Magnetohydrodynamic duct flow in a uniform transverse magnetic field of arbitrary orientation
- 28 July 1971
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 48 (3), 429-461
- https://doi.org/10.1017/s0022112071001691
Abstract
The paper presents an approximate analysis for high Hartmann number of the flow of an electrically conducting, incompressible fluid in a duct of square crosssection, having one pair of opposite walls insulating, and the other pair perfectly conducting and inclined at arbitrary orientation to a uniform transverse magnetic field. The flow is considered to be either pressure-driven with the two perfectly conducting electrodes short-circuited together or electrically driven by a potential difference applied between these electrodes in the absence of axial pressure gradient. The paper describes experiments on the pressure-driven, short circuited case using mercury in copper ducts to investigate the variation of the streamwise pressure gradient and of the potential distribution along one insulating wall with orientation, magnetic field and flow rate.At general orientations the analysis suggests and the experiments confirm the existence of regions of stationary fluid in the corners of the duct, together with viscous shear layers parallel to the magnetic field. For the case in which the electrodes are parallel to the magnetic field the experimental results for the pressure gradient, but not those for the potential distribution, agree reasonably well with Hunt & Stewartson's (1965) asymptotic solution. Both pressure gradient and potential results agree closely with the analysis by Hunt (1965) of the case in which the electrodes are perpendicular to the magnetic field.Keywords
This publication has 11 references indexed in Scilit:
- Some electrically driven flows in magnetohydrodynamics Part 3. The asymptotic theory for flow between circular electrodesJournal of Fluid Mechanics, 1969
- Hydromagnetic Duct Flow: Theory and ExperimentPhysics of Fluids, 1968
- Some electrically driven flows in magnetohydrodynamics Part 2. Theory and experimentJournal of Fluid Mechanics, 1968
- Steady electrically driven flowsMathematical Proceedings of the Cambridge Philosophical Society, 1968
- Some electrically driven flows in magnetohydrodynamics. Part 1. TheoryJournal of Fluid Mechanics, 1968
- Magnetohydrodynamic flow in rectangular ducts. IIJournal of Fluid Mechanics, 1965
- Magnetohydrodynamic flow in rectangular ductsJournal of Fluid Mechanics, 1965
- Steady longitudinal motion of a cylinder in a conducting fluidJournal of Fluid Mechanics, 1960
- The flow of conducting fluids in circular pipes under transverse magnetic fieldsJournal of Fluid Mechanics, 1956
- Steady motion of conducting fluids in pipes under transverse magnetic fieldsMathematical Proceedings of the Cambridge Philosophical Society, 1953