Pressure gradient-influenced two dimensional unsteady boundary layer viscous flow over a flat plate

2D-UNSTEADY BOUNDARY LAYER

Abstract

We study unsteady behavior in 2D BL flow over a flat plate which is moving opposite to unsteady free-stream velocity. It is considered that the power of the distance from the leading edge determines the outer unsteady flow to the power of distance from the leading edge. The system is described by the third-order nonlinear ordinary differential equation that has parameters: k, beta and lambda respectively measure the unsteady, pressure gradient and wedge speed, and thus their effects are studied. Two approaches are used: the available exact solution for a particular set of parameters is modified, rewritten and used to obtain the solution in the convergent series form for other set of parameters; and asymptotic behavior far away from the surface and for strong unsteadiness. There is a good agreement in predicting the wall shear stress and velocity profiles in the BL. The velocity profiles for the pressure gradient have the BL character analogous to the steady solutions. The findings indicate that when there is an adverse pressure gradient, both overshoots and undershoots occur close to the wall surface and move forward farther from the wall. The physical mechanisms underlying these results are explored in detail. There are some interesting results regarding mechanisms linked to an important class of UBL flows.