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 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.

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 ARBTools: A Tricubic Spline Interpolator for Three-Dimensional Scalar or Vector Fields

2019 ◽  
Author(s):  
Paul Walker ◽  
Ulrich Krohn ◽  
Carty David
Keyword(s):  
Magnetic Field ◽  
Vector Field ◽  
Vector Fields ◽  
Three Dimensional ◽  
Spline Method ◽  
Particle Trajectories ◽  
The Core ◽  
Numerical Integrators ◽  
Data Points ◽  
System Requirements

ARBTools is a Python library containing a Lekien-Marsden type tricubic spline method for interpolating three-dimensional scalar or vector fields presented as a set of discrete data points on a regular cuboid grid. ARBTools was developed for simulations of magnetic molecular traps, in which the magnitude, gradient and vector components of a magnetic field are required. Numerical integrators for solving particle trajectories are included, but the core interpolator can be used for any scalar or vector field. The only additional system requirements are NumPy.

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 Simulations of Core Convection Dynamos in Rotating A-type Stars

2004 ◽  
Vol 215 ◽  
pp. 376-377
Author(s):  
Matthew Browning ◽  
Allan Sacha Brun ◽  
Juri Toomre
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Differential Rotation ◽  
Three Dimensional ◽  
Dynamo Action ◽  
The Core ◽  
Core Convection ◽  
Seed Field ◽  
Initial Seed ◽  
Three Dimensional Simulations

We have conducted preliminary numerical simulations of a core convection dynamo operating within an A-type star of two solar masses. Convection within the core clearly can admit magnetic dynamo action. Magnetic field strengths in our three-dimensional simulations grow by many orders of magnitude, from an initial seed field to kilo-Gauss levels. We discuss the differential rotation and magnetic field sustained in our simulations.

scholarly journals Three-dimensional numerical study of mixed convection within a ventilated cavity (Shape ‘ L ‘) crossed by a nanofluid under the effect of a magnetic field

2020 ◽  
Vol 307 ◽  
pp. 01027
Author(s):  
S. KHERROUBI ◽  
K. RAGUI ◽  
N. LABSI ◽  
Y.K. BENKAHLA ◽  
A. BOUTRA
Keyword(s):  
Magnetic Field ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Numerical Study ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Left Wall ◽  
Ventilated Cavity ◽  
The Right

The present work is dedicated to the three-dimensional numerical study of mixed convection heat transfer, taking place within a ventilated cavity (of shape L) crossed by Cu-water nanofluid. The enclosure is subjected to the action of a magnetic field. The ventilation is assured by two openings of the same size. The cold flow enters by an opening practiced at the top of the left wall, and exits by another opening practiced at the bottom of the right vertical wall. All the cavity walls are maintained at the same temperature, superior to that of the entering flow, except the side walls which are considered as adiabatic. The control parameters are: the Reynolds number and the Hartmann number as well as the nanoparticles volume fraction.

The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

1971 ◽  
Vol 69 (2) ◽  
pp. 337-351 ◽  
Author(s):  
D. J. Temperley ◽  
L. Todd
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Classical Model ◽  
Critical Discussion ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Wall Conductivity ◽  
Expansion Procedure

AbstractLaminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.

Numerical Study of Magnetic Field Influence on Three-Dimensional Flow Regime and Combined-Convection Heat Exchange Within Concentric and Eccentric Rotating Cylinders

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Javad Sodagar-Abardeh ◽  
Payam Nasery ◽  
Ahmad Arabkoohsar ◽  
Mahmood Farzaneh-Gord
Keyword(s):  
Magnetic Field ◽  
Heat Exchange ◽  
Flow Regime ◽  
Axial Magnetic Field ◽  
Numerical Study ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Convection Heat ◽  
Combined Convection ◽  
Number Variation

Abstract The forced and natural flows of fluid within an annulus caused by the rotation of cylinders and temperature differences of the inner and outer walls are observed in various engineering applications. In this research, the laminar flow regime and mixed convection inside a ring-shaped horizontal concentric and eccentric space for an incompressible fluid are studied in the existence of an axial magnetic field. The present work is the first effort to investigate the influence of a magnetic field on flow and combined-convection heat exchange characteristics within an annulus with a cold outer cylinder and an inner hot cylinder. Here, the properties of the flow and heat transfer characteristics are studied using the finite volume method. Numerical procedures are mainly investigated for recognizing the influence of Hartmann number (in the range of 0 ≤ Ha ≤ 100), as the representative of the magnetic force, on velocity components, Nusselt number, streamlines, and isothermal lines. One of the notable effects is that when Ha number increases, it will reduce the vorticity of the fluid and buoyancy forces. As a result, streamlines and isothermal lines can be seen more constant as regular concentric circles. A rise in Ha number decreases the range of local Nu number variation for both cylinders. The average Nu number for the outer and inner cylinders has different trends when Ha number increases. Taking concentric cylinders as an example, this parameter for the inner and the outer cylinders increases and decreases by about 1.2 and 1.6, respectively.

Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field. Part 1. Two-dimensional flow

1997 ◽  
Vol 333 ◽  
pp. 23-56 ◽  
Author(s):  
HAMDA BEN HADID ◽  
DANIEL HENRY ◽  
SLIM KADDECHE
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Scaling Laws ◽  
Hartmann Number ◽  
Numerical Study ◽  
Flow Region ◽  
Horizontal Layer ◽  
Vertical Magnetic Field ◽  
Two Dimensional Flow ◽  
Thermocapillary Forces

Studies of convection in the horizontal Bridgman configuration were performed to investigate the flow structures and the nature of the convective regimes in a rectangular cavity filled with an electrically conducting liquid metal when it is subjected to a constant vertical magnetic field. Under some assumptions analytical solutions were obtained for the central region and for the turning flow region. The validity of the solutions was checked by comparison with the solutions obtained by direct numerical simulations. The main effects of the magnetic field are first to decrease the strength of the convective flow and then to cause a progressive modification of the flow structure followed by the appearance of Hartmann layers in the vicinity of the rigid walls. When the Hartmann number is large enough, Ha > 10, the decrease in the velocity asymptotically approaches a power-law dependence on Hartmann number. All these features are dependent on the dynamic boundary conditions, e.g. confined cavity or cavity with a free upper surface, and on the type of driving force, e.g. buoyancy and/or thermocapillary forces. From this study we generate scaling laws that govern the influence of applied magnetic fields on convection. Thus, the influence of various flow parameters are isolated, and succinct relationships for the influence of magnetic field on convection are obtained. A linear stability analysis was carried out in the case of an infinite horizontal layer with upper free surface. The results show essentially that the vertical magnetic field stabilizes the flow by increasing the values of the critical Grashof number at which the system becomes unstable and modifies the nature of the instability. In fact, the range of Prandtl number over which transverse oscillatory modes prevail shrinks progressively as the Hartmann number is increased from zero to 5. Therefore, longitudinal oscillatory modes become the preferred modes over a large range of Prandtl number.

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