Vortex instability of natural convection flow on inclined surfaces

The linear stability of laminar natural convection flow adjacent to a heated, inclined, upwardfacing plate is investigated for disturbances having the form of longitudinal vortices. The stability problem is formulated with account being taken of the fact that the basic flow and temperature fields depend on the streamwise coordinate. One of the demonstrated consequences of retaining the transverse velocity of the basic flow is the so-called bottling effect, wherein the disturbance vorticity and temperature are contained within the respective boundary layers of the basic flow. The calculated neutral stability curves exhibit an altogether different character depending upon whether the streamwise dependence of the basic flow and temperature fields is taken into account or suppressed; the magnitude of the critical Grashof numbers from the two models differs by several orders of magnitude. The results also show that the greater the inclination of the plate from the vertical, the more susceptible is the flow to the vortex-type instability. The relationship of the analytical results to available experimental information is discussed.