Linear stability of natural convection in a tall vertical slot with a moving sidewall

Abstract

The effect of a shear force on the stability of natural convection in a tall vertical slot has been studied utilizing linear theory. Our results show that the stability of natural convection is significantly affected by the motion of the sidewall and that sidewall motion creates three types of instability. At small Prandtl numbers, the shear instability is dominant. At higher Prandtl numbers, the flow becomes unstable, creating a buoyant instability induced by the boundary layer near the fixed (unmoving) sidewall. When the sidewall moves slightly downward, the buoyant instability induced by the boundary layer near that moving wall occurs for Prandtl numbers near 10. The critical Prandtl number which marks the transition between the shear and buoyant modes is strongly dependent on the direction and speed of the sidewall movement.