Convective Boundary Layer Flow Adjacent to an Inclined and Linearly Heated Semi-Infinite Plate

Abstract

The transient convective flow adjacent to an inclined semi-infinite plate which is heated by a linear temperature gradient is investigated with scaling analysis and direct numerical simulation (DNS) in this study. Both Pr < 1 and Pr > 1 fluids are considered. The initial ambient fluid is quiescent and thermally homogeneous. Important parameters characterizing the thermal boundary layer flow are thickness, characteristic velocity, and time to reach the steady stage. Scaling analysis is carried out to obtain scales for these flow parameters. Compared to previous similar studies, the obtained scale relations are more generalized and they can be utilized for different inclination angles. The derived scales are compared against the DNS results for a variety of flow parameters, e.g., Rayleigh number Ra, Prandtl number Pr, stratification factor s (s = dθw(y)/dy, where θw(y) is the local temperature at a streamwise location of y), inclination angle of the heated plate α, evolutionary time τ, and streamwise location y. The scale relations and the DNS results compare well suggesting the proposed scale laws can provide a sound description for the dynamics of the convective flow subjected to a tilted surface and a linear heating condition.