Discussion
Which of the following non-dimensional terms is an estimate of Nusselt number?
Answer: C
The Nusselt number is a non-dimensional temperature gradient.
At a wall, the convective flux equals the conduction flux through the fluid in contact with it, \(h(T_{s} - T_{\infty}) = -k_{f}\,\partial T/\partial y\) at the wall. Writing \(\theta = (T - T_{s})/(T_{\infty} - T_{s})\) and \(y^{*} = y/L\),
\[ \begin{aligned} Nu &= \frac{hL}{k_{f}} \\ &= \frac{\partial \theta}{\partial y^{*}}\Big|_{y^{*} = 0} \end{aligned} \]
so Nu is the dimensionless temperature gradient at the surface.
The other descriptions are other groups. Internal conduction resistance of a solid over the external convective resistance is the Biot number, \(hL/k_{s}\), which uses the solid's conductivity. Advection over conduction is the Peclet number, \(Re \times Pr\). A non-dimensional velocity gradient at the wall relates to the skin friction coefficient, not to the Nusselt number.
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