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Title: Hopf bifurcation in the double-glazing problem with conducting boundaries

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. 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.
Authors:
Publication Date:
OSTI Identifier:OSTI ID: 5476637
Resource Type:Journal Article
Resource Relation:Journal Name: Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States); Journal Volume: 109:4
Country of Publication:United States
Language:English
Subject: 42 ENGINEERING; 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