Onset of penetrative convection of cold water in a porous layer under mixed boundary conditions

In the present work, the onset of convection in a two-dimensional horizontal porous layer saturated with cold water is studied numerically, using the linear stability analysis. The Dirichlet-Dirichlet, Neumann-Dirichlet and Dirichlet-Neumann thermal boundary conditions are applied on the horizontal walls of the cavity, respectively. Both the infinite and the confined layers are investigated. The finite element method is used to solve the linearized perturbation equations. The onset of convection is found to be dependent of the aspect ratio of the cavity, A and the inversion parameter, γ. The effect of these control parameters is studied for both infinite and finite layer cases. The effect of various thermal boundary conditions imposed on the horizontal layer is also investigated in this study.