A spectral method determination of the first critical Rayleigh number for a low-Prandtl number crystal melt in a cylindrical container
Files
TR Number
Date
1993-04-05
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Virginia Tech
Abstract
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.