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The Quarterly Journal of Mechanics and Applied Mathematics 1982 35(2):279-290; doi:10.1093/qjmam/35.2.279
© 1982 by Oxford University Press
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STABILITY OF TWO-DIMENSIONAL NATURAL CONVECTION IN A POROUS LAYER

BARBARA BORKOWSKA-PAWLAK and WLODZIMIERZ KORDYLEWSKI

( Technical University of Wroclaw, Institute of Power Engineering and Fluid Mechanics ul. Wybrzeze Wyspianskiego 27, 50–370 Wroclaw, Poland )

A stability analysis of the two-dimensional natural convection in a porous layer is given. The Galerkin method is used, truncating the series to four and six terms.

For finite Prandtl numbers the system of three ordinary differential equations obtained has the same properties as that of Lorenz for the classical Bénard problem.

In the case of infinite Prandtl numbers, four ordinary differential equations are examined. The first branch of nontrivial steady-state solutions loses stability at the Rayleigh number equal to 30{pi}2. At this point the subcritical Hopf bifurcation takes place, but unlike the previous case the trajectories are not limited to the neighbourhood of origin.


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