Definition of Nusselt Number
Definition
In fluid mechanics, the dimensionless quantity formed by dividing the product of the heat transfer coefficient $h$ and the characteristic length $L$ by the thermal conductivity $k$ is called the Nusselt number. $$ \mathrm{Nu} := {{h L} \over k} $$
Explanation
Put simply, a high Nusselt number indicates efficient heat transfer, while a low Nusselt number indicates inefficient transfer. In convective heat transfer through a fluid, a high Nusselt number means heat is being transferred effectively; for example, in water-cooled cooling systems it is natural to pursue a high Nusselt number.
Difference from the Biot number
Although the formula may look almost identical to the Biot number, the Biot number pertains to solids, whereas the Nusselt number concerns convective heat transfer within fluids. The Biot number is especially relevant when considering multiple particles: if the Biot number is small, the difference between surface and internal temperatures is negligible, allowing the particles to be treated simply (lumped-capacitance approximation).