#### Question

Consider a liquid metal $\operatorname{Pr} \ll 1$, 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 (x=0) and boundary conditions, solve this equation for the boundary layer temperature field, T(x, y). 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.

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#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionRandall D. Knight
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