Application of a non-linear local analysis method for the problem of mixed convection instability |
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Authors: | Christophe Guillet Thierry Mare |
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Affiliation: | a Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne, 9 Avenue Alain Savary, BP 47870, 21078 Dijon Cedex, France b Laboratoire de thermique des bâtiments, GRGC INSA de Rennes 35043 Rennes, France c Faculty of Engineering, Université de Moncton, Nouveau-Brunswick, Canada E1A 3E9 |
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Abstract: | We consider the problem of laminar mixed convection flow between parallel, vertical and uniformly heated plates where the governing dimensionless parameters are the Prandtl, Rayleigh and Reynolds numbers. Using the method based on the centre manifold theorem which was derived from the general theory of dynamical systems, we reduce a three-dimensional simplified model of ordinary differential amplitude equations emanating from the original Navier-Stokes system of the problem in the vicinity of a trivial stationary solution. We have found that when the forcing parameter, the Rayleigh number, increases beyond the critical value Ras, the stationary solution is a pitchfork bifurcation point of the system. |
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Keywords: | Centre manifold reduction Mixed convection Amplitude equations Bifurcation |
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