Hopf bifurcation in the double-glazing problem with conducting boundaries
- Harwell Lab., Didcot (England)
Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. The author shows that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.
- OSTI ID:
- 5476637
- Journal Information:
- Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States), Vol. 109:4; ISSN 0022-1481
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
CAVITIES
NATURAL CONVECTION
FLOW MODELS
DOUBLE GLAZING
PRANDTL NUMBER
RAYLEIGH-TAYLOR INSTABILITY
SQUARE CONFIGURATION
TIME DEPENDENCE
CONFIGURATION
CONVECTION
COVERINGS
ENERGY TRANSFER
GLAZING
HEAT TRANSFER
INSTABILITY
MASS TRANSFER
MATHEMATICAL MODELS
RECTANGULAR CONFIGURATION
420400* - Engineering- Heat Transfer & Fluid Flow