Natural convection along a finite vertical plate

The discrepancy between a measured mean heat transfer rate of a finite vertical plate and the solution of Pohlhausen, Schmidt and Beckmann has been known for a long time, but no theoretical explanation has ever been provided. In this paper a double-deck structure is introduced to account for the trailing-edge effect. The double-deck solution shows that the flow accelerates near the trailing edge due to the discontinuity of the geometry of the solid plate which results in a less flow constraint. An inward normal flow is induced by the local flow acceleration and generates a change of the displacement of the thin viscous layer near the plate. Consequently a pressure disturbance is developed due to the flow displacement effect of the thin viscous layer, and is transmitted upstream from the trailing edge. The heat transfer rate predicted by the double-deck theory agrees well with previously developed empirical correlations.