On the stability of natural convection boundary layer flow over horizontal and slightly inclined surfaces

Abstract

This is an analytical and experimental study of the stability of natural convection boundary layer flow adjacent to horizontal and to slightly inclined surfaces. The additional buoyancy effects resulting from small surface inclinations are taken into account. Also considered are the effect of additional buoyancy arising from the diffusion of chemical species. The limits and conditions for attached boundary flow are determined. The question of flow separation is considered. Stability of such a flow to two-dimensional disturbances was studied by linear stability theory. Neutral stability and amplification rate contours were obtained by numerical integration of the resulting eighth-order coupled momentum and energy stability equations for air ( Pr = 0.7). The effect of a small surface inclination upon stability was studied using the results of a perturbation analysis of such flows. Effect of simultaneous mass diffusion on stability was also found for the case of equal Prandtl and Schmidt numbers. Experimental verification of the stability predictions was carried out by disturbing the actual flows, over a frequency range, with a thin vibrating ribbon and observing the behavior of the convected disturbance. A Mach-Zehnder interferometer was used to study flow characteristics under both disturbed and and undisturbed conditions. The more complicated three-dimensional disturbances, which also arose, were made visible by smoke injection into the boundary region. The stability theory predicts the correct trend of the stability limits for both horizontal and slightly inclined surfaces. However, the calculations are not in as good an agreement with observations as in flows adjacent to vertical surfaces or in freely thermal plumes. The discrepancies found are believed to result from the rapid growth of three-dimensional effects in the attached boundary-layer region and from a downstream separation-like phenomenon.