Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-18T15:30:12.605Z Has data issue: false hasContentIssue false
  • English
  • Français

Global stability of time-dependent flows: impulsively heated or cooled fluid layers

Published online by Cambridge University Press:  29 March 2006

G. M. Homsy
G. M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

The method of energy is used to discuss the stability of time-dependent diffusive temperature profiles in fluid layers subject to impulsive changes in surface temperature.

Bounds for the ratio of disturbance energy production to dissipation are found to be parametric functions of time because the basic temperature develops through diffusion. This time dependence leads to the demarcation of regions of stability in a Rayleigh number-time plane and the interpretation of these regions is given. Numerical results are presented for the cases of impulsive heating and cooling of initialty isothermal fluid layers. New global stability results which give the Rayleigh number below which the diffusive solution to the Boussinesq equations is unique are reported for these cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 1 , 21 August 1973 , pp. 129 - 139
Copyright
© 1973 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.
Chen, C. F. & Kirchner, R. P. 1971 J. Fluid Mech. 48, 365.
Conrad, P. W. & Criminale, W. O. 1965a Z. angew. Math. Phys. 16, 233.
Conrad, P. W. & Criminale, W. O. 1965b Z. angew. Math. Phys. 16, 569.
Currie, I. G. 1967 J. Fluid Mech. 29, 337.
Davenport, I. F. & King, C. J. 1972 The initiation of natural convection caused by time-dependent profiles. Lawrence Berkeley Lab. Rep. University of California, Berkeley, no. 660.Google Scholar
Davis, S. H. 1969 J. Fluid Mech. 39, 347.
Davis, S. H. 1971 J. Fluid Mech. 45, 33.
Davis, S. H. 1972 Quart. J. Mech. Appl. Math. 25, 459.
Foster, T. D. 1965 Phys. Fluids, 8, 1249.
Foster, T. D. 1968 Phys. Fluids, 11, 1257.
Gresho, P. M. & Sani, R. L. 1970 J. Fluid Mech. 40, 783.
Gresho, P. M. & Sani, R. L. 1971 Int. J. Mass. Trans. 14, 251.
Joseph, D. D. 1965 Arch. Rat. Mech. Anal. 20, 59.
Joseph, D. D. 1966 Arch. Rat. Mech. Anal. 22, 163.
Joseph, D. D. 1971 In Instability of Continuous Systems IUTAM Symp. Herrenalb 1969 (ed. H. Leipholz). Springer.
Joseph, D. D. & Shir, C. C. 1966 J. Fluid Mech. 26, 753.
Lick, W. 1965 J. Fluid Mech. 21, 565.
Mahler, E. G. & Schechter, R. S. 1970 Chem. Eng. Sci. 25, 955.
Mahler, E. G. Schechter, R. S. & Wissler, E. H. 1968 Phys. Fluids, 11, 1901.
Martin, R. S. & Wilkinson, J. H. 1968 Numer. Math. 11, 99.
Rosenblat, S. & Herbert, D. M. 1970 J. Fluid Mech. 43, 385.
Rosenblat, S. & Tanaka, G. A. 1971 Phys. Fluids, 14, 1319.
Venezian, G. 1969 J. Fluid Mech. 35, 243.
Yih, C.-S. 1968 J. Fluid Mech. 31, 737.
Yih, C.-S. & Li, C.-H. 1972 J. Fluid Mech. 54, 143.