Blasius boundary layer approach

Equation 11.12 does not fit velocity profiles measured in a turbulent boundary layer and an alternative approach must be used. In the simplified treatment of the flow conditions within the turbulent boundary layer the existence of the buffer layer, shown in Figure 11.1, is neglected and it is assumed that the boundary layer consists of a laminar sub-layer, in which momentum transfer is by molecular motion alone, outside which there is a turbulent region in which transfer is effected entirely by eddy motion (Figure 11.7). The approach is based on the assumption that the shear stress at a plane surface can be calculated from the simple power law developed by Blasius, already referred to in Chapter 3. 

Similarity is perhaps best know in the context of external boundary-layer flow, such as the Blasius solution (cf., the books by Schlichting [350] or White [429]). In these cases an independent-variable transformation is found in which a single new independent variable is a special combination of the physical spatial coordinates. In this book we are generally more concerned with internal flows where the approaches to finding similarity can differ. 

The form of Eq. 6.241 applies for Re, < 4 x 106, where the Blasius skin friction equation (Eq. 6.16) is reasonably accurate and 2 St cf = PrM and Pr-04 for laminar and turbulent flow, respectively. It also uses the laminar reference enthalpy approach to define p p /pcpc (see the section on uniform free-stream conditions) and uses the turbulent boundary layer transfor-... 

It appears that our measurement follows the Smith model. But it is noted that the Reynolds number of our data for low Gortler parameter is considerably small. Then, it seems that the Blasius flow no longer holds good for those data. In connection with this problem Ragab and Nayfeh computed the neutral stability curves taking into account of the effect of displacement thickness of boundary layer. According to their results the curves approach to that of the Smith model departing from that of modified Smith model at low wave number when R becomes small. 

In section 3.IOC an exact solution was obtained for the velocity profile for isothermal laminar flow past a flat plate. The solution of Blasius can be extended to include the convective heat-transfer problem for the same geometry and laminar flow. In Fig. 5.7-1 the thermal boundary layer is shown. The temperature of the fluid approaching the plate is Tjj and that of the plate is Tg at the surface. 

As discussed in the analysis of the hydrodynamic boundary layer, the Blasius solution is accurate but limited in its scope. Other more complex systems cannot be solved by this method. The approximate integral analysis was used by von Karman to calculate the hydrodynamic boundary layer and was covered in Section 3.10. This approach can be used to analyze the thermal boundary layer. 

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