THE THERMAL STABILITY OF COMPLETELY CONFINED FLUIDS INCLUDING MAGNETOHYDRODYNAMIC EFFECTS.
CASE INST OF TECH CLEVELAND OHIO FLUID THERMAL AND AEROSPACE SCIENCES
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The current research concerns the determination of the conditions needed to induce a state of convective motion in a fluid where a constant temperature gradient is directed parallel to a body force. The fluid is contained in a rather arbitrary region bounded by rigid walls. The principle of exchange of stability is established for arbitrary regions with a generalized thermal boundary condition on the bounding walls. The thermal stability problem is reduced to an eigenvalue problem for the critical Rayleigh number the stability criterion and then is reformulated as a variational principle. A method is developed for estimating upper and lower bounds to the critical Rayleigh number for regions in which the critical Rayleigh number cannot be calculated exactly. An extension of the thermal stability problem to include magnetohydrodynamic effects is presented. Here the fluid and the bounding walls are electrical conductors. A constant magnetic field is applied to the configuration. Author