Cover: Onset of thermal instability in a horizontal circular cylinder

Onset of thermal instability in a horizontal circular cylinder

Published 1966

by Michael Sherman

Purchase Print Copy

 Format Price
Add to Cart Paperback33 pages $20.00

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.

This report is part of the RAND research memorandum series. The Research Memorandum was a product of RAND from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

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.