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The Quarterly Journal of Mechanics and Applied Mathematics 1980 33(2):125-139; doi:10.1093/qjmam/33.2.125
© 1980 by Oxford University Press
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THE STABILITY OF FREE CONVECTION IN A HORIZONTAL CYLINDRICAL ANNULUS

I. C. WALTON

( Department of Mathematics, Imperial College London SW7 2BZ )

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 {varepsilon}, the ratio of gap width to the radius of the inner cylinder, is small, by expanding in powers of {varepsilon} 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.


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