Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries

Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection i...

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Bibliographic Details
Published in:Journal of heat transfer 1987-11, Vol.109 (4), p.894-898
Main Author: Winters, K. H
Format: Article
Language:English
Subjects:
420400 - Engineering- Heat Transfer & Fluid Flow
CAVITIES
CONFIGURATION
CONVECTION
COVERINGS
DOUBLE GLAZING
ENERGY TRANSFER
ENGINEERING
Exact sciences and technology
FLOW MODELS
Fluid dynamics
Fundamental areas of phenomenology (including applications)
GLAZING
HEAT TRANSFER
INSTABILITY
MASS TRANSFER
MATHEMATICAL MODELS
NATURAL CONVECTION
Physics
PRANDTL NUMBER
RAYLEIGH-TAYLOR INSTABILITY
RECTANGULAR CONFIGURATION
SQUARE CONFIGURATION
TIME DEPENDENCE
Turbulent flows, convection, and heat transfer
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Summary:Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show 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.
ISSN:0022-1481
1528-8943
DOI:10.1115/1.3248200