DRBEM solutions of Stokes and Navier–Stokes equations in cavities under point source magnetic field

2016 ◽  
Vol 64 ◽  
pp. 158-175 ◽  
Author(s):  
P. Senel ◽  
M. Tezer-Sezgin
Keyword(s):  
Magnetic Field ◽  
Point Source ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Submerged Jet of a Conducting Fluid in the Presence of the Magnetic Field

2012 ◽  
Vol 7 (2) ◽  
pp. 25-38
Author(s):  
Rustam Mullyadzhanov ◽  
Nikolay Yavorsky
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Point Source ◽  
Electric Current ◽  
Stokes Equations ◽  
Conducting Fluid ◽  
Mhd Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Submerged Jet

We consider a steady flow of a viscous incompressible conducting fluid. New exact solution of the magnetohydrodynamic (MHD) equations is obtained, when the flow is induced by the point source of hydrodynamic momentum located at the end of a semi-infinite linear conductor with a set value of the electric current. The effects of the confinement of the current density and the loss of existence of the solution with the finite values of electric current and various values of the Reynolds number and the Batchelor number (magnetic Prandtl number) are found. The non-self-similar problem is considered, when the flow is induced by the point source of momentum, angular momentum, flow rate and electric current that are set at the origin. In this case, the first term of the asymptotic expansion of the velocity at the infinity is described by the exact solution of the Navier – Stokes equations of the submerged jet (Slezkin – Landau – Squire solution). We analyze the conservation laws. It is shown that the induced magnetic field reduces the intensity of the jet flow

Combined Marangoni and buoyancy convection in a porous annular cavity filled with Ag-MgO/water hybrid nanofluid

2021 ◽  
Vol 17 ◽  
Author(s):  
B. Kanimozhi ◽  
M. Muthtamilselvan ◽  
Qasem M. Al-Mdallal ◽  
Bahaaeldin Abdalla
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Axial Magnetic Field ◽  
Vertical Wall ◽  
Navier Stokes ◽  
Hybrid Nanofluid ◽  
Radial Magnetic Field ◽  
Navier Stokes Equations ◽  
Buoyancy Convection

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for other two boundaries. The effect of magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows.Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

scholarly journals MHD convection ow in a constricted channel

2018 ◽  
Vol 26 (2) ◽  
pp. 267-283
Author(s):  
M. Tezer-Sezgin ◽  
Merve Gürbüz
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Particular Solution ◽  
Laminar Convection ◽  
Long Channel ◽  
Velocity Pressure

Abstract We consider the steady, laminar, convection ow in a long channel of 2D rectangular constricted cross-section under the inuence of an applied magnetic field. The Navier-Stokes equations including Lorentz and buoyancy forces are coupled with the temperature equation and are solved by using linear radial basis function (RBF) approximations in terms of the velocity, pressure and the temperature of the fluid. RBFs are used in the approximation of the particular solution which becomes also the approximate solution of the problem. Results are obtained for several values of Grashof number (Gr), Hartmann number (M) and the constriction ratios (CR) to see the effects on the ow and isotherms for fixed values of Reynolds number and Prandtl number. As M increases, the ow is flattened. An increase in Gr increases the magnitude of the ow in the channel. Isolines undergo an inversion at the center of the channel indicating convection dominance due to the strong buoyancy force, but this inversion is retarded with the increase in the strength of the applied magnetic field. When both Hartmann number and constriction ratio are increased, ow is divided into more loops symmetrically with respect to the axes.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

Magnetic field effects on the slip velocity and temperature jump of nanofluid forced convection in a microchannel

2015 ◽  
Vol 230 (11) ◽  
pp. 1921-1936 ◽  
Author(s):  
Arash Karimipour ◽  
Masoud Afrand
Keyword(s):  
Magnetic Field ◽  
Forced Convection ◽  
Slip Velocity ◽  
Temperature Jump ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Computer Code ◽  
Navier Stokes ◽  
Magnetic Field Effects ◽  
Navier Stokes Equations

Forced convection of water–Cu nanofluid in a two-dimensional microchannel is studied numerically. The microchannel wall is divided into three parts. The entry and exit ones are kept insulated while the middle one has more temperature than the inlet fluid. The whole of microchannel is under the influence of a magnetic field with uniform strength of B0. Slip velocity and temperature jump are involved along the microchannel walls for different values of slip coefficient such as B = 0.001, B = 0.01, and B = 0.1 for Re = 10, Re = 50, and Re = 100. Navier–Stokes equations are discretized and numerically solved by a developed computer code in FORTRAN. Results are presented as the velocity, temperature, and Nusselt number profiles. Moreover, the effect of magnetic field on slip velocity and temperature jump is investigated for the first time in the present work. Larger Hartmann number, Reynolds number, and volume fraction correspond to more heat transfer rate; however, the effects of Ha and ϕ are more significant at higher Re.

Effect of Nanofluid Properties on Magnetohydrodynamic Pump (MHD)

2011 ◽  
Vol 403-408 ◽  
pp. 663-669 ◽  
Author(s):  
Azadeh Shahidian ◽  
Majid Ghassemi ◽  
Rafat Mohammadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Al2o3 Nanoparticles ◽  
Nacl Solution ◽  
Navier Stokes Equations ◽  
Side Walls

A Magnetohydrodynamic pump uses the Lorentz effect. It is based on the injection of an electric field into two electrodes located at facing side walls of a channel. The purpose of this study is to numerically investigate the effect of Nanofluid properties on the flow field as well as the temperature distribution in a MHD pump. To solve the non-linear governing differential equations, a finite difference based code is developed and utilized. The temperature and velocity are calculated by solving the energy and Navier-Stokes equations. Result shows that temperature stays almost constant with magnetic field. Furthermore velocity and temperature behaviours are similar for each period. However heat transfer inside the MHD pump varies with nanofluid (NaCl solution and Al2O3 nanoparticles) in comparison with the NaCl solution.

Electrically driven vortices in a strong magnetic field

1988 ◽  
Vol 189 ◽  
pp. 553-569 ◽  
Author(s):  
Joël Sommeria
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Opposite Sign ◽  
Electric Pulse ◽  
Lateral Wall ◽  
Horizontal Layer ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Magnetic Field ◽  
Lower Plane

A steady isolated vortex is produced in a horizontal layer of mercury (of thickness a), subjected to a uniform vertical magnetic field. The vortex is forced by an electric current going from an electrode in the lower plane to the circular outer frame. The flow is investigated by streak photographs of small particles following the free upper surface, and by electric potential measurements. The agreement with the asymptotic theory for high values of the Hartmann number M is excellent for moderate electric currents. In particular all the current stays in the thin Hartmann layer of thickness a/M, except in the vortex core of horizontal extension a/M½. For higher currents, the size of the core becomes larger and depends only on the local interaction parameters. When the current is switched off, we measure the decay due to the Hartmann friction. A similar study is carried out for a vortex created by an initial electric pulse, and for a pair of vortices of opposite sign. For all these examples, the dynamics can be described by the two-dimensional Navier-Stokes equations with Hartmann friction, except in the vortex cores. Finally a vortex is produced near a lateral wall and a detachment of the boundary layer parallel to the magnetic field occurs, by which a second vortex of opposite sign is generated.

Simulation of Microfluidic Flow Using Ferrofluids

2008 ◽  
Author(s):  
Akshay C. Gunde ◽  
Sushanta K. Mitra
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Flow Control ◽  
Magnetic Particles ◽  
Stokes Equations ◽  
Maximum Velocity ◽  
Additional Term ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Microfluidic Flow

Present day microfluidics widely uses electrokinetic effects like eletrosmosis and electrophoresis to achieve flow control. These methods require extensive micromachining processes. Also, the fabrication of valves and valve-seats is difficult, which frequently leads to leakages and eventual breakdown of the system. This paper introduces the use of ferrofluids as an alternative for flow control in microchannels. Numerical simulation of flow through a microchannel using a ferrofluid in the presence of an external magnetic field is performed by coupling the flow and magnetic phenomena. An additional term calculated from the ferrofluid magnetization equations, is introduced in the Navier-Stokes equations to account for the magnetic force. The maximum velocity in a magnetically driven flow is shown to be a linear function of magnitude of magnetization of the permanent magnet. Further, the insertion of micron-size magnetic particles (referred here as magnetic plugs) in the flow field has been discussed. These plugs can be used to provide appropriate barriers to the flow by controlling their movement externally. Using the combination of ferrofluid and magnetic plugs, flow control can be achieved by the variation of external magnetic field alone.

Sign in / Sign up

Export Citation Format

Share Document