Discussion
Consider incompressible laminar flow over a flat plate with freestream velocity of \(u_{\infty}\). The Nusselt number corresponding to this flow velocity is \(Nu_{1}\). If the freestream velocity is doubled, the Nusselt number changes to \(Nu_{2}\). Choose the correct option for \(Nu_{2}/Nu_{1}\).
Answer: A
The ratio \(Nu_{2}/Nu_{1}\) is \(\sqrt{2}\).
For laminar flow over a flat plate, both the local and the average Nusselt numbers follow \(Nu \propto Re^{1/2}Pr^{1/3}\); for example the average value is \(\overline{Nu}_{L} = 0.664\,Re_{L}^{1/2}Pr^{1/3}\). With the same fluid and plate, doubling the freestream velocity doubles the Reynolds number:
\[ \begin{aligned} \frac{Nu_{2}}{Nu_{1}} &= \left(\frac{Re_{2}}{Re_{1}}\right)^{1/2} \\ &= \sqrt{2} \end{aligned} \]
2 would require Nu to vary linearly with Re. 1.26 is \(2^{1/3}\), the effect of doubling the Prandtl number rather than the velocity, and 1 would mean the heat transfer did not depend on velocity at all.
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