Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-18T20:38:49.270Z Has data issue: false hasContentIssue false
  • English
  • Français

The onset of convection in fluid layers heated rapidly in a time-dependent manner

Published online by Cambridge University Press:  20 April 2006

Bharat S. Jhaveri  and
G. M. Homsy
Bharat S. Jhaveri
Affiliation:
Department of Chemical Engineering, Stanford University, California 94305 Current address: Department of Physics, University of Utah, Salt Lake City, Utah.
G. M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

We treat the onset of convective motions for the case in which the base-state density profile is evolving in time. The formulation is in terms of random forcing which we take to be thermodynamic in origin, following our earlier work (see Jhaveri & Homsy 1980). Experimental evidence is reviewed which clearly demonstrates the need for such a stochastic formulation. The randomly forced initial-value problem is solved numerically at high Rayleigh numbers in the mean-field approximation for both a step change and linear temporal increase in surface temperature. The numerical results give both an expected value for the onset time for which convection is measurable and the variance of that expected value. The results are in good agreement with available experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 251 - 260
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Blair, L. M. & Quinn, J. A. 1969 J. Fluid Mech. 36, 385.
Currie, I. G. 1967 J. Fluid Mech. 29, 337.
Davenport, I. F. 1972 The initiation of natural convection by time-dependent profiles. Ph.D. thesis, University of California, Berkeley, California.
Davenport, I. F. & King, J. C. 1974 Int. J. Heat Mass Transfer 17, 77.
Foster, T. D. 1965 Phys. Fluids 8, 1249.
Foster, T. D. 1968 Phys. Fluids 11, 1257.
Gough, D. O., Spiegel, E. A. & Toomre, J. 1975 J. Fluid Mech. 68, 695.
Gresho, P. M. & Sani, R. L. 1971 Int. J. Heat Mass Transfer 14, 207.
Gumerman, R. J. & Homsy, G. M. 1975 J. Fluid Mech. 68, 191.
Homsy, G. M. 1973 J. Fluid Mech. 60, 129.
Jhaveri, B. S. 1979 Rayleigh — Bénard Convection from Thermodynamic Fluctuations. Ph.D. thesis, Stanford University, Stanford, California.
Jhaveri, B. & Homsy, G. M. 1980 J. Fluid Mech. 98, 329.
Lick, W. 1965 J. Fluid Mech. 21, 565.
Mahler, E. G., Schechter, R. S. & Wissler, E. H. 1968 Phys. Fluids 11, 1901.
Mahler, E. G. & Schechter, R. S. 1970 Chem. Engng Sci. 25, 955.
Orszag, S. A. 1971 Stud. Appl. Math. 4, 293.
Spangenberg, W. G. & Rowland, W. R. 1961 Phys. Fluids 4, 743.
Wankat, P. C. & Homsy, G. M. 1977 Phys. Fluids 20, 1200.