Stanton number


The Stanton number, is a dimensionless number that measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. The Stanton number is named after Thomas Stanton . It is used to characterize heat transfer in forced convection flows.

Formula

where
It can also be represented in terms of the fluid's Nusselt, Reynolds, and Prandtl numbers:
where
The Stanton number arises in the consideration of the geometric similarity of the momentum boundary layer and the thermal boundary layer, where it can be used to express a relationship between the shear force at the wall and the total heat transfer at the wall.

Mass transfer

Using the heat-mass transfer analogy, a mass transfer St equivalent can be found using the Sherwood number and Schmidt number in place of the Nusselt number and Prandtl number, respectively.
where
  • is the mass Stanton number;
  • is the Sherwood number based on length;
  • is the Reynolds number based on length;
  • is the Schmidt number;
  • is defined based on a concentration difference ;
  • is the velocity of the fluid

    Boundary layer flow

The Stanton number is a useful measure of the rate of change of the thermal energy deficit in the boundary layer due to heat transfer from a planar surface. If the enthalpy thickness is defined as:
Then the Stanton number is equivalent to
for boundary layer flow over a flat plate with a constant surface temperature and properties.

Correlations using Reynolds-Colburn analogy

Using the Reynolds-Colburn analogy for turbulent flow with a thermal log and viscous sub layer model, the following correlation for turbulent heat transfer for is applicable
where