The Effect of Nonlinear Density Stratification on the Stability of a Vertical Water Layer in the Conduction Regime

[+] Author and Article Information
A. H. Shaaban, M. N. Özişik

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, N. C. 27650

J. Heat Transfer 105(1), 130-137 (Feb 01, 1983) (8 pages) doi:10.1115/1.3245531 History: Received March 01, 1982; Online October 20, 2009


The thermal stability of a layer of water between two vertical parallel plates maintained at different temperatures, T1 and T2 , is investigated for the conduction regime. Three cases are considered include where: (a) the maximum density layer is within the water region; (b) is at the boundary; and (c) is outside the water region. Cubic polynomials are used to represent the density-temperature relation in the temperature range 0–55°C. The numerical results show that the critical states of stability do not depend on Prandtl number but instead depends on the combinations of T1 and T2 . Of the three cases considered, the first case is the most unstable. In all three cases, the instabilities set in as a traveling wave, moving against gravity, for most T1 and T2 combinations. Stationary waves were also found for case (c).

Copyright © 1983 by ASME
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