Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.
The three-dimensional time-dependent Navier-Stokes equations (Boussinesq approximation) for an incompressible viscous fluid are approximated using finite-differences. A uniform cylindrical mesh consisting of LxMxN discrete points in the radial (r), azimuthal ( φ ) and axial (z) directions respectively is superimposed on the solution domain. The energy and vorticity transport equations are solved using a modified transient Samarskii-Andreyev ADI scheme. The elliptic equation for the vector-potential is solved using by direct Fourier series using a fast Fourier transform algorithm. Transient numerical solutions of time dependent threedimensional equations for Rayleigh-Bénard convection in a vertical cylinder are presented. Results are presented for aspect ratio (radius to height) of 8, a Prandtl number Pr=7 and Rayleigh numbers 1000 ≤ Ra ≤ 20000.