Accession Number : AD0646621

Title :   THERMAL INSTABILITY IN A SPHERICAL REGION HEATED FROM BELOW,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Sherman,Michael ; Catton,Ivan

Report Date : JAN 1967

Pagination or Media Count : 24

Abstract : The classical Rayleigh thermal stability problem of an infinite horizontal fluid layer heated from below is extended 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 ('heated from below'). 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 a unit height). The results are compared with a previously published analysis and are found to be 10 percent lower. (Author)

Descriptors :   (*THERMAL PROPERTIES, STABILITY), (*FLUIDS, THERMAL PROPERTIES), HEATING, SPHERES, WALLS, APPROXIMATION(MATHEMATICS)

Subject Categories : Thermodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE