The DRBEM solution of incompressible MHD flow equations

Bozkaya, Nuray; Tezer‐Sezgin, M.

doi:10.1002/fld.2413

Cited by 13 publications

(11 citation statements)

References 23 publications

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“…In addition, ferrofluid can exhibit non-Newtonian behaviour [26][27][28][29]. However, most of the available works reported only on the effect of FHD on Newtonian fluid [2,23,[30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Even if the magnetic field effect is included in power-law fluid flow, the works only used magnetic field effect of MHD [44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

2020

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The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

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Section: Introductionmentioning

confidence: 99%

“…Tzirakis [39] studied biomagnetic fluid flow in circular ducts. For the works on magnetic fluid flow in lid driven cavity, it has been studied by Tzirtzilakis and Xenos [40], Marioni et al [41], Bozkaya et al [42] and by Senel and Tezer-Sezgin [43].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

2020

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“…Also, the Navier‐Stokes equations to describe the motion of an incompressible viscous fluid are

\begin{align} \nabla \cdot boldu & = 0, \end{align}

\begin{align} \frac{\partial boldu}{\partial t} + boldu \cdot \nabla boldu & = prefix- \frac{1}{ρ} \nabla p + ν \nabla^{2} boldu + boldf, \end{align}

in which u , ν, ρ, p , and f are the velocity field, diffusion coefficient, the density, the pressure, and the external force, respectively. Now, the incompressible MHD flow is

\begin{align} \frac{\partial boldu}{\partial t} + boldu \cdot \nabla boldu & = prefix- \nabla p + \frac{1}{μ_{1}} \nabla^{2} boldu + A l ((), \nabla prefix\times boldb) prefix\times boldb + boldg, \end{align}

\begin{align} \frac{\partial boldb}{\partial t} prefix- \nabla prefix\times ((), boldu prefix\times boldb) & = \frac{1}{μ_{2}} \nabla^{2} boldb, \end{align}

\begin{align} \nabla \cdot boldu & = 0, \end{align}

\begin{align} \nabla \cdot boldb & = 0, \end{align}

such that u , b , p , μ 1 , Al , and μ 2 are velocity field, magnetic field, pressure, the Reynolds number, the Alfven number, and magnetic Reynolds number, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…The MHD model is simulated by meshless local Petrov‐Galerkin (MLPG) method, meshfree weak‐strong (MWS) form, local radial point interpolation method, boundary element method, finite difference method, finite element method, local point collocation method, the variational multiscale EFG method, and other numerical techniques …”

Section: Introductionmentioning

confidence: 99%

A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

Abbaszadeh

Dehghan

Navon

2020

Numerical Methods in Fluids

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Summary In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element‐free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced‐order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced‐order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two‐dimensional cases.

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“…For this, we start with the reduced resistive MHD model of (see also in a different context) and using the principles established in , we generalize it so as to accommodate different varieties of models for the non‐inductive current drives and at the same time allow for a variable density profile(s). The different types of models for the non‐inductive current drives will help in making the model comply with the realistic models of these drives, and variable density might allow us to introduce turbulent fluctuations, generally seen in the tokamak plasmas.…”

Section: Introductionmentioning

confidence: 99%

Unconditionally stable numerical simulations of a new generalized reduced resistive magnetohydrodynamics model

Malapaka

Després

Sart

2013

Numerical Methods in Fluids

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SUMMARY Reduced‐resistive magnetohydrodynamics (MHD) models are used in understanding different phenomenon in various domains, for example, astrophysics to model magnetotail or for solar arcades [Finn Bozkaya JM, Guzdar PN. Loss of equilibrium and reconnection in tearing of two dimensional equilibrias. Physics of Fluids B 1993; 5:2870–2876], modeling plasma confinements in reverse field pinch [Strauss HR. The dynamo effect in fusion plasmas. Physics of Fluids 1985; 28:2786–2792] and tokamaks [Strauss HR. Reduced MHD in nearly potential magnetic fields. Journal of Plasma Physics 1997; 57(1):83–87; Freidberg J. Plasma Physics and Fusion Energy. Cambridge University Press: Cambridge, 2008]. In this context, recently, a new generalized reduced‐resistive MHD model, which can make use of an arbitrary density profile was proposed [Després B, Sart R. Reduced resistive MHD in Tokamaks with general density. ESAIM: Mathematical Modelling and Numerical Analysis 2012; 46(5):1081–1106. EDP Sciences, SMAI, 2012 online 2011]. We in this work show that this proposed theoretical model can be realized numerically as well, and that it is very robust if the equation set is written in a very particular form using the properties of FEM. To illustrate these points, we pick the current hole configuration [Fujita T, Oikawa T, Suzuki T, Ide S, Sakamoto Y, Koide Y, Hatae T, Naito O, Isayama A, Hayashi N, Shirai H. Plasma equilibrium and confinement in a tokamak with nearly zero central current density in JT‐60U. Physical Review Letters 2001; 87(11):245001; Hawkes NC, Stratton BC, Tala T, Challis CD, Conway G, DeAngelis R, Giroud C, Hobirk J, Joffrin E, Lomas P, Lotte P, Mailloux J, Mazon D, Rachlew E, Reyes‐Cortes S, Solano E, Zastrow K‐D. Observation of zero current density in the core of JET discharges with lower hybrid heating and current drive. Physical Review Letters 2001; 87(11):115001], which was modeled using reduced‐resistive MHD and remodel it using different combinations of current sources and density profiles. Our model can be implemented with reasonable computational resources at the price of solving a well‐posed global linear system and it is unconditionally stable. These features are also demonstrated as a part of our numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.

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The DRBEM solution of incompressible MHD flow equations

Cited by 13 publications

References 23 publications

Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

Unconditionally stable numerical simulations of a new generalized reduced resistive magnetohydrodynamics model

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