Local thermal non-equilibrium analysis of the thermoconvective instability in an inclined porous layer

The two-temperature model of local thermal non-equilibrium (LTNE) is employed to investigate the onset of secondary convective flow in a fluid-saturated porous layer inclined to the horizontal and heated from below. The layer is assumed to be bounded by impermeable plane parallel walls with uniform and unequal temperatures. The linear instability of the stationary pure-conduction single-cell basic flow is studied by employing a normal mode decomposition of the disturbances. A Squire-like transformation is adopted to map all the oblique roll modes onto equivalent transverse roll modes. It is shown that the longitudinal rolls are the most unstable modes at the onset of the instability. The neutral stability condition for the longitudinal modes corresponds to that for a horizontal layer, by scaling the Darcy-Rayleigh number with cosine of the inclination angle to the horizontal. This scaling law, coincident with that well-known for the local thermal equilibrium (LTE) regime, implies a monotonic increment in the stability of the basic flow as the inclination to the horizontal increases.