Showing papers on "Hartmann number published in 1982"

Convective dynamos with intermediate and strong fields

Abstract: The weak-field Benard-type dynamo treated by Soward is considered here at higher levels of the induced magnetic field. Two sources of instability are found to occur in the intermediate field regime M ∼ T 1/12, where M and T are the Hartmann and Taylor numbers. On the time scale of magnetic diffusion, solutions may blow up in finite time owing to destabilization of the convection by the magnetic field. On a faster time scale a dynamic instability related to MAC-wave instability can also occur. It is therefore concluded that the asymptotic structure of this dynamo is unstable to virtual increases in the magnetic field energy. In an attempt to model stabilization of the dynamo in a strong-field regime we consider two approximations. In the first, a truncated expansion in three-dimensional plane waves is studied numerically. A second approach utilizes an ad hoc set of ordinary differential equations which contains many of the features of convection dynamos at all field energies. Both of these models ...

Combined effect of free and forced convection on MHD flow in a rotating porous channel

Abstract: This paper gives a steady linear theory of the combined effect of the free and forced convection in rotating hydromagnetic viscous fluid flows in a por- ous channel under the action of a uniform magnetic field. The flow is governed by the Grashof number G, the Hartmann number H, the Ekman number E, and the suction Reynolds number S. The solutions for the velocity field, temperature distribution, magnetic field, mass rate of flow and the shear stresses on the channel boundaries are obtained using a perturbation method with the small parameter S. The nature of the associated boundary layers is investigated for various values of the governing flow parameters. The velocity, the temperature, and the shear stresses are dis- cussed numerically by drawing profiles with reference to the variations in the flow

On Combined Effects of Coriolis Force and Hall Current on Steady MHD Couette Flow and Hear Transfer

Abstract: The effects of Hall current on Couette flow and heat transfer of a conducting fluid between two plates in a rotating system are discussed. Both Hall and rotation parameters introduce secondary velocity and secondary induced magnetic field. The resultant shear stress and heat transfer from the moving plate has been calculated assuming it to be non-conducting and taking the fixed plate to be infinitely conducting. The resultant shear stress increases with increase in Hartmann number as well as rotation parameter while it decreases with increase in Hall parameter. The role of each parameter on heat transfer is always opposite to its role on shear stress. In the absence of Hall current this opposing character remains unalterned even if direction of rotation is reversed.

A dynamic runaway effect associated with flux expulsion in magnetohydrodynamic channel flow

Abstract: Pressure-driven flow along a channel in the presence of an applied magnetic field which is periodic in the streamwise direction is considered. The configuration is such that the transverse component of field By, is non-zero on the centreline y = 0, but its streamwise average 〈By〉 is zero. In this situation, flux expulsion due to reconnection of field lines occurs when the pressure gradient is sufficiently large. This leads to a decrease in the Lorentz forces, hence to an acceleration of the flow, and hence to stronger flux expulsion. When viscous effects are weak (i.e. at high Hartmann number) this creates a runaway effect, which appears at a critical value of the pressure gradient. This critical value is determined in the inviscid limit, and numerical and analytical methods are used to explore the associated ‘cusp-catastrophe’ behaviour when effects of weak viscosity are taken into account.

Stability of flow of films of a conducting viscous liquid in longitudinal magnetic field

Abstract: The critical Reynolds number is computed for the laminar flow of an incompressible viscous liquid metal thin film. (AIP)

MHD oscillatory flow with heat transfer in a flat plate channel

Abstract: An analysis of the oscillatory MHD channel flow of an electrically conducting, viscous, incompressible fluid under a transverse magnetic field is presented. The transient velocity and the transient temperature are exhibited graphically, whereas the numerical values of the amplitude, phase of the skin-friction and the first and second harmonics of the rate of heat transfer are displayed in tabular form. Also discussed are the effects of M (the Hartmann number), e (the loading parameter), ω* (the frequency), and E (the Eckert number).

An application of the method of multiple scales to magnetohydrodynamic flow

Abstract: In this paper we study the flow of an incompressible conducting fluid along an elliptic duct imposed in an uniform magnetic field. In case Hartmann number of the flow is sufficiently large, the method of multiple scales is adopted for constructing the asymptotic approximation of solution up to any order. Our method can also be applied to study the magnetohydrodynamic flow along any duct whose cross section has smooth boundary.