Showing papers on "Hartmann number published in 1975"

Overstable hydromagnetic convection in a rotating fluid layer

Abstract: The effect of the simultaneous action of a uniform magnetic field and a uniform angular velocity on the linear stability of the Benard layer to time-dependent convective motions is examined in the Boussinesq approximation. Four models, characterized by the relative directions of the magnetic field, angular velocity and gravitational force, are discussed under a variety of boundary conditions. Apart from a few cases, the treatment applies when the Taylor number T and the Chandrasekhar number Q (the square of the Hartmann number) are large. (These parameters are dimensionless measures of angular velocity and magnetic field, respectively.)It is shown that the motions at the onset of instability can be of three types. If the Coriolis forces dominate the Lorentz forces, the results for the rotating non-magnetic case are retained to leading order. If the Coriolis and Lorentz forces are comparable, the minimum temperature gradient required for instability is greatly reduced. Also, in this case, the motions that ensue at marginal stability are necessarily three-dimensional and the Taylor-Proudman theorem and its analogue in hydromagnetics are no longer valid. When the Lorentz forces dominate the Coriolis forces, the results obtained are similar to those for the magnetic non-rotating case at leading order.The most unstable mode is identified for all relations T = KQα, where K and α are positive constants, taking into account both time-dependent and time-independent motionsVarious types of boundary layers developing on different boundaries are also examined.

Combined influence of Hall effect, ion slip, viscous dissipation and Joule heating on MHD heat transfer in a channel

Abstract: To investigate the combined influence of Hall effect, ion slip, viscous dissipation and Joule heating on the fully developed laminar MHD channel heat transfer, the exact solution of the energy equation is derived assuming a constant wall heat flux, finely segmented electrodes and a small magnetic Reynolds number. It is concluded that there can be a substantial difference, depending upon Hartmann number, electric field intensity and Brinkman number, between the Nusselt number considering the Hall effect and that neglecting it. Representative results are presented in diagrams and in tables.

Some duct flow problems at high Hartmann number

Abstract: Fully-developed magnetohydrodynamic duct flow under a uniform transverse field at high Hartmann numberM is generally well understood, but the case where the duct has two plane, highly-conducting electrodes parallel to the magnetic field, connected by an external conductor of negligible resistance, and two arbitrarily-shaped, insulating walls intersecting the magnetic field shows unusual features. The flow is remarkably sensitive to whether the field line lengthh within the duct varies or not; velocities suddenly change by a factor of orderM as this condition is changed. Ifh varies there are regions of high forwards and backwards flow, whereas ifh is constant the velocities are smaller but can vary in an even more complicated way, with forwards and backwards flow at much higher speeds in the boundary layers on the electrodes. A major novelty in comparison with other high-M duct flows is that the main flow cannot be solved without a scrutiny of these boundary layers. Another novelty is that significant vorticity normal to the imposed field persists. This situation is compared with other duct flows in which such vorticity persists. The stability of the very distorted velocity profiles is not examined.

Combined influence of wall conductance, pressure work, viscous dissipation and joule heating on MHD channel flow heat transfer

Abstract: To investigate the combined influence of viscous dissipation, pressure work, Joule heating, arbitrary voltage ratio, unequal wall conductances and wall heat fluxes on the fully developed laminar MHD channel flow heat transfer, the exact solution of the energy equations for fluid and channel walls are derived assuming the Hartmann velocity profile. It is concluded that there can be a substantial difference, depending upon Hartmann number, electric field and Brinkman number, between the Nusselt number considering the wall conductance and that neglecting it. Representative results are presented in diagrams.