Stability of Natural Convection Boundary Layer Flow on an Evenly Heated Vertical Plate

Stability of natural convection flow adjacent to a vertical plate with uniform heat flux is studied using direct numerical simulation (DNS). Stability of the fully developed boundary layer is examined by adding a perturbation to the simulation in the region of the plate origin, with the resulting traveling waves tracked as they travel up the boundary layer. The approach allows the critical height on the plate at which the traveling waves become unstable to be identified, providing a critical Rayleigh number for the occurrence of instability in this flow. The full details available from the numerical solution also allow the phase speed and amplitude of the most unstable mode to be identified. Flow with Rayleigh number Ra = 1.0 X 1010 and Prandtl number Pr = 6.7 is studied. Finally the DNS results are compared with the results obtained using the conventional linearized stability analysis.