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Abstract
This article presents numerical predictions of axisymmetric natural convection within a tall annular cavity with an aspect ratio of 10 and a radius ratio of 0.6. The temperature of the bounding inner vertical cylinder is hot at its base and decreases linearly with height, while the outer cylinder is cold at its base and its temperature increases linearly with height. These boundary conditions promote a steady bi-cellular flow at low Rayleigh numbers. As the Rayleigh number is increased, the flow transitions to a time-varying state in which the interface between the two natural-convection cells starts to oscillate. If the Rayleigh number is further increased, hysteresis, subharmonics, multiple solutions, and a reverse transition back to a steady state are all predicted. Results predicting the onset of unsteady flow for the Cartesian case are also presented.
We are pleased to acknowledge support for this work from the National Science Foundation, Grant ECS 9734438.
