Longitudinal vortex instabilities in laminar boundary layers over curved heated surfaces

Abstract

An analysis has been performed of penetrative convective instabilities arising from the combined action of thermal and centrifugal buoyancy forces. The objective has been to examine the effect of various mean temperature and velocity profiles on the critical limit and convective penetration of the disturbances. The linearized perturbation equations have been solved employing an approximate technique. The close analogy between stream-line curvature and thermal stratification effects has been demonstrated. It is found that for parallel layers of fluid along curved heated walls, a unique stability curve for neutral disturbances may be obtained if the quantity plotted along the abscissa is Ra + κNG2 where Ra is the Rayleigh number, NG is the Görtler number, and k is a constant which expresses the relative importance of the mean temperature and velocity profiles.