Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-29T14:41:39.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Centrifugally driven thermal convection in a rotating cylinder

Published online by Cambridge University Press:  28 March 2006

G. M. Homsy  and
J. L. Hudson
G. M. Homsy
Affiliation:
Department of Chemistry and Chemical Engineering, University of Illinois, Urbana
J. L. Hudson
Affiliation:
Department of Chemistry and Chemical Engineering, University of Illinois, Urbana
Get access Rights & Permissions [Opens in a new window]

Abstract

Thermally induced convection in a rotating cylinder of fluid heated from above and strongly influenced by centrifugal accelerations is treated using boundary-layer methods. As in the theory of homogeneous rotating fluids, the horizontal Ekman layers control the inviscid axial flow. The solution also largely depends upon the thermal conditions assumed at the side wall, and if these be insulated, consideration of the side-wall boundary layers is necessary for complete specification of the problem. For perfectly conducting side walls, the side layers do not influence the zeroth-order flow, but contribute a second-order correction, which would be absent if the lateral boundaries were ignored. The critical parameters governing the solutions in both cases are found to be γ and the group σβε−½, where γ is the aspect ratio, σ the Prandtl number, ε the Ekman number, and β the thermal Rossby number for the flow. Boundary-layer solutions are given for a wide range of parameters, and gravity is seen to have at most only a local effect on the flow near the side walls.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 35 , Issue 1 , 16 January 1969 , pp. 33 - 52
Copyright
© 1969 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

Barcilon, V. & Pedlosky, J. 1967a A unified linear theory of homogeneous and stratified rotating fluids J. Fluid Mech. 29, 609.Google Scholar
Barcilon, V. & Pedlosky, J. 1967b On the steady motions produced by a stable stratification in a rapidly rotating fluid J. Fluid Mech. 29, 673.Google Scholar
Duncan, I. B. 1966 Axisymmetric convection between two rotating disks J. Fluid Mech. 24, 417.Google Scholar
Greenspan, H. P. & Howard, L. N. 1963 On a time-dependent motion of a rotating fluid J. Fluid Mech. 17, 385.Google Scholar
Hudson, J. L. 1968a Convection near a cooled disk rotating with its environment Int. J. Heat Mass Transfer, 11, 407.Google Scholar
Hudson, J. L. 1968b Non-isothermal flow between rotating disks Chem. Eng. Sci. 23, 1007.Google Scholar
Hunter, C. 1967 The axisymmetric flow in a rotating annulus due to a horizontally applied temperature gradient J. Fluid Mech. 27, 753.Google Scholar
Káarmán, T. Von 1921 Laminare und turbulente reibung Z. Angew. Math. Mech. 1, 244.Google Scholar
Lighthill, M. J. 1953 Theoretical considerations on free convection in tubes Quart. J. Mech. Appl. Math. 6, 398.Google Scholar
Ostrach, S. & Braun, W. H. 1958 Natural convection inside a flat rotating container. NACA TN 4323.
Riley, N. 1967 Thermally induced boundary-layer flows in a rotating environment J. Fluid Mech. 29, 241.Google Scholar
Schmidt, E. H. 1951 Heat transmission by natural convection at high centrifugal acceleration in wrater-cooled gas-turbine blades. General Discussion on Heat Transfer, Inst. Mech. Engr., London, pp. 361–3.
Stewartson, K. 1957 On almost rigid rotations J. Fluid Mech. 3, 17.Google Scholar
Thiriot, H. K. 1940 Über die laminare Anlaufstömung einer Flüssigkeit einem rotierenden Boden bei plötzlicher Änderung des Drehungszustandes Z. Angew. Math. Mech. 20, 1.Google Scholar