Onset of thermal instability in a horizontal circular cylinder
Presentation of a method for determining when convective motions can be induced in confined regions. The problem is important in the design of fluid-flow and heat-transfer equipment. 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, horizontal, circular cylinder whose wall is nonuniformly heated. The temperature distribution on the wall is so specified that, in the quiescent state, a constant temperature gradient in the fluid is established in the direction of the body force. The governing perturbation equations form a self-adjoint eigenvalue problem for the critical Rayleigh number (stability criterion). Two different variational principles are presented, each equivalent to the eigenvalue problem. Using these principles, two approximate methods are developed for calculating upper bounds to the critical Rayleigh number. It is found that this number for the cylindrical configuration (based on a unit diameter) is about 3.8 times that for the horizontal configuration (based on a unit height). 33 pp. Bibliog.