A GALERKIN FINITE-ELEMENT STUDY OF THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN AN INCLINED POROUS ENCLOSURE

The Darcy model with the: Boussinesq approximation is used to study th e onset of double-diffusive natural convection in an inclined porous c avity. Transverse gradients of heat and solute are applied on two oppo sing walls of the cavity, while the other two walls are impermeable an d adiabatic. The analysis deals with the particular situation where th e buoyancy forces induced by the thermal and solutal effects are oppos ing and of equal intensity. The objective of this study is to investig ate the critical stability of this system in terms of the inclination angle, the aspect ratio of the cavity and the Lewis number. The subseq uent behavior of the convective flow is also discussed in terms of the governing parameters of the problem. Numerical procedures based on th e Galerkin and finite element methods are carried out to investigate t he onset of double-diffusive convection using the linear stability ana lysis. It is shown that for values of Lewis number around unit, overst ability is possible provided that the normalized porosity of the porou s medium epsilon is made smaller than unity. For supercritical convect ion, the occurrence of multiple solutions, for a given range of the go verning parameters, is demonstrated. The numerical results also indica te the existence of subcritical convective regimes. (C) 1998 Elsevier Science Ltd. All rights reserved.