Hydrodynamic Boundary Layer on a Flat Plate

Statement of the problem. Numerous practical applications stimulated the appearance of a vast variety of papers dealing with the boundary layer theory 

Let us consider a steady-state isothermal flow of a power-law fluid past a thin flat plate. The velocity of the incoming flow is U. We assume that the coordinates X and Y are directed along the plate and transverse to the plate, respectively, and the origin is placed at the front edge of the plate. We denote the tangential and transverse velocities by Vx and Vy, respectively. 

The main dimensionless parameter for power-law fluids is the generalized Reynolds number introduced by the formula 

At high Reynolds numbers, the terms in the equation of motion (see Supplement 6) and in the continuity equation with regard to the expressions (6.1.1) and (6.1.4) can be estimated by the same scheme as for Newtonian fluids. As a result, after isolating the leading terms of the corresponding asymptotic expansions, we obtain 

These equations, which are considered in the domain X 0, Y 0, must be supplemented by the boundary conditions 

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Hydrodynamic and Thermal Boundary Layers on a Flat Plate, Where Heating Starts at x = Xo... 

FIGURE 2.3-17 Hydrodynamic and composiston boundary layers on a flat plate. 

Instead of the numerical factor 4.0 in Equation 7.10, hydrodynamic theory predicts a factor near 6.0 for the effective boundary layer thickness adjacent to a flat plate (both numbers increase about 3% per 10°C Schlichting and Gersten, 2003). However, wind tunnel measurements under an appropriate turbulence intensity, as well as field measurements, indicate that 4.0 is more suitable for leaves. This divergence from theory relates to the relatively small size of leaves, their irregular shape, leaf curl, leaf flutter, and, most important, the high turbulence intensity under field conditions. Moreover, the dependency of 6bl on /° 5, which applies to large flat surfaces, does... 

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