Stability of hydromagnetic dissipative Couette flow with non-axisymmetric disturbance

1998 ◽  
Vol 366 ◽  
pp. 135-158 ◽  
Author(s):  
CHA'O-KUANG CHEN ◽  
MIN HSING CHANG
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Hartmann Number ◽  
Axial Magnetic Field ◽  
Outer Cylinder ◽  
Numerical Procedure ◽  
Stationary Mode ◽  
Instability Modes ◽  
Wide Range ◽  
Axisymmetric Instability

A linear stability analysis has been implemented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field. The small-gap equations with respect to non-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 wide ranges of μ, the ratio of angular velocity of the outer cylinder to that of inner cylinder, and Q, the Hartmann number which represents the strength of axial magnetic field, is conducted. Results show that the stability characteristics depend on the conductivity of the cylinders. For the case of non-conducting walls, it is found that the critical disturbance is a non-axisymmetric mode as the value of μ is sufficiently negative and the domain of Q where non-axisymmetric instability modes prevail is limited. Similar results are obtained for conducting walls at low Hartmann number. In addition, the transition of the onset of instability from non-axisymmetric modes to axisymmetric modes for the case μ=−1 with increasing strength of magnetic field are discussed in detail. For high values of the Hartmann number, the critical disturbance is always the axisymmetric stationary mode for non-conducting walls but not for conducting walls. For −1[les ]μ<1, it is demonstrated that non-axisymmetric instability modes prevail in a wide range of Q for conducting walls and axisymmetric oscillatory modes may, in fact, become more critical than both of the non-axisymmetric and axisymmetric stationary modes at higher values of the Hartmann number.

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.

Second Law Analysis of Magnetorheological Rotational Flow With Viscous Dissipation

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Abbas Hazbavi
Keyword(s):  
Magnetic Field ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Outer Cylinder ◽  
Base Flow ◽  
Convection Flow ◽  
Fluid Temperature ◽  
Brinkman Number ◽  
Fluid Elasticity

In this study, the influences of the applied magnetic field and fluid elasticity were investigated for a nonlinear viscoelastic fluid obeying the Carreau equation between concentric annulus where the inner cylinder rotates at a constant angular velocity and the outer cylinder is stationary. The governing motion and energy balance equations are coupled while viscous dissipation is taken into account, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, the Deborah number, and the fluid elasticity on the stability of the flow were investigated. The application of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slowdown the fluid motion and thus increases the fluid temperature. However, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and it increases with increasing Brinkman number.

Numerical Study of Magnetic Field Influence on Three-Dimensional Flow Regime and Combined-Convection Heat Exchange Within Concentric and Eccentric Rotating Cylinders

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Javad Sodagar-Abardeh ◽  
Payam Nasery ◽  
Ahmad Arabkoohsar ◽  
Mahmood Farzaneh-Gord
Keyword(s):  
Magnetic Field ◽  
Heat Exchange ◽  
Flow Regime ◽  
Axial Magnetic Field ◽  
Numerical Study ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Convection Heat ◽  
Combined Convection ◽  
Number Variation

Abstract The forced and natural flows of fluid within an annulus caused by the rotation of cylinders and temperature differences of the inner and outer walls are observed in various engineering applications. In this research, the laminar flow regime and mixed convection inside a ring-shaped horizontal concentric and eccentric space for an incompressible fluid are studied in the existence of an axial magnetic field. The present work is the first effort to investigate the influence of a magnetic field on flow and combined-convection heat exchange characteristics within an annulus with a cold outer cylinder and an inner hot cylinder. Here, the properties of the flow and heat transfer characteristics are studied using the finite volume method. Numerical procedures are mainly investigated for recognizing the influence of Hartmann number (in the range of 0 ≤ Ha ≤ 100), as the representative of the magnetic force, on velocity components, Nusselt number, streamlines, and isothermal lines. One of the notable effects is that when Ha number increases, it will reduce the vorticity of the fluid and buoyancy forces. As a result, streamlines and isothermal lines can be seen more constant as regular concentric circles. A rise in Ha number decreases the range of local Nu number variation for both cylinders. The average Nu number for the outer and inner cylinders has different trends when Ha number increases. Taking concentric cylinders as an example, this parameter for the inner and the outer cylinders increases and decreases by about 1.2 and 1.6, respectively.

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.

scholarly journals Spin-Up from Rest of a Liquid Metal with Deformable Free Surface in a Cylinder under the Influence of a Uniform Axial Magnetic Field

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 438
Author(s):  
Toshio Tagawa ◽  
Kewei Song
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Liquid Metal ◽  
Hartmann Number ◽  
Viscosity Ratio ◽  
Axial Magnetic Field ◽  
Density Ratio ◽  
Striking Difference ◽  
Gas Phases ◽  
Component Velocity

Spin-up from rest of a liquid metal having deformable free surface in the presence of a uniform axial magnetic field is numerically studied. Both liquid and gas phases in a vertically mounted cylinder are assumed to be an incompressible, immiscible, Newtonian fluid. Since the viscous dissipation and the Joule heating are neglected, thermal convection due to buoyancy and thermocapillary effects is not taken into account. The effects of Ekman number and Hartmann number were computed with fixing the Froude number of 1.5, the density ratio of 800, and the viscosity ratio of 50. The evolutions of the free surface, three-component velocity field, and electric current density are portrayed using the level-set method and HSMAC method. When a uniform axial magnetic field is imposed, the azimuthal momentum is transferred from the rotating bottom wall to the core region directly through the Hartmann layer. This is the most striking difference from spin-up of the nonmagnetic case.

scholarly journals Axial Magnetic Field Effect on Taylor-Couette Flow

2015 ◽  
Vol 8 (2) ◽  
pp. 255-264
Author(s):  
Sofiane ABERKANE ◽  
IHDENE malika ◽  
mouderes mourad ◽  
A. Ghezal ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Field Effect ◽  
Axial Magnetic Field ◽  
Magnetic Field Effect ◽  
Taylor Couette ◽  
Taylor Couette Flow

Control of Thermo Magnetic Heat Transfer in Porous Cavity With Baffle(s)

2009 ◽  
Author(s):  
H. Heidary ◽  
M. Davoudi ◽  
M. Pirmohammadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Hartmann Number ◽  
Numerical Procedure ◽  
Simple Algorithm ◽  
Convection Flow ◽  
Central Difference ◽  
Diffusion Term ◽  
Left Wall ◽  
Porous Cavity

Steady, laminar, natural-convection flow in the presence of a magnetic field in a porous cavity heated from left wall sinusoidally and cooled from right wall is considered. It is well known that unavoidable hydrodynamic movements can be damped with the help of a magnetic field. The Finite Volume method and SIMPLE algorithm for discretizing is used to solve the non-dimensional governing equations. The Convection and Diffusion term of the equations are discretized by Central Difference Scheme (CDS). The numerical procedure has been done over a range of Rayleigh number, Ra, and value of Hartmann number (Ha), 0 ≤ Ha ≤ 150 and effect of them is investigated on average and local Nusselt number. Effect of position and length of baffle in cavity in different models is studied in this paper. It is shown that as the value of Hartmann number (Ha) increases and with growth of baffle length, the convection heat transfer reduces. Also position and numbers of baffle play an important role in control of heat transfer.

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