Natural Convection Along a Finite Vertical Plate

Abstract

The discrepancy between the measured mean heat flux for natural convection on a finite vertical plate and the solution of Pohlhausen, Schmidt, and Beckmann has been known for a long time; no theoretical explanation has ever been provided. In this paper, a double-deck structure is introduced to account for the trailing-edge effect. This solution shows that the flow accelerates near the training edge due to the geometric discontinuity which leads to a decreased flow constraint. An inward normal flow is induced by the local flow acceleration and generates a change in the displacement of the thin viscous layer near the plate. Consequently a pressure disturbance is developed and transmits information upstream. The heat flux and wall shear stress both increase due to this flow acceleration. Even though the effect on the total heat flux is small, the local heat flux is modified substantially. Thus the smaller effects due to the leading edge, the displacement, and the wake cannot be the reason for the discrepancy.