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The Quarterly Journal of Mechanics and Applied Mathematics 1980 33(1):93-103; doi:10.1093/qjmam/33.1.93
© 1980 by Oxford University Press
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ELECTROHYDRODYNAMIC INSTABILITY IN A DIELECTRIC FLUID BETWEEN TWO COAXIAL CYLINDERS

M. TAKASHIMA

( Department of Physics, Faculty of Science, Osaka City University Osaka, Japan )

Linear stability theory is applied to the problem of the onset of convective instability in a layer of dielectric fluid confined between two vertical coaxial cylinders under the simultaneous action of a radial ac electric field and a radial temperature gradient. Applying approximations analogous to the usual Boussinesq approximations, an equation of eighth order and the relevant boundary conditions are derived. After neglecting terms of the second and higher orders in {lambda}, the method of power series expansion is used to obtain the eigenvalue relationship which is then computed numerically, where {lambda} = (r2–r1)/r1, r1 and r2 being the radii of the inner and the outer cylinders respectively. It is shown that (1) when the temperature of the inner cylinder is higher than that of the outer cylinder, the fluid layer becomes more unstable as {lambda} increases; (2) when the temperature of the outer cylinder is higher than that of the inner cylinder, the fluid layer becomes more stable as {lambda} increases and becomes completely stable when {lambda} exceeds some finite value.


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