scholarly journals Stability of narrow-gap MHD Taylor-Couette flow with radial heating and constant heat flux at the outer cylinder

2005 ◽  
Vol 32 (4) ◽  
pp. 359-384 ◽  
Author(s):  
R.K. Deka
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Outer Cylinder ◽  
Constant Heat Flux ◽  
Wave Number ◽  
Narrow Gap ◽  
Critical Wave Number ◽  
Constant Heat

A linear stability analysis has been presented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field and constant heat flux at the outer cylinder. The narrow-gap equations with respect to axisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of boundary conditions, conducting and non-conducting walls are considered. A parametric study covering on the basis of ?, the ratio of the angular velocity of the outer cylinder to that of inner cylinder, Q, the Hartmann number which represents the strength of the axial magnetic field, and N, the ratio of the Rayleigh number and Taylor number representing the supply of heat to the outer cylinder at constant rate is presented. The three cases of ? < 0 (counter rotating), ? > 0 (co-rotating) and ? = 0 (stationary outer cylinder) are considered wherein the magnetic Prandtl number is assumed to be small. Results show that the stability characteristics depend mainly on the conductivity on the cylinders and not on the heat supplied to the outer cylinder. As a departure from earlier results corresponding to isothermal as well as hydromagnetic flow, it is found that the critical wave number is strictly a monotonic decreasing function of Q for conducting walls. Also, the presence of constant heat flux leads to a fall in the critical wave number for counter rotating cylinders, which states that for large values of -?, there occur transition from axisymmetric to non-axisymmetric disturbance whether the flow is hydrodynamic or hydromagnetic and this transition from axisymmetric to non-axisymmetric disturbance occur earlier as the strength of the magnetic field increases.

Stability of Taylor–Couette Magnetoconvection With Radial Temperature Gradient and Constant Heat Flux at the Outer Cylinder

2006 ◽  
Vol 129 (3) ◽  
pp. 302-310 ◽  
Author(s):  
R. K. Deka ◽  
A. S. Gupta
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Outer Cylinder ◽  
Constant Heat Flux ◽  
Taylor Number ◽  
Wave Number ◽  
Constant Heat ◽  
Radial Temperature ◽  
Electrically Conducting ◽  
Wide Gap

An analysis is made of the linear stability of wide-gap hydromagnetic (MHD) dissipative Couette flow of an incompressible electrically conducting fluid between two rotating concentric circular cylinders in the presence of a uniform axial magnetic field. A constant heat flux is applied at the outer cylinder and the inner cylinder is kept at a constant temperature. Both types of boundary conditions viz; perfectly electrically conducting and electrically nonconducting walls are examined. The three cases of μ<0 (counter-rotating), μ>0 (co-rotating), and μ=0 (stationary outer cylinder) are considered. Assuming very small magnetic Prandtl number Pm, the wide-gap perturbation equations are derived and solved by a direct numerical procedure. It is found that for given values of the radius ratio η and the heat flux parameter N, the critical Taylor number Tc at the onset of instability increases with increase in Hartmann number Q for both conducting and nonconducting walls thus establishing the stabilizing influence of the magnetic field. Further it is found that insulating walls are more destabilizing than the conducting walls. It is observed that for given values of η and Q, the critical Taylor number Tc decreases with increase in N. The analysis further reveals that for μ=0 and perfectly conducting walls, the critical wave number ac is not a monotonic function of Q but first increases, reaches a maximum and then decreases with further increase in Q. It is also observed that while ac is a monotonic decreasing function of μ for N=0, in the presence of heat flux (N=1), ac has a maximum at a negative value of μ (counter-rotating cylinders).

Three-Dimensional Numerical Analysis for Convection of Air in a Bore Space of a Superconducting Magnet

2003 ◽  
Author(s):  
G. Tomita ◽  
M. Kaneda ◽  
T. Tagawa ◽  
H. Ozoe
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Natural Convection ◽  
Numerical Analysis ◽  
Strong Magnetic Field ◽  
Three Dimensional ◽  
Superconducting Magnet ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Magnetizing Force

Three-dimensional numerical computations were carried out for the natural convection of air in a horizontal cylindrical enclosure in a magnetic field, which is modeled for a bore space of a horizontal superconducting magnet. The enclosure was cooled from the circumferential sidewall at the constant heat flux and vertical end walls were thermally insulated. A strong magnetic field was considered by a one-turn electric coil with the concentric and twice diameter of the cylinder. Without a magnetic field, natural convection occurs along the circumferential sidewall. When a magnetic field was applied, magnetizing force induced the additional convection, that is, the cooled air at the circumferential wall was attracted to the location of a coil. Consequently, the temperature around the coil decreased extensively.

An exact solution in the stability of m. h. d. Couette flow

1972 ◽  
Vol 327 (1569) ◽  
pp. 269-278 ◽  
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Couette Flow ◽  
Stability Problem ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Mhd Stability ◽  
Arbitrary Magnetic Field ◽  
The Stability ◽  
Conducting Cylinders

The MHD stability problem for dissipative Couette flow in a narrow gap between corotating, conducting cylinders with an axial magnetic field is solved exactly. Results are presented for an arbitrary magnetic field; in particular, previous results on the zero and infinite magnetic field limits are verified.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

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