The stability of natural convection in narrow-gap spherical annuli to axisymmetric disturbances

M. T. Farmer, R. W. Douglass, S. A. Trogdon

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The linear stability with respect to axisymmetric disturbances of natural convection in narrow-gap, spherical annuli is investigated. The basic motion is an eight-order perturbation solution in the small parameter ε = 1-η, where η is the ratio of inner radius of the annulus to outer radius. The disturbance equations are reduced to a system of ordinary differential equations by means of a method of partial spectral expansions. These equations constitute an eigenvalue problem which is solved for the critical Rayleigh number as a function of η and Prandtl number, Pr. Cases considered are Pr = 0.1, 1, 10, and 100 for 0.900 ≤ η ≤ 0.995. A comparison with the experimental results found in the literature indicates that non-axisymmetric time periodic bifurcation will most likely take precedence over the case considered herein for Pr = 1,10. However, it appears that steady axisymmetric bifurcation is possible for Pr = 0.1.

Original languageEnglish (US)
Pages (from-to)1575-1584
Number of pages10
JournalInternational Journal of Heat and Mass Transfer
Issue number10
StatePublished - Oct 1986


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