Numerical solutions of the three-dimensional equations for Rayleigh-Bénard convection in a vertical cylinder are presented. The energy and vorticity transport equations are solved using the Samarskii-Andreyev alternating direction implicit (ADI) scheme. A fast Fourier transform algorithm is used to solve for the vector potential. Solutions are presented for aspect ratios of 2 and 4, a Prandtl number Pr = 7, and Rayleigh numbers 12 h Ra h 37500. A conductive (no motion) state exists when Ra h Ra c = 1860. For Ra > Ra c , there are four main types of flow structures. These are concentric, radial, parallel, and cross rolls. The Nusselt number depends on the type of flow structure.
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S. S. Leong (2002) studied this question.
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