# Nusselt number

The **Nusselt number** (**Nu**) is the ratio of convective to conductive heat transfer.

where is the convective heat transfer coefficient, is a characteristic length, and is the thermal conductivity of the fluid.

- The characteristic length depends on the geometry and flow direction of the fluid.
- 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.

The Nusselt number can either be an average, sometimes reported with an overbar such as , or a local (non-averaged) value that depends on a distance, often reported with a subscript , .

The mass transfer analog of the Nusselt number is the Sherwood number.

## Empirical Correlations

**free convection**: the Nusselt number is typically a function of the Grashof number and the Prandtl number, written as**forced convection**: the Nusselt number is generally a function of the Reynolds number and the Prandtl number, written as

### Forced convection in pipes

Forced convection can either be turbulent or laminar. Common correlations are given in the table below

Correlation | Equation | Validity | Other comments |
---|---|---|---|

Gnielinski | , | The friction factor can be obtained from the Moody chart or appropriate correlation | |

Sieder-Tate | , , | is the fluid viscosity at the bulk fluid temperature and is the fluid viscosity at the heat-transfer boundary surface temperature. | |

Dittus-Boelter | , , | for the fluid being heated, and for the fluid being cooled. It is easy to solve but is less accurate when there is a large temperature difference across the fluid. It is tailored to smooth tubes, so use for rough tubes (most commercial applications) is cautioned. | |

Laminar flow with constant heat flux | |||

Laminar flow with constant surface temperature |