Nusselt number

From Chemepedia

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