Stability Analysis of Rayleigh-Benard Convection in the Presence of Side Walls

by P. Diplas, (M.ASCE), Virginia Polytechnic Inst and State, Univ, Blacksburg, United States,
C. Dietz, Virginia Polytechnic Inst and State, Univ, Blacksburg, United States,



Document Type: Proceeding Paper

Part of: Hydraulic Engineering

Abstract:

The onset of laminar axisymmetric Rayleigh-Benard convection is investigated for a low-Prandtl number liquid metal in a cylindrical container, in the presence of a vertical temperature gradient. All surfaces are considered to be solid and no-slip. The side wall is treated as an insulated surface. 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 set of equations determines the first critical Rayleigh number. The result is compared with experimental data and a Rayleigh-Ritz formulation of the same problem.

Subject Headings: Thermal analysis | Walls | Mathematical models | Differential equations | Thermal properties | Metals (material) | Data analysis

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