Mixed Convection on a Vertical Flat Plate With Transition and Separation

A numerical method has been developed and used to calculate the flow properties of laminar, transitional, and turbulent boundary layers on a vertical flat plate with heat transfer. The governing boundary-layer equations include a buoyancy-force term and are solved by a two-point finite-difference method due to Keller and results obtained for heating and cooling and, in the case of the laminar flows, for an isothermal surface corresponding to that of Merkin. Cooled plates with unheated sections can give rise to boundary-layer separation and reattachment and, on occasions, transition can occur within the separation bubble. Flows of this type have been examined with the inviscid-viscous interaction procedure developed by Cebeci and Stewartson and the location of transition obtained by the eⁿ method based on the linear stability theory for air with Pr = 1. Results are given in dimensionless form as a function of Reynolds number, Richardson number, and Prandtl number and quantify those parameters that give rise to separation. Consequences of the use of interaction and stability theory are examined in detail.