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.

Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field

2002 ◽  
Vol 469 ◽  
pp. 189-207 ◽  
Author(s):  
B. C. HOUCHENS ◽  
L. MARTIN WITKOWSKI ◽  
J. S. WALKER
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hartmann Number ◽  
Critical Rayleigh Number ◽  
Vertical Wall ◽  
Vertical Cylinder ◽  
Vertical Magnetic Field

This paper presents two linear stability analyses for an electrically conducting liquid contained in a vertical cylinder with a thermally insulated vertical wall and with isothermal top and bottom walls. There is a steady uniform vertical magnetic field. The first linear stability analysis involves a hybrid approach which combines an analytical solution for the Hartmann layers adjacent to the top and bottom walls with a numerical solution for the rest of the liquid domain. The second linear stability analysis involves an asymptotic solution for large values of the Hartmann number. Numerically accurate predictions of the critical Rayleigh number can be obtained for Hartmann numbers from zero to infinity with the two solutions presented here and a previous numerical solution which gives accurate results for small values of the Hartmann number.

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.

scholarly journals Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 177 ◽  
Author(s):  
Tagawa
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Liquid Metal ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Uniform Magnetic Field ◽  
Metal Flow ◽  
Rectangular Duct ◽  
Liquid Metal Flow ◽  
External Uniform Magnetic Field

Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present analysis, since the Joule heating and induced magnetic field were neglected, the governing equations consisted of the continuity of mass, momentum equation, Ohm’s law, and conservation of electric charge. A set of linearized disturbance equations for the complex amplitude was decomposed into real and imaginary parts and solved numerically with a finite difference method using the highly simplified marker and cell (HSMAC) algorithm on a two-dimensional staggered mesh system. The difficulty of the complex eigenvalue problem was circumvented with a Newton—Raphson method during which its corresponding eigenfunction was simultaneously obtained by using an iterative procedure. The relation among the Reynolds number, the wavenumber, the growth rate, and the angular frequency was successfully obtained for a given value of the Hartmann number as well as for a direction of external uniform magnetic field.

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