Controlling the separation of laminar boundary layers in water - Heating and suction

We present an analysis of the minimum surface overheat, TW — T(XJ that will delay separation of a laminar boundary layer for a prescribed adverse pressure gradient in water. The analysis is for a Falkner-Skan wedge flow corresponding to negative values of ft. The energy and momentum equations are coupled through the viscosity variation with temperature. We employ a high Prandtl number approximation to obtain an asymptotic solution to these equations. The heat-transfer and viscosity variations are localized to a thin layer near the wall, well within the momentum boundary layer, and their primary effect on separation is to provide a "slip" velocity for the outer main parts of the flow, enabling the outer, shear-layer like part of the flow to sustain a more adverse pressure gradient than it could in the absence of heating. Although heating does delay separation, its effect is shown to be small for practical values of wall overheat, particularly compared to the effect of suction. For example, a suction velocity ratio of less than 0.0001 would have a comparable effect in maintaining an attached flow as an overheat of 40°F.