Thermal instability of viscoelastic fluids in horizontal porous layers as initial value problem

The instability of a viscoelastic fluid saturating a horizontal porous layer heated from below is studied theoretically with a dynamical system approach. The viscoelastic character of the flow is taken into account by a modified Darcy's law. The conservation equations of mass, momentum and energy are approximated by a reduced-order system of nonlinear, ordinary differential equations, which is similar to the well-known system derived by Lorenz to describe atmospheric convection. Equilibrium points and their stability are expressed as functions of a dimensionless heat capacity and of two relaxation parameters. Qualitative expressions of the Nusselt number when the system is out of equilibrium are also derived. (c) 2006 Elsevier Ltd. All rights reserved.