Pergamon Int. Comnt Heat Mass Transfer, Vol. 26, No. 6, pp. 761-770, 1999 Copyright © 1999 Elsevier ScienceLtd Printed in the USA. All rights reserved 0735-1933/99IS-see front matter PII S0735-1933(99)00064-0 MULTIPLE STEADY STATES FOR NATURAL CONVECTION IN A SHALLOW POROUS CAVITY SUBJECT TO UNIFORM HEAT FLUXES L. Kalla, M. Mamou, P. Vasseur and L. Robillard Ecole Polytechnique, Montrral, P.Q., H3C 3A7, Canada (Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT Multiplicity of steady states in natural convection within a shallow porous cavity, exposed to uniform heat fluxes on all sides, is investigated. Analytical solution for the stream function and temperature fields, in the central region of the cavity, is obtained using a parallel flow assumption. It is demonstrated that multiple steady states are possible, some of which are unstable. A finite difference method is used to obtain numerical solutions of the full governing equations. A good agreement is observed between the analytical predictions and the numerical simulations. © 1999 Elsevier Science Ltd Introduction Convective heat transfer in porous media is of fundamental importance in such technologies as geothermal exploitation, oil recovery and radioactive waste management. It is also important to geophysics and environmental sciences. Much of this activity, both numerical and experimental, has been summarized in a book by Nield and Bejan [1]. A review of the literature shows that most previous studies, on natural convection in porous enclosures, focused on the case of rectangular cavities heated and cooled only through two opposing sides while the two other are kept adiabatic. However, in practice, all the faces of the enclosure may be thermally active. The resulting natural convection heat transfer is expected to be considerably different to that induced by horizontal or vertical temperature gradients solely (see, for instance, Sen et al. [2]). Despite this, natural convection in enclosures heated and cooled on all sides has received relatively little attention. 761