Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries

[+] Author and Article Information
K. H. Winters

Theoretical Physics Division, Harwell Laboratory, Didcot, Oxon OX11 0RA, United Kingdom

J. Heat Transfer 109(4), 894-898 (Nov 01, 1987) (5 pages) doi:10.1115/1.3248200 History: Received July 21, 1986; Online October 20, 2009


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.

Copyright © 1987 by ASME
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