The linear stability of a developing thermal front in a porous medium: The effect of local thermal non-equilibrium

In this paper we analyze the stability of the developing thermal boundary layer which is induced by a step-change in the temperature of the lower horizontal boundary of a uniformly cold semi-infinite porous medium. Particular attention is paid to the influence of local thermal non-equilibrium between the fluid and solid phases and how this alters the stability criterion compared with corresponding criterion when the phases are in local thermal equilibrium. A full linear stability analysis is developed without approximation, and this yields a parabolic system of equations for the evolving disturbances. Criteria for the onset of convection are derived as a function of the three available nondimensional parameters, the inter-phase heat transfer coefficient, H, the porosity-scaled conductivity ratio, γ, and the diffusivity ratio, α.