Stability of flow between two rotating cylinders in the presence of a constant heat flux at the outer cylinder and radial temperature gradient - wide gap problem

1997 ◽  
Vol 33 (3) ◽  
pp. 257-260 ◽  
Author(s):  
P. M. Eagles ◽  
V. M. Soundalgekar
Keyword(s):  
Heat Flux ◽  
Temperature Gradient ◽  
Outer Cylinder ◽  
Constant Heat Flux ◽  
Radial Temperature Gradient ◽  
Rotating Cylinders ◽  
Constant Heat ◽  
Radial Temperature ◽  
Wide Gap

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).

The Effect of Thermal Diffusion on Flow Stability Between Two Rotating Cylinders

1977 ◽  
Vol 99 (3) ◽  
pp. 318-322 ◽  
Author(s):  
Chin-Hsiu Li
Keyword(s):  
Temperature Gradient ◽  
Prandtl Number ◽  
Outer Cylinder ◽  
Variable Density ◽  
Radial Temperature Gradient ◽  
Rotating Cylinders ◽  
Radial Temperature ◽  
Stabilizing Effect ◽  
The Stability ◽  
Very High

The influence of variable density on the stability of the flow between two rotating cylinders is re-examined. The instability is shown to set in as an oscillatory secondary flow which was overlooked by previous investigators. Results indicate that the radial temperature gradient destabilizes the flow if the outer cylinder is hotter than the inner one, and the destabilizing effect is enhanced if the Prandtl number is high. For the case where the inner cylinder is hotter than the outer one, the stabilizing effect due to the temperature gradient is shown to be weak for any Prandtl number. This modifies previous results which predicted a very high stabilizing effect due to the temperature gradient. The bifurcating structure of the stability curve is shown.

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