Blasius Flow Past a Flat Plate

After a pastoral interlude revisiting singular perturbation theory by determining higher order terms in the Method of Matched Asymptotic Expansions and comparing these results with those obtained by the method of multiple scales for the constant coefficient second-order ordinary differential equation treated in Chapter , steady-state Blasius boundary-layer flow of a viscous fluid streaming uniformly past a flat plate is investigated. This is accomplished by applying singular perturbation theory techniques to the governing partial differential equation satisfied by the relevant stream function governing that flow. The solution of the resulting boundary-layer equation to lowest order requires a similarity solution argument. When the drag on the plate is calculated for that lowest order solution it is nonzero resolving D’Alembert’s paradox in this instance. In order to make an interpretation of these results the second order term in the outer free stream solution is calculated and compared with that deduced for inviscid flow past an effective body consisting of the flat plate plus the boundary layer. The problems involve two extensions: The first extending the singular perturbation techniques developed in the pastoral interlude for a constant coefficient example to a variable coefficient one and the second extending the Blasius flow methodology employed in the chapter for a uniform stream flow situation to a variable flow one.