Magnetohydrodynamic flow in rectangular ducts

1965 ◽  
Vol 21 (4) ◽  
pp. 577-590 ◽  
Author(s):  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Boundary Layers ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Rectangular Duct ◽  
Conducting Liquid ◽  
The Core ◽  
Thin Walls ◽  
The Magnetic Field

The paper presents an analysis of laminar motion of a conducting liquid in a rectangular duct under a uniform transverse magnetic field. The effects of the duct having conducting walls are investigated. Exact solutions are obtained for two cases, (i) perfectly conducting walls perpendicular to the field and thin walls of arbitrary conductivity parallel to the field, and (ii) non-conducting walls parallel to the field and thin walls of arbitrary conductivity perpendicular to the field.The boundary layers on the walls parallel to the field are studied in case (i) and it is found that at high Hartmann number (M), large positive and negative velocities of order MVc are induced, where Vc is the velocity of the core. It is suggested that contrary to previous assumptions the magnetic field may in some cases have a destabilizing effect on flow in ducts.

Numerical Study of the Buoyancy Effect on Magnetohydrodynamic Three-Dimensional LiPb Flow in a Rectangular Duct

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Tigrine Zahia ◽  
Mokhtari Faiza ◽  
Bouabdallah Ahcène ◽  
Merah AbdelKrim ◽  
Kharicha Abdellah
Keyword(s):  
Magnetic Field ◽  
Hartmann Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Liquid Lead ◽  
Buoyancy Effect ◽  
Rectangular Duct ◽  
Buoyant Force ◽  
The Core

In this paper, the effect of transverse magnetic field on a laminar liquid lead lithium flow in an insulating rectangular duct is numerically solved with three-dimensional (3D) simulations. Cases with and without buoyancy force are examined. The stability of the buoyant flow is studied for different values of the Hartmann number from 0 to 120. We focus on the combined influence of the Hartmann number and buoyancy on flow field, flow structure in the vicinity of walls and its stability. Velocity and temperature distributions are presented for different magnetic field strengths. It is shown that the magnetic field damps the velocity and leads to flow stabilization in the core fluid and generates magnetohydrodynamic (MHD) boundary layers at the walls, which become the main source of instabilities. The buoyant force is responsible of the generation of vortices and enhances the velocities in the core region. It can act together with the MHD forces to intensify the flow near the Hartmann layers. Two critical Hartmann numbers (Hac1 = 63, Hac2 = 120) are found. Hac1 is corresponding to the separation of two MHD regimes: the first one is characterized by a core flow maximum velocity, whereas the second regime is featured by a maximum layer velocity and a pronounced buoyancy effect. Hac2 is a threshold value of electromagnetic force indicating the onset of MHD instability through the generation of small vortices close to the side layers.

Magnetohydrodynamic channel flows with weak transverse magnetic fields

2014 ◽  
Vol 372 (2020) ◽  
pp. 20130344
Author(s):  
A. P. Rothmayer
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Hartmann Number ◽  
Plane Channel ◽  
Transverse Magnetic ◽  
Unsteady Viscous Flow ◽  
High Reynolds ◽  
Magnetohydrodynamic Channel ◽  
The Magnetic Field

Magnetohydrodynamic flow of an incompressible fluid through a plane channel with slowly varying walls and a magnetic field applied transverse to the channel is investigated in the high Reynolds number limit. It is found that the magnetic field can first influence the hydrodynamic flow when the Hartmann number reaches a sufficiently large value. The magnetic field is found to suppress the steady and unsteady viscous flow near the channel walls unless the wall shapes become large.

Liquid-metal flow in a rectangular duct with a strong non-uniform magnetic field

1984 ◽  
Vol 139 ◽  
pp. 309-324 ◽  
Author(s):  
John C. Petrykowski ◽  
John S. Walker
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Metal Flow ◽  
Velocity Profiles ◽  
Transverse Magnetic ◽  
Secondary Flows ◽  
Rectangular Duct ◽  
Liquid Metal Flow ◽  
Displacement Thickness ◽  
The Magnetic Field

Liquid-metal flows in rectangular ducts having electrically insulating tops and bottoms and perfectly conducting sides and in the presence of strong, polar, transverse magnetic fields are examined. Solutions are presented for the boundary layers adjacent to the sides that are parallel to the magnetic field. Overshoots in the radial velocity profiles show that the side layers have zero displacement thickness and do not perturb the inviscid core. Very weak secondary flows involve four significant vortices, as reflected in the polar velocity profiles.

Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 2. Variable-area rectangular ducts with conducting sides

1971 ◽  
Vol 46 (4) ◽  
pp. 657-684 ◽  
Author(s):  
J. S. Walker ◽  
G. S. S. Ludford ◽  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Side Wall ◽  
Transverse Magnetic ◽  
Reverse Direction ◽  
Wall Boundary ◽  
Strong Transverse ◽  
Side Walls ◽  
The Magnetic Field

In this paper the general analysis, developed in part 1, of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section. It is found that, with the magnetic field parallel to one pair of the sides, the essential problem is the analysis of the boundary layers on these (side) walls. Assuming that they are highly conducting and that those perpendicular to the magnetic field are non-conducting, the flow is found to have some interesting properties: if the top and bottom walls diverge, the side walls remaining parallel, then an O(1) velocity overshoot occurs in the side-wall boundary layers; but if the top and bottom walls remain parallel, the side walls diverging, these boundary layers have conventional velocity profiles. The most interesting flows occur when both pairs of walls diverge, when it is found that large, 0(M½), velocities occur in the side-wall boundary layers, either in the direction of the mean flow or in the reverse direction, depending on the geometry of the duct and the external electric circuit!The mathematical analysis involves the solution of a formidable integral equation which, however, does have analytic solutions for some special types of duct.

scholarly journals Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct

2012 ◽  
Vol 708 ◽  
pp. 111-127 ◽  
Author(s):  
Jānis Priede ◽  
Svetlana Aleksandrova ◽  
Sergei Molokov
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Strong Magnetic Field ◽  
Linear Stability ◽  
Critical Reynolds Number ◽  
Metal Flow ◽  
Transverse Magnetic ◽  
Rectangular Duct ◽  
Instability Modes ◽  
The Magnetic Field

AbstractWe analyse numerically the linear stability of a liquid-metal flow in a rectangular duct with perfectly electrically conducting walls subject to a uniform transverse magnetic field. A non-standard three-dimensional vector stream-function/vorticity formulation is used with a Chebyshev collocation method to solve the eigenvalue problem for small-amplitude perturbations. A relatively weak magnetic field is found to render the flow linearly unstable as two weak jets appear close to the centre of the duct at the Hartmann number $\mathit{Ha}\approx 9. 6. $ In a sufficiently strong magnetic field, the instability following the jets becomes confined in the layers of characteristic thickness $\delta \ensuremath{\sim} {\mathit{Ha}}^{\ensuremath{-} 1/ 2} $ located at the walls parallel to the magnetic field. In this case the instability is determined by $\delta , $ which results in both the critical Reynolds number and wavenumber scaling as ${\ensuremath{\sim} }{\delta }^{\ensuremath{-} 1} . $ Instability modes can have one of the four different symmetry combinations along and across the magnetic field. The most unstable is a pair of modes with an even distribution of vorticity along the magnetic field. These two modes represent strongly non-uniform vortices aligned with the magnetic field, which rotate either in the same or opposite senses across the magnetic field. The former enhance while the latter weaken one another provided that the magnetic field is not too strong or the walls parallel to the field are not too far apart. In a strong magnetic field, when the vortices at the opposite walls are well separated by the core flow, the critical Reynolds number and wavenumber for both of these instability modes are the same: ${\mathit{Re}}_{c} \approx 642{\mathit{Ha}}^{1/ 2} + 8. 9\ensuremath{\times} 1{0}^{3} {\mathit{Ha}}^{\ensuremath{-} 1/ 2} $ and ${k}_{c} \approx 0. 477{\mathit{Ha}}^{1/ 2} . $ The other pair of modes, which differs from the previous one by an odd distribution of vorticity along the magnetic field, is more stable with an approximately four times higher critical Reynolds number.

The Effect of Magnetic Field on Buoyancy-Driven Convection in a Differentially Heated Square Cavity With Two Insulated Baffles Attached to Its Isothermal Walls

2008 ◽  
Author(s):  
M. Ghassemi ◽  
M. Pirmohammadi ◽  
G. A. Sheikhzadeh
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Hartmann Number ◽  
Core Region ◽  
Temperature Stratification ◽  
Square Cavity ◽  
The Core ◽  
Numerical Predictions ◽  
Vertical Walls ◽  
The Magnetic Field

Steady, laminar, natural-convection flow in the presence of a magnetic field in a differentially heated square cavity which two insulated horizontal baffles attached to its vertical walls is considered. The vertical walls are at different temperatures while the horizontal walls are adiabatic. In our formulation of governing equations, mass, momentum, energy and induction equations are applied to the cavity. To solve the governing differential equations a finite volume code based on Patankar’s SIMPLER method is utilized. Numerical predictions are obtained for various Rayleigh number (Ra), Hartmann number (Ha) and baffles position at the Prandtl number Pr = 0.733. At low Rayleigh number regime with weak magnetic field, a circulating flow is formed in the cavity. When the magnetic field is relatively strengthened, the thermal field resembles that of a conductive distribution, and the fluid in much of the interior is nearly stagnant. Further, when the magnetic field is weak and the Rayleigh number is high, the convection is dominant and vertical temperature stratification is predominant in the core region. However, for sufficiently large Ha, the convection is suppressed and the temperature stratification in the core region diminishes. The numerical results show that the effect of the magnetic field is to decrease the rate of convective heat transfer. The average Nusselt number decreases as Hartmann number increases.

Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field

1995 ◽  
Vol 117 (3) ◽  
pp. 668-673 ◽  
Author(s):  
S. Alchaar ◽  
P. Vasseur ◽  
E. Bilgen
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Transverse Magnetic Field ◽  
Hartmann Number ◽  
Convection Heat Transfer ◽  
Transverse Magnetic ◽  
Temperature Profiles ◽  
Flow Approximation ◽  
Buoyancy Driven Convection ◽  
The Magnetic Field

In this paper the effect of a transverse magnetic field on buoyancy-driven convection in a shallow rectangular cavity is numerically investigated (horizontal Bridgman configuration). The enclosure is insulated on the top and bottom walls while it is heated from one side and cooled from the other. Both cases of a cavity with all rigid boundaries and a cavity with a free upper surface are considered. The study covers the range of the Rayleigh number, Ra, from 102 to 105, the Hartmann number, Ha, from 0 to 102, the Prandtl number, Pr, from 0.005 to 1 and aspect ratio of the cavity, A, from 1 to 6. Comparison is made with an existing analytical solution (Garandet et al., 1992), based on a parallel flow approximation, and its range of validity is delineated. Results are presented for the velocity and temperature profiles and heat transfer in terms of Ha number. At high Hartmann numbers, both analytical and numerical analyses reveal that the velocity gradient in the core is constant outside the two Hartmann layers at the vicinity of the walls normal to the magnetic field.

scholarly journals Enhanced X-ray emission arising from laser-plasma confinement by a strong transverse magnetic field

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Evgeny D. Filippov ◽  
Sergey S. Makarov ◽  
Konstantin F. Burdonov ◽  
Weipeng Yao ◽  
Guilhem Revet ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic ◽  
Radiative Properties ◽  
Magnetic Field Direction ◽  
Solid Target ◽  
Total Plasma ◽  
Plasma Confinement ◽  
X Ray ◽  
Magnetic Compression ◽  
The Magnetic Field

AbstractWe analyze, using experiments and 3D MHD numerical simulations, the dynamic and radiative properties of a plasma ablated by a laser (1 ns, 10$$^{12}$$ 12 –10$$^{13}$$ 13 W/cm$$^2$$ 2 ) from a solid target as it expands into a homogeneous, strong magnetic field (up to 30 T) that is transverse to its main expansion axis. We find that as early as 2 ns after the start of the expansion, the plasma becomes constrained by the magnetic field. As the magnetic field strength is increased, more plasma is confined close to the target and is heated by magnetic compression. We also observe that after $$\sim 8$$ ∼ 8  ns, the plasma is being overall shaped in a slab, with the plasma being compressed perpendicularly to the magnetic field, and being extended along the magnetic field direction. This dense slab rapidly expands into vacuum; however, it contains only $$\sim 2\%$$ ∼ 2 % of the total plasma. As a result of the higher density and increased heating of the plasma confined against the laser-irradiated solid target, there is a net enhancement of the total X-ray emissivity induced by the magnetization.

Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Subramanian Muthukumar ◽  
Selvaraj Sureshkumar ◽  
Arthanari Malleswaran ◽  
Murugan Muthtamilselvan ◽  
Eswari Prem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Transfer Rate ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Bottom Wall ◽  
Uniform Heating ◽  
The Magnetic Field

Abstract A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

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