Chapter 7, Problem 7.6P

Consider a steady, turbulent boundary layer on and isothermal flat plate of temperature $T_s.$ The boundary layer is "tripped" at the leading edge $x=0$ by a fine wire. Assume constant physical properties and velocity and temperature profiles of the form
   $\frac{u}{u_{\infty }}={\left(\frac{y}{\delta }\right)}^{1/7}\text{and}\frac{T-T_{\infty }}{T_s-T_{\infty }}=1-{\left(\frac{y}{{\delta }_t}\right)}^{1/7}$

1. From experiment it is known that the surface shear stress is related to the boundary layer thickness by an expression of the form
   ${\tau }_s=0.0228\rho u_{\infty }^2{\left(\frac{u_{\infty }\delta }{v}\right)}^{-1/4}$
Beginning with the momentum integral equation (Appendix G), show that
$\delta /x=0.376{\mathrm{Re}}_x^{-1/5}.$
Determine the average friction coefficient ${\bar{C}}_{f,x}.$

2. Beginning with the energy integral equation, obtain an expression for the local Nusselt number $N{u}_x$ and use this result to evaluate the average Nusselt number ${\overline{Nu}}_x.$