Chapter 7, Problem 7.4P

Consider a liquid metal $\left(\mathrm{Pr}\ll 1\right),$ with free stream conditions $u_{\infty }$ and $T_{\infty },$ in parallel flow over an isothermal flat plate at $T_s.$ Assuming that $u=u_{\infty }$ throughout the thermal boundary layer, write the corresponding form of the boundary layer energy equation. Applying appropriate initial $\left(x=0\right)$ and boundary conditions, solve this equation for the boundary layer temperature field, $T\left(x,y\right).$ Use the result to obtain an expression for the local Nusselt number $N{u}_x.$ Hint: This problem is analogous to one-dimensional heat transfer in a semi-infinite medium with a sudden change in surface temperature.