Stability analysis of double diffusive convection in a vertical brinkman porous enclosure

In this paper a linear stability analysis is presented for the problem of thermosolutal convection in a rectangular cell filled with a Brinkman (sparsely packed) porous medium saturated by a binary fluid. Transverse gradients of heat and solute are applied on the Vertical walls while the horizontal ones are adiabatic and impermeable. When the buoyancy forces induced by the thermal and solutal effects are opposing each other and of equal intensity an equilibrium solution, corresponding to the rest state, is possible. The critical parameters for the onset of motion are determined using numerical procedures based on the Galerkin and finite element methods. The boundaries defining the regions of stationary and oscillatory instabilities are delineated. The Brinkman-extended momentum equation is used to model the flow in the porous medium. Results for a pure viscous fluid and a Darcy (densely packed) porous medium emerge from the present analysis as limiting cases. (C) 1998 Elsevier Science Ltd.