Editing Nusselt number (section)

==Definition==
The Nusselt number is the ratio of total heat transfer (convection + conduction) to conductive heat transfer across a boundary. The convection and conduction heat flows are [[Parallel (geometry)|parallel]] to each other and to the surface normal of the boundary surface, and are all [[perpendicular]] to the [[mean]] fluid flow in the simple case.

:<math>\mathrm{Nu}_L = \frac{\mbox{Total heat transfer }}{\mbox{Conductive heat transfer }} = \frac{h}{k/L} = \frac{hL}{k}</math>

where ''h'' is the [[convective]] [[heat transfer coefficient]] of the flow, ''L'' is the [[characteristic length]], and ''k'' is the [[thermal conductivity]] of the fluid.

* Selection of the characteristic length should be in the direction of growth (or thickness) of the boundary layer; some examples of characteristic length are: the outer diameter of a cylinder in (external) [[cross flow]] (perpendicular to the cylinder axis), the length <!-- height or width? --> of a vertical plate undergoing [[natural convection]], or the diameter of a sphere. For complex shapes, the length may be defined as the volume of the fluid body divided by the surface area.
* The thermal conductivity of the fluid is typically (but not always) evaluated at the [[film temperature]], which for engineering purposes may be calculated as the [[mean]]-average of the bulk fluid temperature and wall surface temperature.

In contrast to the definition given above, known as ''average Nusselt number'', the local Nusselt number is defined by taking the length to be the distance from the surface boundary<ref name="çengel" />{{page needed|date=February 2022}} to the local point of interest.

:<math>\mathrm{Nu}_x = \frac{h_x x}{k}</math>

The ''mean'', or ''average'', number is obtained by integrating the expression over the range of interest, such as:<ref>{{cite journal|title=Transitional natural convection flow and heat transfer in an open channel|year=2012|author=E. Sanvicente|doi=10.1016/j.ijthermalsci.2012.07.004|volume=63|pages=87–104|journal=International Journal of Thermal Sciences|display-authors=etal}}</ref>

:<math>\overline{\mathrm{Nu}}=\frac{\frac{1}{L} \int_0^L h_x\ dx\ L}{k}=\frac{\overline{h} L}{k}</math>