Numerical study of formation of longitudinal vortices in natural convection flow over horizontal and inclined surfaces

This paper presents a numerical study of the formation of longitudinal vortices in natural convection flow over horizontal and inclined plates. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, wave number, and the inclined angle φ from the horizontal. The flow is found to become more stable to the vortex mode of instability as the value of inclined angle increases, owing to a decrease in buoyancy force in the normal direction. However, the Prandtl number has a destabilizing effect on the flow. The results of the present numerical prediction show a reasonable agreement with the experimental data in the literature.