Vortex instability in natural convection flow on an inclined uniform-heat-flux surface

Buoyancy-induced fluid motions formed on an inclined surface with a uniform heat flux are studied from the standpoint of the linear vortex stability theory. The effects of nonparallelism of the main flow on the thermal fields are taken into account in the analysis. The disturbances are assumed to have the form of a stationary longitudinal vortex mode that is time-invariant and periodic in the spanwise direction. The local wall shear stress, the local Nusselt number, neutral stability curves, and critical disturbance amplitude distributions are presented for Prandtl numbers of 0.7, 7, 10, 50, and 100 over the various angles of inclination. The present results are compared with available experimental data and also with results from the wave mode of stability for vertical natural convection flow. It is found that as the angle of inclined surface increases, the critical Ra number or Gr number increases. As Pr number increases, the critical Gr number decreases, while the critical Ra number increases.