Cover: Thermal Instability in a Spherical Region Heated from Below.

Thermal Instability in a Spherical Region Heated from Below.

Published 1967

by Mark Steven Sherman, I. Catton

Purchase Print Copy

 Format Price
Add to Cart Paperback23 pages $20.00

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.

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.