General Von Mises Boundary Layer

We begin with the general boundary-layer equations (Section 7.2) where the stream function takes the form 

An additional transformation may be used to convert the (r coordinate to a normalized stream function , which facilitates treatment of mass loss or gain at the boundaries such as can occur at a chemically reacting surface. The normalized stream function is defined as 

To transform the governing equations from the x, y) to the (x, -) coordinates the partial derivatives with respect to x and y need to be re-evaluated in terms of x and as follows  

The continuity equation, Eq. 7.38, is satisfied trivially by definition when expressed in (jc, ) coordinates. As a result it is eliminated, in the sense that it is not considered explicitly in a solution algorithm. The momentum equation, Eq. 7.39, transforms to 

With some further manipulation the momentum equation can be simplified as 9m pu 

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Fig. 7.5 A simple DAE problem to illustrate the need for consistent initial conditions. 7.7 GENERAL VON MISES BOUNDARY LAYER...

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