Bifurcation of convection flows in a rectangular cavity subjected to uniform heat fluxes

A study is made of free convection flow in ii horizontal rectangular cavity submitted to a uniform heat flux at the horizontal as well as vertical wal ls. As the flow under such heating condition is quasi-parallel, it is possi ble to derive an equation for the flow amplitude having the canonical form phi (3) - delta phi - 9!R*/384(3) = 0 where R* is the Rayleigh number based on the heat flux applied at the side walls and delta is the reduced Raylei gh number based on the heat flux applied at the horizontal boundaries. Base d on this equation, various diagrams were constructed to show the unfolding of the well-known pitchfork bifurcation. (C) 2001 Elsevier Science Ltd.