Thermal instability of viscoelastic fluids in porous media

A theoretical analysis of thermal instability driven by buoyancy forces is conducted in an initially quiescent, horizontal porous layer saturated by viscoelastic fluids. Modified Darcy’s law is used to explain characteristics of fluid motion. The linear stability theory is employed to find the critical condition of the onset of convective motion. The results of the linear stability analysis show that the overstability is a preferred mode for a certain parameter range. Based on the results of linear stability analysis, a nonlinear stability analysis is conducted. The onset of convection has the form of a supercritical and stable bifurcation independent of the values of the elastic parameters. The Landau equations and the Nusselt number variations are derived for steady and oscillatory modes.