New Releases by Michael Sherman

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).

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 specified such 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 (the 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 the critical Rayleigh number for the cylindrical configuration (based on a unit diameter) is about 3.8 times that for the horizontal-layer configuration (based on a unit height). The value for the cylinder is considerably lower than values calculated in previous analyses. (Author).

A consideration of the possibility of inducing a convective secondary flow in the fully developed channel flow of a quasi-incompressible (Boussinesq) fluid. Instabilities of this type occur only when the temperature gradient in the direction of the body force exceeds a certain critical value. This temperature gradient is proportional to the Rayleigh number of the fluid. 12 pp. (Author).

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).