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Convection in a rotating, horizontal cylinder with radial and normal gravity forces

Published online by Cambridge University Press:  26 April 2006

Foluso Ladeinde  and
K. E. Torrance
Foluso Ladeinde
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA Present address: Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794, USA.
K. E. Torrance
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853, USA
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Abstract

Convection driven by radial and normal gravity forces in a rotating, horizontal cylinder is examined. The cylinder is subjected to uniform volumetric heating and constant-temperature wall cooling. The parameters are the radial-gravity and normal-gravity Rayleigh numbers, Rar and Rag (with Rar, Rag ≤ 106), the rotational Reynolds number, Re = 2Ω r02/v (0 ≤ Re ≤ 250), and the Prandtl number (Pr = 7). Critical conditions for the radial-gravity rest state correspond to a two-cell flow in the azimuthal plane with Rar,c = 13738. Finite-amplitude transient and steady flows are obtained with a Galerkin finite element method for Rayleigh number ratios in the range 0.1 ≤ Rar/Rag ≤ 100. When radial gravity dominates the flows tend to be multicellular and, during transients, initial high-wavenumber forms evolve to lower-wavenumber forms. When normal gravity dominates the flows are bicellular. When radial and normal gravity forces are comparable, in the presence of rotation, complex time-dependent motions occur and the largest rates of fluid circulation and heat transfer are observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 228 , July 1991 , pp. 361 - 385
Copyright
© 1991 Cambridge University Press

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