For arbitrary Rayleigh number, Ra, Prandtl number, and any ratio of the cylindrical radii, existence of steady solutions of the two-dimensional Oberbeck-Boussinesq system is proved. We show nonlinear stability for large values of the aspect ratio and {Ra}<{Ra}_L, for some number {Ra}_L which is bounded from below (cf. Theorem 4.4). We prove that for large aspect ratio, Ra}_L approaches the critical Rayleigh number for the stability of the rest state solution of a suitable linear problem.

Theoretical results on steady convective flows between horizontal coaxial cylinders

PASSERINI, Arianna;FERRARIO, Carlo;
2011

Abstract

For arbitrary Rayleigh number, Ra, Prandtl number, and any ratio of the cylindrical radii, existence of steady solutions of the two-dimensional Oberbeck-Boussinesq system is proved. We show nonlinear stability for large values of the aspect ratio and {Ra}<{Ra}_L, for some number {Ra}_L which is bounded from below (cf. Theorem 4.4). We prove that for large aspect ratio, Ra}_L approaches the critical Rayleigh number for the stability of the rest state solution of a suitable linear problem.
2011
Passerini, Arianna; Ferrario, Carlo; Ruzicka, M; Thaeter, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1482315
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