Instability of a horizontal porous layer with local thermal non-equilibrium: Effects of free surface and convective boundary conditions

The onset of convective instability in a horizontal porous layer saturated by a fluid is studied. A regime of local thermal non-equilibrium (LTNE) is considered. The lower plane boundary is an impermeable isothermal wall, while the upper boundary is a free surface with finite heat transfer coefficients to the external environment. The temperature boundary conditions at the free surface are parametrised by two Biot numbers: one for the solid and one for the fluid. A modal linear stability analysis of the basic motionless state is carried out. Limiting cases allowing for an analytical dispersion relation are defined and analysed. The general regime of linear instability is investigated by a numerical solution of the governing differential equations for the normal modes. The neutral stability condition, as well as the critical value of the Darcy-Rayleigh number, is studied in some asymptotic cases and in the general case.