Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-18T23:10:58.526Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of mixed-convection flow in a tall vertical channel under non-boussinesq conditions

Published online by Cambridge University Press:  26 April 2006

Sergey A. Suslov  and
Samuel Paolucci
Sergey A. Suslov
Affiliation:
Department of Aerospace and Mechanical Engineering University of Notre Dame, Notre Dame, IN 46556, USA
Samuel Paolucci
Affiliation:
Department of Aerospace and Mechanical Engineering University of Notre Dame, Notre Dame, IN 46556, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We have examined the linear stability of the fully developed mixed-convection flow in a differentially heated tall vertical channel under non-Boussinesq conditions. The Three-dimensional analysis of the stability problem was reduced to an equivalent two-dimensional one by the use of Squire's transformation. The resulting eigenvalue problem was solved using an integral Chebyshev pseudo-spectral method. Although Squire's theorem cannot be proved analytically, two-dimensional disturbances are found to be the most unstable in all cases. The influence of the non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Grashof and Reynolds numbers on the temperature difference. The results show that four different modes of instability are possible, two of which are new and due entirely to non-Boussinesq effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 302 , 10 November 1995 , pp. 91 - 115
Copyright
© 1995 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

Aung, W. Worku, G. 1986 Developing flow and flow reversal in a vertical channelwith asymmetricwall temperatures. J. Heat Transfer 108, 299–304.Google Scholar
Bergholz, R. F. Instability of steady natural convection in a verticalluid layer. J. Fluid mech. 84, 743–768.
Busse F. H. 1967 The stability of finite amplite cellular convection and its relation to an extremum principle.. J. Fluid Mech. 30 625–649.Google Scholar
Chait, A. & Korpela, A. 1988 The Secondary flow and its stability for natural convection in a tall vertical enclosure. J. Fluid mech. 30 189–216.Google Scholar
Cenoweth, D. R. & Paolucci S. 1985 Gas flow in vertical slots with large horizontal temperature differences. Phys. Fluids 28 2365–2374.Google Scholar
Chenoweth, D. R. & Palocci S. 1986 Gas flow in open vertical slots with lage horizontal temperature differences and arbitrary external temperature. Phys. Fluids. 29 3187–3198.Google Scholar
Choli I. G. & Korpela S. A. 1980 Stability of the conduction regime of natural convection in a tall vertical annulus.. J. Fluid Mech. 99, 725–738.Google Scholar
Drazin, P. G. & Reid W. H. 1987 Hydrodynamics Stability. Cambridge University Press.
Fukui, K., Nakajima, M., Ueda, H. & Miushina, T. 1982 Flow instability and transport Phenomena in combined free and forced convection between vertical parallel plates. J. Chem. Engng. Japan 15, 17–180.Google Scholar
Gray, D. D. & Girogini, A. 1976 The validity of the Boussinesqapproximation for liquids andgases. Intl J. Heat Mass Transfer 19, 545–551.Google Scholar
Hart, J. E. 1971 Stability of The flow in a differentially hearted inclined box.. J. Fluid. Mech. 47 547–576.Google Scholar
Hatiziavramidis, D. & Ku, H.-C. 1985 An integral Chebyshev expansion method for boundary-value problems of O. D. E. type. Computers Maths. Applics. 11, 581–586.Google Scholar
Hilsenrath, J., Beckett, C. W. Benedictw, S., Fano L., Hoddge, H. J., Masi, J. F., Nuttall, R. L., Touloukian, Y. S. & Wooley, H. W. 1960 Tables of Thermodynamic and Trasnsport Properties Pergamon.IMSL Inc.1989IMSL Mathematical Library Version 1.1
Korpela, S. A., Gözüm, D & Baxi C. B. 1973 On the stability of the conduction regime of natural convection in a vertical vertical slod. Int. J. HeatMass Transfer 16, 1683–1690.Google Scholar
Ku, H-C. & Hatziavramidis, D 1984 Chebyshev expansion methods for of the extended Graetz Problem. J. Comput. Phys. 56 495–512.Google Scholar
Lee, Y. & Korplea, S. A. 1983 Multicellular natural convection in a vertical slot.. J. Fluid Mech. 126 91–121.Google Scholar
Lee, Y. & Korplea, S. A. 1982 Structure of multicellular natural convection in a tall vertical annulus. In Heat Transfer 1982 (ed. U. Grigull, E. Hahne, K. Stephan& J. Straub), Vol. 2, 00. 221–226.
Lin, C. C 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Orszag, S. A. 1971 Accurate solution of the Orr-Sommerfeld stability equationl.. J. Fluid. Mech. 50Google Scholar
Paolucci, S. 1982 On the filtering of sound from the Navier-equations. Tech. Rep. Sandia National Laboratories. Rep.Google Scholar
Rogers, B. B. Ghosh Moulic, S. & Yao, L. S. 1993 Finite-amplitude instability of mixed. Convection. J. Fluid Mech. 254, 229–250.Google Scholar
Rudakov, R. N. 1967 Spectrum of perturbations and stability of convective motion between vertical plates. Appl. Math. Mech. 31 376–383.Google Scholar
Suslov, S. A. & Paolucci, S. 1995 Stability of convection floow in a tall vertical enclosure under non-Boussinesa conditions. Intl. J. Ehat. Mass. Trasnster 38, 2143–2157.Google Scholar
Thangam, S. & Chen C. F. 1986 Stability analysis on the convection of variable viscosity fluid in an infinite vertical slot. Phys. Fluids 29, 1367–1372.Google Scholar
Vasilyev, O. V. & Paolucci S 1994, Stability of unstably shear flow in a channel under non-Boussinesq. Conditions. Acta Mechanica (in press).Google Scholar
Vest C. M. & Arpaci, V. S. 1969 Stability of natural convection in a vertical slot. J. Fluid. Mech. 36 1–15.Google Scholar
White, F. M. 1974, Viscous Fluid Fluw. McGraw-Hill.
Yao, L. S. & Rogers, B. B. 1989 Mixed convection in an annulusof of large aspect ratio. J. Heat Transfer 111, 683–689.Google Scholar