I had a look at it and after a few minutes I got a transformed result, but indeed it is not the one given. However there seems to be a term missing in the left hand side containing the time t. After using the transformation I got (without the term with the time):
[tex]u^*\frac{\partial u^*}{\partial x^*}+ v^*\frac{\partial u^*}{\partial y^*}= m\cdot \frac{U^{n-1}}{L^n}\cdot \left[M\cdot \theta + \frac{\partial}{\partial y^*} \left[\left|\frac{\partial u^*}{\partial y^*}\right| ^{n-1} \right]\cdot \frac{\partial u^*}{\partial y^*}\right][/tex]
Maybe the term with t can shed some light on the necessary next step, otherwise I do not see how to reach the end result.
coomast