THE STABILITY OF FREE CONVECTION IN A HORIZONTAL CYLINDRICAL ANNULUS

Fluid fills the annulus between two concentric horizontal cylinders maintained at constant temperatures. When the inner cylinder is hotter than the outer a steady flow results but this may become unstable to small perturbations for a sufficiently large value of the Rayleigh number. We examine the on...

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Veröffentlicht in:Quarterly journal of mechanics and applied mathematics 1980-05, Vol.33 (2), p.125-139
1. Verfasser: WALTON, I. C.
Format: Artikel
Sprache:eng
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Zusammenfassung:Fluid fills the annulus between two concentric horizontal cylinders maintained at constant temperatures. When the inner cylinder is hotter than the outer a steady flow results but this may become unstable to small perturbations for a sufficiently large value of the Rayleigh number. We examine the onset of this instability when ε, the ratio of gap width to the radius of the inner cylinder, is small, by expanding in powers of ε and employing a WKB formulation for the perturbed solution. Values of the critical Rayleigh number at which instability first occurs are obtained for several values of the Prandtl number and a comparison with experimental and numerical results is made.
ISSN:0033-5614
1464-3855
DOI:10.1093/qjmam/33.2.125