Hopf bifurcation in the double-glazing problem with conducting boundaries

Journal Article · Sun Nov 01 04:00:00 EST 1987 · Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States)

DOI:https://doi.org/10.1115/1.3248200· OSTI ID:5476637

Winters, K H ^[1]

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1. 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), Journal Name: Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States) Vol. 109:4; ISSN 0022-1481; ISSN JHTRA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
CAVITIES
CONFIGURATION
CONVECTION
COVERINGS
DOUBLE GLAZING
ENERGY TRANSFER
FLOW MODELS
GLAZING
HEAT TRANSFER
INSTABILITY
MASS TRANSFER
MATHEMATICAL MODELS
NATURAL CONVECTION
PRANDTL NUMBER
RAYLEIGH-TAYLOR INSTABILITY
RECTANGULAR CONFIGURATION
SQUARE CONFIGURATION
TIME DEPENDENCE