal flows in a circular duct and through a stenosis in conjunction with both Newtonian and non-Newtonian fluids, although their approach neglects the non-isothermal magnetocaloric FHD effects. Due to the fact that there is a lack of experimental data available for non-isothermal and non-Newtonian blood flows in the presence of MHD and FHD effects, therefore the objective of this study is to establish adequate validation test cases in order to assess the reliability of the implemented non-isothermal and non-Newtonian MHD-FHD models. The non-isothermal Hartmann flow has been chosen as a benchmark physical problem to study velocity and temperature distributions for Newtonian fluids and non-Newtonian blood flows in a planar microfluidic channel. In addition to this, the numerical behaviour of an incompressible and non-isothermal non-Newtonian blood flow has been investigated from computational aspects when a dipole-like rotational magnetic field generated by infinite conducting wires. The numerical results are compared to available computational data taken from literature [2].

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Biomagnetic channel flow in spatially varying magnetic field

Cited by 115 publications

References 20 publications

A simple numerical methodology for BFD problems using stream function vorticity formulation

A simple numerical methodology for BFD problems using stream function vorticity formulation

Mixed Finite Element Formulation for Magnetic Fluid Oil Flow in Electromagnetic Field

Validation of a Magneto- And Ferro-Hydrodynamic Model for Non-Isothermal Flows in Conjunction With Newtonian and Non-Newtonian Fluids

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