Laminar boundary layer integral method

The foregoing analysis considered the fluid dynamics of a laminar-boundary-layer flow system. We shall now develop the energy equation for this system and then proceed to an integral method of solution. 

Laminar Boundary Layer Theory - The Integral Method... 

It is noted that the integral method gives only approximate values for the mass transfer coefficient as the model derivation is based on several simplifying assumptions regarding the concentration and velocity profiles. Nevertheless, the given relation has been confirmed by experiments for laminar boundary layer flows over a flat plate (e.g., [134], p 80 and p 201 [27], p 345). 

Introduction and derivation of integral expression. In the solution for the laminar boundary layer on a fiat plate, the Blasius solution is quite restrictive, since it is for laminar flow over a flat plate. Other more complex systems cannot be solved by this method. An approximate method developed by von Karman can be used when the configuration is more complicated or the flow is turbulent. This is an approximate momentum integral analysis of the boundary layer using an empirical or assumed velocity distribution. 

Some of the commonly used methods for obtaining solutions to problems involving laminar external flows have been discussed in this chapter. Many such problems can be treated with adequate accuracy using the boundary layer equations and similar ity integral and numerical methods of solving these equations have been discussed. A brief discussion of the solution of the full governing equations has also been presented. 

The physical situation where the fluid stream parallel to the moving plate is in an opposite direction to the motion of the plate (Fig. 18.11c) is also encountered in materials processing. Using a similarity method, Klemp and Acrivos [75] found that a critical value of the moving surface to the free stream velocity ratio (A/ = USIUJ) was 0.3541. The inability to obtain similarity solutions of the boundary layer equations for laminar flow was attributed to the boundary layer separation from the moving plate. Similarity and integral solutions for fluid friction... 

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