Parabolic, cubic, and higher order expressions have been used in previous investigations to relate temperature to density in the vicinity of the density extremum. Another equation of state, based on the careful measurement of the density variations of both pure and saline water, has been used here to determine the onset of convection in a horizontally confined layer of water near its density extremum. The simplicity of this equation gives rise to a minimum number of problem particular parameters, and relatively easily allows for the inclusion of both pressure and salinity level effects (neglecting saline diffusion). The boundaries are considered to be rigid-rigid and of infinite thermal capacity. Present numerical results are compared with those previously calculated using other density relationships, including that embodied in the linear Oberbeck-Boussinesq approximation. Density extremum effects are seen to be stabilizing, with critical Rayleigh numbers calculated to be about 10 percent below those obtained using a parabolic density-temperature relationship and quite close to those found using a fifth-order polynomial. There is an associated increase in calculated wave number with the inclusion of density extremum effects.
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Onset of Convection in a Horizontal Layer of Cold Water
J. C. Mollendorf,
J. C. Mollendorf
Mechanical and Aerospace Engineering, State University of New York at Buffalo, Amherst, N.Y. 14260
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K. H. Jahn
K. H. Jahn
Dupont/Sorvall, Newton, Conn. 06470
Search for other works by this author on:
J. C. Mollendorf
Mechanical and Aerospace Engineering, State University of New York at Buffalo, Amherst, N.Y. 14260
K. H. Jahn
Dupont/Sorvall, Newton, Conn. 06470
J. Heat Transfer. Aug 1983, 105(3): 460-464 (5 pages)
Published Online: August 1, 1983
Article history
Received:
October 25, 1982
Online:
October 20, 2009
Citation
Mollendorf, J. C., and Jahn, K. H. (August 1, 1983). "Onset of Convection in a Horizontal Layer of Cold Water." ASME. J. Heat Transfer. August 1983; 105(3): 460–464. https://doi.org/10.1115/1.3245607
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