Effect of Radial Temperature Gradient on Stability of Hydromagnetic Couette Flow in Narrow-Gap Annulus with Constant Heat Flux at Outer Cylinder

2015 ◽  
Vol 85 (3) ◽  
pp. 373-384
Author(s):  
Rajendra Prasad ◽  
A. K. Singh
Keyword(s):  
Heat Flux ◽  
Temperature Gradient ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Constant Heat Flux ◽  
Narrow Gap ◽  
Radial Temperature Gradient ◽  
Constant Heat ◽  
Radial Temperature

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).

Experimental Study of Taylor-Couette Flow With Constant Radial Temperature Gradient

2009 ◽  
Author(s):  
Dong Liu ◽  
Seok-Hwan Choi ◽  
Sang-Hyuk Lee ◽  
Jung-Ho Lee ◽  
Hyoung-Bum Kim
Keyword(s):  
Temperature Gradient ◽  
Couette Flow ◽  
Flow Instability ◽  
Outer Cylinder ◽  
Taylor Vortex ◽  
Radial Temperature Gradient ◽  
Obvious Effect ◽  
Radial Temperature ◽  
Taylor Couette ◽  
Taylor Couette Flow

The flow between two concentric cylinders with the inner one rotating and with an imposed radial temperature gradient is studied using digital particle image velocimetry (DPIV) method. Four models of the outer cylinder without and with different numbers of slits (6, 9 and 18) are considered, and the radius ratio and aspect ratio of each models were 0.825 and 48, respectively. The flow regime in the Taylor-Couette flow was studied by increasing the Reynolds number. The results showed that smaller number of slits has no obvious effect on the transition process, which only change the shape of the vortex, and the transition to turbulent Taylor vortex is accelerated as the number of slit increases in both isothermal and non-isothermal conditions. It is also shown that the presence of temperature gradient increased the flow instability obviously as the Froude number larger than 0.0045.

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