Mixed convection boundary layer flow over a horizontal plate

The flow of an incompressible fluid with small viscosity around a plate is one of the fundamental problems in fluid mechanics. About 100 years ago Prandtl introduced the concept of boundary layers. This made it possible to calculate the drag coefficent. Boundary layer theory describes the flow field as well near the plate as well as in the wake. However it is not valid near the leading and trailing edge of the plate. In the seventies the concept of interacting boundary layers had been introduced. This made it possible to remove singularities from the solution of the boundary layer equation near the trailing edge. Despite the long history of boundary layer research there are several physically and technically relevant problems in boundary layer theory open. One of these problems is the mixed-convection boundary-layer flow over a cooled horizontal plate in a uniform horizontal free stream. The analysis shows that the boundary layer equations supplemented with the usual boundary and matching conditions fail due to a non-uniqueness of the solution. As a consequence perturbations can propagate upstream in the boundary layer without interacting with the outer flow field and separation. In this project the complete flow and temperature field around a cooled finite plate will be investigated. We expect the trailing edge problem and the wake problem are of crucial importance. The usual triple deck approach has to be generalised to incorporate buoyancy effects. Due to the density differences induced by the cooling of the plate there is a pressure jump across the wake. Thus the outer flow field has to react with a circulation. However the circulation generates a lift force onto the plate. We consider this problem is of fundamental theoretical interest and for the heat transfer at horizontal surfaces of practical interest as well.

Buoyancy driven flows are common to almost everybody. In general heated fluid is lighter than cold one and thus tends to rise upwards. In the current project the effect of buoyancy onto a horizontal flow along a heated plate is considered. Since the buoyancy force is normal to the main flow direction the flow is influenced only indirectly by a non-uniform hydrostatic pressure distribution. Of special interest is the behaviour of the flow close to the trailing edge of the plate and the wake behind the plate. New properties of the triple deck solution at the trailing edge and the far wake have been found. For practical purposes the most important result is that buoyancy due to heating of a plate reduces the lift of the plate due to a (small) angle of attack.