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ISSN Online: 2377-424X

International Heat Transfer Conference 12
August, 18-23, 2002, Grenoble, France

Natural convection in a rectangular cavity with piece-wise heated vertical walls: multiple states, stability and bifurcations

Get access (open in a dialog) DOI: 10.1615/IHTC12.60
6 pages

Abstract

A natural convection flow in a two-dimensional rectangular vertical cavity with partially and symmetrically heated vertical walls is studied numerically. The base flow is symmetric with respect to the central vertical plane and can be divided into the stably and unstably thermally stratified regions. The stability of this flow is affected by the Rayleigh-Bénard mechanism in the unstably stratified part, by flow damping in the stably stratified part, and by the symmetry-breaking instability having a purely hydrodynamic origin. The interaction of these factors leads to a multiplicity of steady state flows. In the following we present a parametric study of the multiplicity, stability and bifurcations of the steady flow states. Linear stability analysis, weakly nonlinear approximation of slightly supercritical states and the arc-length path-continuation technique are implemented. It is found that a series of turning point bifurcations takes place when the Grashof is increased beyond a certain value. Folding of the solution branches leads to the existence of multiple steady and oscillatory states. The stability of each steady state branch is studied separately.