Showing papers on "Hartmann number published in 1977"

Combined effects of free and forced convection on magnetohydrodynamic flow in a rotating channel

Abstract: The steady flow in a channel rotating with an angular velocity\(\vec \Omega \) and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains three parameters: the Grash of number,G, the Hartmann number,M 2 and the rotation parameter,K 2. The effects of these parameters on the velocity and magnetic field distributions are studied. For large values ofK 2 andM 2, there arise thin boundary layers on the walls of the channel which may be identified as the Ekman-Hartmann layers.

Stationary convective-like modes in a plasma slab with magnetic shear

Abstract: The combined effects of resistivity and viscosity on a magnetohydrodynamically unstable plasma slab are shown to be responsible for the existence of a stationary (marginal) mode. This mode gives rise to plasma convection in a shear‐free situation when nonlinear effects are taken into account. In the case of a sheared magnetic field, it still extends over the entire width of the slab and is driven by what would be an interchange localized about the resonant (k⋅B(0)=0) surface in the absence of dissipation. The critical value of the plasma analog of the Rayleigh number in hydrodynamics is calculated as a function of shear, mode wavenumber, and dissipation (represented by the square of the Hartmann number).

Boundary-value problem for plasma centrifuge at arbitrary magnetic Reynolds numbers

Abstract: We solve in closed form the boundary-value problem for the partial differential equations which describe the (azimuthal) rotation velocity and induced magnetic fields in a cylindrical plasma centrifuge with ring electrodes of different radii and an external, axial magnetic field. The electric field, current density, and velocity distributions are discussed in terms of the Hartmann number H and the magnetic Reynolds number R. For small Hall coefficients, the induced magnetic field does not affect the plasma rotation. As a result of the Lorentz forces, the plasma rotates with speeds as high as 100,000 cm/sec around its axis of symmetry at typical conditions, so that the lighter (heavier) ion and atom components are enriched at (off) the center of the discharge cylinder.

Stability of MHD Viscous Flow in a Curved Channel

Abstract: The purpose of this paper is to consider by the method of small perturbations how an external magnetic field suppresses the onset of a secondary vortex flow in a two-dimensional, incompressible, electrically conducting viscous flow in a curved channel. The magnetic field is applied in the direction perpendicular to the channel walls. The results show: (1) the critical Dean number KC begins to increase as the Hartmann number Ha becomes larger than about 2, and in the limit Ha → ∞ the Dean number KC tends to a relation proportinal to Ha3/2; (2) the associated dimensionless wavenumber σC of the vortices also increases with Ha, and the location of the vortex center comes closer to the outer concave wall. In addition the effect of electrical conductivity of the wall material on the present stability problem is discussed.

Effects of mass transfer on free convective flow of an electrically conducting, viscous fluid past an infinite porous plate with constant suction and transversely applied magnetic field

Abstract: An analysis of the mass transfer effects on the free convective flow of an incompressible, electrically conducting, viscous fluid past an infinite porous plate with constant suction and transverse magnetic field, has been carried out. Approximate solutions to coupled non-linear equations governing the flow are derived. The velocity and the temperature fields are shown graphically. The effects ofG t (Grashof number),G c (modified Grashof number),S c (Schmidt number),E(Eckert number),P(Prandtl number) andM(the Hartmann number) on the flow field are described during the course of discussion.

On the dispersion of a dye with a harmonically varying concentration in the hydromagnetic flow in a channel

Abstract: An analysis of the dispersion of a dye with a harmonically varying concentration in a magnetohydrodynamic channel flow has been carried out. An estimate is obtained for the axial distance along which the fluctuations in concentration decay in the case of low‐frequency input. It is observed that the decay distance for the fluctuations in concentration increases with an increase in the Hartmann number M.

The Current-content of Hartmann Layers

Abstract: This paper considers two questions: whether the disadvantageous short-circuiting effect of Hartmann layers in non-conducting ducts can be reduced by having streamwise insulating fins, corrugations, etc., to impede the current flow; and how the classical relation between current-content and velocity jump is modified by non-uniformity of the fluid properties, e.g., in plasmas or alloys near solidification.

Linearized analysis of magnetohydrodynamic entrance flow in a vertical channel with combined thermal convection

Abstract: A linearized analysis is presented for the magnetohydrodynamic entrance flow with combined forced and free convection in a vertical, constant wall temperature parallel-plate channel. Numerical results are obtained for slug velocity profile at the entrance and for various Hartmann and Grashof Numbers. The results agree well with the finite difference numerical solutions obtained elsewhere. They demonstrate that the velocity development and pressure gradient in the channel entrance region are greatly influenced by the Hartmann Number and the Grashof Number. Increasing Hartmann Number decreases velocity entrance length while increasing Grashof Number increases it. Thermal development is also found to be dependent on the above mentioned parameters, but to a relatively minor extent.

Heat transfer by magnetohydrodynamic laminar flow in circular pipe

Abstract: This paper presents the influence of magnetic field on heat due to viscous and electrical dissipations for an incompressible, viscous, electrically conducting fluid through a circular pipe in the presence of an applied (transverse) uniform magnetic field. The walls of the pipe are assumed to be non-conducting and kept at uniform temperature gradient in one case and at a constant temperature gradient in another case. The heat equation governing the present problem is solved exactly in hypergeometric series. The temperature at the centre of the pipe Te, unweighted mean temperature Tm and weight mean temperature TM are calculated. The temperature profiles are shown graphically for different values of Hartmann number M, Brinkman number Br and a non-dimensional number S. Numerical calculations are made for the Nusselt number and are entered in the table.

Two-phase Hartmann flows in the MHD generator configuration. Annual report, December 1975--December 1976. [Two-phase liquid metal flow]

Abstract: Two-phase Hartmann flows in an MHD generator duct of rectangular cross-section are examined and numerical values for the velocity fields and induced current streamlines for fluids of spatially-dependent electrical conductivity are determined as a function of load factor, Hartmann number and channel aspect ratio This study is of considerable practical interest in connection with some experimental work on two phase liquid metal-gas MHD generators and the results presented herein may enhance the understanding of the operating characteristics of such devices Results indicate that conductivity gradients can produce inflected velocity profiles which may be hydrodynamically unstable, that for larger load factors the shunt current in the Hartmann boundary layers become considerable and that two-phase MHD flows of moderate void fractions have sound speeds considerably lower than in its components Turbulent effects are not considered in these studies since turbulent fluctuations are expected to be suppressed for the high Hartmann number flows of interest in two-phase MHD generators

Effect of sudden suction on the hydromagnetic natural convection from a vertical plate

Abstract: The effects of step function change in suction velocity are investigated for a natural convection flow from a vertical porous flat plate of infinite length in the presence of transverse magnetic field for two cases namely (i) when the plate is suddenly raised to a uniform higher temperature, (ii) when the plate suddenly begins to generate a uniform heat flux at its surface In (i) the coefficient of heat transfer becomes independent of the Hartmann numberM In either case for a fixed time t except for correct steady state t→ ∞, the effect of the Hartmann number is to decrease both the velocity of the fluid and the skin-friction at the plate In the correct steady state the velocity field and the skin-fiiction become independent of the Hartmann number