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The Nusselt number is a non-dimensional parameter that provides a measure of the convection heat transfer at a surface. It is the ratio of convection to pure conduction heat transfer. We will now derive the Nussult number as a function of the given parameters and temperature.
The convection heat transfer at the pipe wall is:

We can rearrange terms to find an expression for h, the convection coefficient:

Substitute the convection coefficient expression into the Nusselt expression:

where
h is the convection coefficient.
k is the thermal conductivity.
L is the length scale. Similar to the Reynold's Number, the length scale is the diameter of the pipe for an internal pipe flow.
qw q''_wall is the heat flux at the heated surface, 37.5 W/m^2.
Tw is the pipe wall temperature at a given location along the pipe.
Tm is the mean temperature in the pipe at the location where Tw is defined.

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