Multiple solutions for double diffusive convection in a shallow porous cavity with vertical fluxes of heat and mass

The Darcy model with the Boussinesq approximation is used to study double-d iffusive natural convection in a shallow porous cavity. The horizontal wall s are subject to uniform fluxes of heat and mass, while the side vertical w alls are exposed to a constant heat flux of intensity aq ', where a is a re al number. Results are presented for -20 less than or equal to R-T less tha n or equal to 50, -20 less than or equal to R-S less than or equal to 20, 5 less than or equal to Le less than or equal to 10, 4 less than or equal to A less than or equal to 8 and -0.7 less than or equal to a less than or eq ual to 0.7, where RT, Rs, Le and A correspond to thermal Rayleigh number, s olutal Rayleigh number, Lewis number and aspect ratio of the enclosure, res pectively. In the limit of a shallow enclosure (A much greater than 1) an a symptotic analytical solution for the stream function and temperature and c oncentration fields is obtained by using a parallel flow assumption in the core region of the cavity and an integral form of the energy and the consti tuent equations. In the absence of side heating (a = 0), the solution takes the form of a standard Benard bifurcation. The asymmetry brought by the si de heating (a not equal 0) to the bifurcation is investigated. For high eno ugh Rayleigh numbers, multiple steady states near the threshold of convecti on are found. These states represent flows in opposite directions. In the r ange of the governing parameters considered in the present study, a good ag reement is observed between the analytical predictions and the numerical si mulations of the full governing equations. (C) 2001 Elsevier Science Ltd. A ll rights reserved.