The Stanton number (St), 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 (engineer) (1865–1931).
[1][2]: 476 It is used to characterize heat transfer in forced convection flows.
ρ u
{\displaystyle \mathrm {St} ={\frac {h}{Gc_{p}}}={\frac {h}{\rho uc_{p}}}}
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 (due to viscous drag) and the total heat transfer at the wall (due to thermal diffusivity).
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.
{\displaystyle \mathrm {St} _{m}={\frac {\mathrm {Sh_{L}} }{\mathrm {Re_{L}} \,\mathrm {Sc} }}}
{\displaystyle \mathrm {St} _{m}={\frac {h_{m}}{\rho u}}}
[4] where The Stanton number is a useful measure of the rate of change of the thermal energy deficit (or excess) in the boundary layer due to heat transfer from a planar surface.
If the enthalpy thickness is defined as:[5]
Then the Stanton number is equivalent to
{\displaystyle \mathrm {St} ={\frac {d\Delta _{2}}{dx}}}
for boundary layer flow over a flat plate with a constant surface temperature and properties.
[6] 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[7]
{\displaystyle \mathrm {St} ={\frac {C_{f}/2}{1+12.8\left(\mathrm {Pr} ^{0.68}-1\right){\sqrt {C_{f}/2}}}}}
Strouhal number, an unrelated number that is also often denoted as
{\displaystyle \mathrm {St} }