A normal magnetic field has a destabilizing influence on a flat interface between a magnetizable and a non-magnetic fluid. Stabilizing influences are provided by interfacial tension and gravity if the lighter fluid is uppermost. The critical level of magnetization for onset of the instability is derived for a fluid having a non-linear relation between magnetization and magnetic induction. Experiments using a magnetizable fluid, which contains a colloidal suspension of ferromagnetic particles, at interfaces with air and water are made and cover a wide range of density differences. Measurements confirm the prediction for critical magnetization, and it was found that, after onset, the interface took a new form in which the elevation had a regular hexagonal pattern. The pattern was highly stable, and the measured spacing of peaks agreed reasonably with that derived from the critical wave-number for the instability of a flat interface.
The equations of continuity, momentum and energy are derived for axisymmetric electric arcs in terms of overall radial integrals. The external flow is assumed to be adiabatic, reversible and one-dimensional, although compressibility and the possibility of time variation are included. The overall integrals define quantities with the dimensions of area when their integrands are normalized. Arc problems can then be solved in principle if relations between the area quantities can be guessed or found empirically, and a formal structure for such empiricism is suggested. It is shown that the enthalpy-flow model of Frost and Liebermann (1971) is equivalent to an integral method at a low level of approximation. The analyses of Topham (1971, 1972a, b) are related to the present general formulation.
Two problems are considered in the present paper as examples of the integral method formulated in part I (the preceding paper). The first concerns arcs in uniform flow, and it is shown that the only form of steady solution, if the conductance shape factor is taken to be a function of power level, is the fully developed arc. A known solution of the full differential equations provides a test of the adequacy of the result. Free recovery is briefly discussed. The second problem concerns steady arcs in nozzles. With the assumptions of constant shape factors and negligible radiation, a simple model is derived which provides insight into behaviour as a nozzle-blocking condition is approached.
In this paper, an experimental study of laminar magnetohydrodynamic (MHD) buoyancy-driven flow in a cylindrical cell with axis horizontal is described. A steady uniform magnetic field is applied vertically to the mercury-filled cell, which is also subjected to a horizontal temperature gradient. The main features of this internal MHD thermogravitational flow are made experimentally evident from temperature and electric potential measurements. Whatever the level of convection, raising the Hartmann number Ha to a value of the order of 10 is sufficient to stabilize an initially turbulent flow. At much higher values of the Hartmann number (Ha∼100) the MHD effects cause a change of regime from boundary-layer driven to core driven. In this latter regime an inviscid inertialess MHD core flow is bounded by a Hartmann layer on the horizontal cylindrical wall and viscous layers on the endwalls. Since the Hartmann layer is found to stay electrically inactive along the cell, the relevant asymptotic (Ha[Gt ]1) laws for velocity and heat transfer are found from the balance between the curl of buoyancy and Lorentz forces in the core, together with the condition that the flow of electric current between core and Hartmann layer is negligible. A modified Rayleigh number RaG/Ha2, which is a measure of the ratio of thermal convection to diffusion when there is a balance between buoyancy and Lorentz forces, is the determining parameter for the flow.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.