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A spectral method determination of the first critical Rayleigh number for a low-Prandtl number crystal melt in a cylindrical containerDietz, Charles Miller 06 October 2009 (has links)
The onset of laminar Rayleigh-Bénard convection is investigated for a low-Prandtl number liquid metal in a cylindrical container. All surfaces are considered to be solid and no-slip. Two cases are considered for the thermal boundary conditions at the side wall: conducting and insulated surfaces. A Chebyshev Galerkin spectral model is used to reduce the governing Boussinesq system to a first-order system of ordinary differential equations. A local stability analysis using the linearized system determines the first critical Rayleigh number. The results are compared with experimental data and a numerical study. / Master of Science
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