Laminar Boundary Layer on a Flat Plate

Consider a uniform free stream of speed that flows parallel to an infinitesimally thin semi-infinite flat plate as shown in Fig. 5.9.1(a). A coordinate system can be defined such that the flow begins at leading edge of the plate which is considered as the origin of the plate. Since the flow is symmetric about x -axis, only the upper half of the flow can be considered. The following assumptions may be made in the discussions;

• •  The nature of the flow is steady, incompressible and two-dimensional.

•  The Reynolds number is high enough that the boundary layer approximation is reasonable.

•  The boundary layer remains laminar over the entire flow domain.

Fig. 5.9.1: Boundary layer on a flat plate: (a) Outer inviscid flow and thin boundary layer; (b) Similarity behavior of boundary layer at any x-location.

 

The outer flow is considered without the boundary layer and in this case, U is a constant so that . Referring to Fig. 5.9.1, the boundary layer equations and its boundary conditions can be written as follows;

(5.9.1)

Boundary conditions:

(5.9.2)