Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-29T14:03:55.484Z Has data issue: false hasContentIssue false

Stability of the conduction regime of natural convection in a tall vertical annulus

Published online by Cambridge University Press:  19 April 2006

Inn G. Choi
Affiliation:
Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43210
Seppo A. Korpela
Affiliation:
Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43210

Abstract

The stability of natural convection in a vertical annular enclosure has been studied by the linear theory. It was found that for all Prandtl numbers the instability sets in as a wave travelling upward. For low Prandtl numbers, the larger the curvature the more stable the flow; the reverse is true for high Prandtl numbers. The theoretical predictions of the mode of instability were verified for air. A multicellular flow pattern was observed to drift upward with the predicted wave speed. The measured wavelength of the cells is in good agreement with the linear analysis.

Type
Research Article
Copyright
© 1980 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

Batchelor, G. K. 1954 Quart. Appl. Math. 12, 209.
Bergholz, R. F. 1978 J. Fluid Mech. 84, 743.
Birikh, R. V., Gershuni, G. Z., Zhukhovitskii, E. M. & Rudakov, R. N. 1972 Prikl. Math. Mech. 36, 707.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
DiPrima, R. C. 1955 Quart. Appl. Math. 16, 55.
Eckert, E. R. G. & Carlson, W. O. 1961 Int. J. Heat Mass Transfer 2, 106.
Elder, J. W. 1965 J. Fluid Mech. 23, 77.
Gershuni, G. Z. 1953 Zh. Tech. Fiz. 23, 1838.
Gill, A. E. 1966 J. Fluid Mech. 26, 515.
Gill, A. E. & Davey, A. 1969 J. Fluid Mech. 35, 775.
Gill, A. E. & Kirkham, C. C. 1970 J. Fluid Mech. 42, 125.
Hart, J. 1971 J. Fluid Mech. 47, 547.
Korpela, S. A., Gözüm, D. & Baxi, C. B. 1973 Int. J. Heat Mass Transfer 16, 1683.
Rudakov, R. N. 1967 Prikl. Math. Mech. 31, 376.
Vest, C. M. & Arpaci, V. S. 1969 J. Fluid Mech. 36, 1.
Walowit, J., Tsao, S. & DiPrima, R. C. 1964 J. Appl. Mech. 31, 585.