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Title: Deformation of free surface in magnetohydrodynamic flows in a strong magnetic field
Author: Cox, I. D.
ISNI:       0000 0001 3392 8428
Awarding Body: Coventry University
Current Institution: Coventry University
Date of Award: 2007
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Thermocapillary motion is considered in an electrically conducting fluid with a free and open surface, and in the presence of a strong vertical magnetic field. The motion is considered initially without specifying the geometry of the fluid. Any walls are electrically insulating. Applications are discussed, for situations such as crystal growth, where thermocapillary motion affects the distribution of dopants, or the use of liquid metal in fusion reactors, where heat and magnetic field are both very large causing potentially significant thermocapillary motions. An inertialess approximation is made, and the characteristic velocity of the fluid is selected so that the surface tension forces governing the thermocapillary motion are as significant as the Lorentz force. Asymptotic solutions are obtained for high values of the Hartmann Number Ha in both the two dimensional and three dimensional cases. The equation of the free surface is found for two dimensional flow in a cavity for various arbitrary temperature distributions. This and the pressure within the fluid is found to be dependent on the dynamic boundary conditions at the surface. The equations governing the free surface of a rivulet flowing in a strong vertical magnetic . field are similar to those obtained using the lubrication approximation for the rivulet where there is no magnetic field. . In the three dimensional case the fluid velocity in the core may be an order higher in Ha than in the two dimensional case. This higher velocity is induced by a ,(relatively) large electric potential, and is two dimensional horizontal flow following .the Contours of the free surface, superimposed on a slower three dimensional flow. 'fhelatter flow returns the fluid back to the free surface to supply the thermocapillary motion The condition for the higher order flow is that vertical cnrrent flow in the core is non-zero, and that this current flow enters and leaves the Hartmann layer that is adjacent to the fluid surface. Jf the heating is synuuetric in the two horizontal coordinate directions, the Hartmann layer is passive, and the vertical current is zero. Flow in the core is slow, and there is a radial flow to supply the thermocapillory motion at the free surface. Electric current lines are in concentric horizontal circles.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available