scholarly journals Effect of the Direction of Uniform Horizontal Magnetic Field on the Linear Stability of Natural Convection in a Long Vertical Rectangular Enclosure

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1689
Author(s):  
Toshio Tagawa
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Linear Stability ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Horizontal Magnetic Field ◽  
Direction Parallel ◽  
Vertical Side ◽  
Rectangular Enclosure

The effect of the direction of external horizontal magnetic fields on the linear stability of natural convection of liquid metal in an infinitely long vertical rectangular enclosure is numerically studied. A vertical side wall is heated and the opposing vertical wall is cooled both isothermally, whereas the other two vertical walls are adiabatic. A uniform horizontal magnetic field is applied either in the direction parallel or perpendicular to the temperature gradient. In this study, the height of the enclosure is so long as to neglect the top and bottom effects where returning flow takes place, and thus the basic flow is assumed to be a parallel flow and the temperature field is in heat conduction state. The Prandtl number is limited to the value of 0.025 and horizontal cross-section is square. The natural convection is monotonously stabilized as increase in the Hartmann number when the applied magnetic field is parallel to the temperature gradient. However, when the applied magnetic field is perpendicular to the temperature gradient, it is once destabilized at a certain low Hartmann number, but it is stabilized at high Hartmann numbers.

Influence of a horizontal magnetic field on the natural convection of paramagnetic fluid in a cube heated and cooled from two vertical side walls

2008 ◽  
Vol 47 (6) ◽  
pp. 668-679 ◽  
Author(s):  
Tomasz Bednarz ◽  
Elzbieta Fornalik ◽  
Hiroyuki Ozoe ◽  
Janusz S. Szmyd ◽  
John C. Patterson ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Horizontal Magnetic Field ◽  
Vertical Side ◽  
Side Walls

Effects of a Magnetic Field on Natural Convection in a Toroidal Channel

1962 ◽  
Vol 29 (3) ◽  
pp. 559-567 ◽  
Author(s):  
Paul Concus
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Convective Motion ◽  
Liquid Sodium ◽  
Fixed Temperature ◽  
Horizontal Magnetic Field ◽  
Thermally Conducting ◽  
Solid Block

The problem of the natural convection of an electrically and thermally conducting fluid within a long, narrow, vertical toroidial channel centered in a large block of an electrically and thermally conducting solid is analyzed. A uniform horizontal magnetic field is applied to the fluid, and the bottom of the solid block is maintained at a higher fixed temperature than the top. The laminar, steady-state, single-cell convective motion of the fluid is considered and an approximate solution is found for the heat-transfer rate between the bottom and top surfaces of the block in the limiting cases of small and large Hartmann number. A numerical example is given for liquid sodium in which the application of a magnetic field of a few hundred gauss is shown to reduce the rate of heat transfer significantly.

scholarly journals Linear Stability Analysis of Thermal Convection in an Infinitely Long Vertical Rectangular Enclosure in the Presence of a Uniform Horizontal Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Takashi Kitaura ◽  
Toshio Tagawa
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Thermal Convection ◽  
Vertical Channel ◽  
Numerical Code ◽  
Convection Flow ◽  
Horizontal Magnetic Field ◽  
Direction Parallel

Stability of thermal convection in an infinitely long vertical channel in the presence of a uniform horizontal magnetic field applied in the direction parallel to the hot and cold walls was numerically studied. First, in order to confirm accuracy of the present numerical code, the one-dimensional computations without the effect of magnetic field were computed and they agreed with a previous study quantitatively for various values of the Prandtl number. Then, linear stability analysis for the thermal convection flow in a square horizontal cross section under the magnetic field was carried out for the case of Pr = 0.025. The thermal convection flow was once destabilized at certain low Hartmann numbers, and it was stabilized at high Hartmann numbers.

scholarly journals Effect of magnetic field on nanofluid free convection in Conical Partially Annular Space

2020 ◽  
Vol 330 ◽  
pp. 01005
Author(s):  
Abderrahmane AISSA ◽  
Mohamed Amine MEDEBBER ◽  
Khaled Al-Farhany ◽  
Mohammed SAHNOUN ◽  
Ali Khaleel Kareem ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Boussinesq Approximation ◽  
Simulation Software ◽  
Comsol Multiphysics ◽  
Governing Equations ◽  
Element Analysis ◽  
Vertical Side ◽  
Side Walls

Natural convection of a magneto hydrodynamic nanofluid in a porous cavity in the presence of a magnetic field is investigated. The two vertical side walls are held isothermally at temperatures Th and Tc, while the horizontal walls of the outer cone are adiabatic. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. Impact of Rayleigh number (Ra), Hartmann number (Ha) and nanofluid volume fraction (ϕ) are depicted. Results indicated that temperature gradient increases considerably with enhance of Ra and ϕ but it reduces with increases of Ha.

scholarly journals CuO–Water Nanofluid Magnetohydrodynamic Natural Convection inside a Sinusoidal Annulus in Presence of Melting Heat Transfer

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sheikholeslami ◽  
R. Ellahi ◽  
C. Fetecau
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Melting Heat ◽  
Melting Heat Transfer ◽  
Limiting Case ◽  
Good Agreement ◽  
Melting Parameter

Impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer is simulated using CVFEM in this research. KKL model is taken into account to obtain properties of CuO–H2O nanofluid. Roles of melting parameter (δ), CuO–H2O volume fraction (ϕ), Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. Results depict that temperature gradient improves with rise of Rayleigh number and melting parameter. Nusselt number detracts with rise of Ha. At the end, a comparison as a limiting case of the considered problem with the existing studies is made and found in good agreement.

Numerical Solution of Melting Processes for Fixed and Unfixed Phase Change Material in the Presence of Magnetic Field: Simulation of Low Gravity Environment

2001 ◽  
Author(s):  
Y. Asako ◽  
E. Gonçalves ◽  
M. Faghri ◽  
M. Charmchi
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Phase Change ◽  
Phase Change Material ◽  
Flow Patterns ◽  
Transport Processes ◽  
Low Gravity ◽  
Horizontal Magnetic Field ◽  
Wall Heating ◽  
Change Material

Abstract Transport processes associated with melting of an electrically conducting Phase Change Material (PCM), placed inside a rectangular enclosure, under low-gravity environment, and in the presence of a magnetic field is simulated numerically. Electromagnetic forces damp the natural convection as well as the flow induced by sedimentation and/or floatation, and thereby simulating the low gravity environment of outer space. Computational experiments are conducted for both side-wall heating and top-wall heating under horizontal magnetic field. The governing equations are discretized using a control-volume-based finite difference scheme. Numerical solutions are obtained for true low-gravity environment as well as for the simulated-low-gravity conditions resulted by the presence of a horizontal magnetic field. The effects of magnetic field on the natural convection, solid phase floatation/sedimentation, liquid-solid interface location, solid melting rate, and flow patterns are investigated. It is found that the melting under low-gravity environment can reasonably be simulated on earth via applying a strong horizontal magnetic field. However, the flow patterns obtained for the true low-gravity cases are not similar to the corresponding cases solved for the simulated-low-gravity environment.

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.

Sign in / Sign up

Export Citation Format

Share Document