Natural Convection in Low Prandtl Number Fluids With a Vertical Magnetic Field

2000 ◽  
Vol 122 (3) ◽  
pp. 602-605 ◽  
Author(s):  
S. Saravanan ◽  
P. Kandaswamy
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Prandtl Number ◽  
Vertical Magnetic Field

[S0022-1481(00)00403-5]

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.

scholarly journals Nonlinear Magneto Convection in a Rotating Fluid due to Vertical Magnetic Field and Vertical Axis of Rotation

2021 ◽  
Vol 39 (3) ◽  
pp. 775-786
Author(s):  
Avula Benerji Babu ◽  
Gundlapally Shiva Kumar Reddy ◽  
Nilam Venkata Koteswararao
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Normal Mode Analysis ◽  
Vertical Axis ◽  
Wave Number ◽  
Mode Analysis ◽  
Vertical Magnetic Field ◽  
Rotating Fluid ◽  
Axis Of Rotation

In the present paper, linear and weakly nonlinear analysis of magnetoconvection in a rotating fluid due to the vertical magnetic field and the vertical axis of rotation are presented. For linear stability analysis, the normal mode analysis is utilized to find the Rayleigh number which is the function of Taylor number, Magnetic Prandtl number, Thermal Prandtl number and Chandrasekhar number. Also, the correlation between the Rayleigh number and wave number is graphically analyzed. The parameter regimes for the existence of pitchfork, Takens-Bogdanov and Hopf bifurcations are reported. Small-amplitude modulation is considered to derive the Newell-Whitehead-Segel equation and using its phase-winding solution, the conditions for the occurrence of Eckhaus and zigzag secondary instabilities are obtained. The system of coupled Landau-Ginzburg equations is derived. The travelling wave and standing wave solutions for the Newell-Whitehead-Segel equation are also presented. For, standing waves and travelling waves, the stability regions are identified.

Magnetofluidconvection in a Rotating Porous Layer Under Modulated Temperature on the Boundaries

2006 ◽  
Vol 129 (7) ◽  
pp. 835-843 ◽  
Author(s):  
B. S. Bhadauria
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Prandtl Number ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Temperature Modulation ◽  
Brinkman Model ◽  
Vertical Magnetic Field

Thermal instability in an electrically conducting fluid saturated porous medium, confined between two horizontal walls, has been investigated in the presence of an applied vertical magnetic field and rotation, using the Brinkman model. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. Only infinitesimal disturbances are considered. The combined effect of permeability, rotation, vertical magnetic field, and temperature modulation has been investigated using Galerkin’s method and Floquet theory. The value of the critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Chandrasekhar number, Taylor number, porous parameter, Prandtl number, and magnetic Prandtl number. It is found that rotation, magnetic field, and porous medium all have a stabilizing influence on the onset of thermal instability. Further, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls’ temperature. In addition the results corresponding to the Brinkman model and Darcy model have been compared for neutral instability.

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