Instability and disturbance amplification in a mixed-convection boundary layer

Abstract

(Received 2 October 1990 and in revised form 8 January 1991) The stability of a laminar mixed-convection boundary layer adjacent to a vertical isothermal surface is examined, using linear stability theory and the parallel-flow approximations. The analysis is valid when the imposed forced-convection effects are small compared to natural-convection effects. The stability equations are solved numerically for aiding and opposing forced-convection effects, for Pr = 0.733 (air) and 6.7 (water). For aiding mixed convection in air, a new feature was found. A small, separated region of instability arises upstream of the ‘conventional ’, or ‘primary’, neutral curve. In this region, selective amplification of a narrow band of disturbance frequencies occurred, but disturbance growth was small. Further downstream, disturbance growth rates in flows with an aiding free stream are slower than in natural convection. The opposite is true for an opposing free stream in air. Selective disturbance amplification occurred downstream for all conditions, as in natural convection. In water, an aiding flow was destablizing compared to natural convection, and an opposing flow was stabilizing. Evidence of a separated upstream region of instability was also found for aiding mixed convection in water. However, converged solutions could not be obtained in this circumstance.