Integral balances can also be used for heat transfer in a turbulent-flow boundary layer if a form for the velocity profile is assumed. A common form is the 1/7th-power law:

\[\frac{v}{v_{\infty}}=\left(\frac{y}{\delta}\right)^{1 / 7}\]

Assume that the temperature is of the same form and also that the thermal and heat boundary layers are of the same thickness. From this derive an expression for \(N u_{x}\). How does this compare with the solutions described in the text?