Dimensionless quantity characterizing the ratio of convective to conductive heat transfer across (normal to) the boundary:

(1)	$\begin{array}{l}\displaystyle {\rm Nu} = \frac{\rm Convective \ heat \ transfer}{\rm Conductive \ heat \ transfer} = \frac{U}{\lambda / L} =\frac{U \cdot L}{\lambda }\end{array}$

where $\begin{array}{l}U\end{array}$ is the convective heat transfer coefficient of the flow, $\begin{array}{l}L\end{array}$ is the characteristic length, $\begin{array}{l}\lambda\end{array}$ is the thermal conductivity of the fluid.

(2)	$\begin{array}{l}\displaystyle {\rm Nu}=3.66\end{array}$

For transient and turbulent flow in pipelines the Nusselt number can be estimated through empirical correlation (Gnielinski):

(3)	$\begin{array}{l}\displaystyle {\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr} }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) }\end{array}$

where

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See also