Thermoconvective instabilities in an inclined porous channel heated from below

摘要

The thermoconvective instability in an inclined rectangular channel filled with a fluid saturated porou medium and heated from below with a uniform flux is investigated. A stationary parallel buoyant flo with a linear temperature change in the transverse direction is considered. The linear stability to tram verse and longitudinal roll disturbances of this basic state is examined. The thermoconvective instabilit onset of transverse rolls occurs when the Darcy-Rayleigh number exceeds a critical value, that increase with the inclination angle. The critical Darcy-Rayleigh number is discontinuous at the inclination angl 23.4749° above the horizontal. It is shown that, when the inclination angle exceeds 31.3618°, either th transverse rolls are stable or a second discontinuous transition to a higher branch of instability occur The longitudinal rolls may be unstable for every inclination except for the vertical. A stability diagrar is sketched displaying the geometrical conditions (inclination angle, aspect ratio) such that either th transverse rolls or the longitudinal rolls is the preferred mode of instability.