Transition to instability of liquid–vapour front in a porous medium cooled from above

The instability of the liquid–vapour front in a geothermal system with a cooling flux at the liquid boundary is investigated by introducing a small perturbation at the front. The mechanisms contributing to the stability and instability of such systems are analysed using a separate-phase model with a sharp interface between liquid and vapour. The governing equations representing incompressibility, Darcy’s law and energy conservation for each phase are linearised about suitable base state and the stability of this state is investigated. A conditional expression for the critical modified Rayleigh number depending on the different physical parameters has been found. It has been shown that advection is not essential for instability, but it encourages the unstable behaviour.