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Stability of steady thermal convection in a tilted rectangular cavity in low-mode approximation

Stability of steady thermal convection in a tilted rectangular cavity in low-mode approximation Abstract The model system of ordinary differential equations [1, 2] governing the behavior of a non-uniformly heated fluid in a tilted cavity is used for studying the stability of steady regimes of thermal convection at arbitrary (not small) tilting of the rectangular cavity. The bifurcation curve is constructed, which separates the region of parameters (the Rayleigh number — the cavity tilting angle) into two regions — the internal and external ones. In the external region, the system has one stable steady solution, and in the internal region, it has three steady solutions. One of them is always unstable in a monotone way, and two others may be both stable and unstable. The neutral curves are constructed, which determine the boundaries of the incipience of the oscillatory and monotone instabilities. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Thermophysics and Aeromechanics Springer Journals

Stability of steady thermal convection in a tilted rectangular cavity in low-mode approximation

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Publisher
Springer Journals
Copyright
2008 Pleiades Publishing, Ltd.
ISSN
0869-8643
eISSN
1531-8699
DOI
10.1134/S0869864308020078
Publisher site
See Article on Publisher Site

Abstract

Abstract The model system of ordinary differential equations [1, 2] governing the behavior of a non-uniformly heated fluid in a tilted cavity is used for studying the stability of steady regimes of thermal convection at arbitrary (not small) tilting of the rectangular cavity. The bifurcation curve is constructed, which separates the region of parameters (the Rayleigh number — the cavity tilting angle) into two regions — the internal and external ones. In the external region, the system has one stable steady solution, and in the internal region, it has three steady solutions. One of them is always unstable in a monotone way, and two others may be both stable and unstable. The neutral curves are constructed, which determine the boundaries of the incipience of the oscillatory and monotone instabilities.

Journal

Thermophysics and AeromechanicsSpringer Journals

Published: Jun 1, 2008

References