Thermal Instability in a Spherical Region Heated from Below.

by Mark Steven Sherman, I. Catton

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An extension of the classical Rayleigh thermal stability problem of an infinite horizontal fluid layer heated from below to the case of a fluid confined within a rigid sphere whose wall is nonuniformly heated. The temperature distribution on the wall is specified so that a constant temperature gradient is established in the direction of the body force acting on the fluid. Two different variational principles are presented, each equivalent to the eigenvalue problem for the critical Rayleigh number (the stability criterion). These principles form the basis for two approximate methods of determining upper bounds to the critical Rayleigh number. The critical Rayleigh number obtained is 16,132 (based on a unit diameter), which is almost ten times greater than that of the horizontal-layer configuration (based on unit height). The results are found to be 10 percent lower than those of a previously published analysis. 23 pp.

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