Stanton number

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 Edward Stanton (1865–1931).^[1] It is used to characterize heat transfer in forced convection flows.

$St={\frac {h}{Gc_{p}}}={\frac {h}{\rho uc_{p}}}$

where

h = convection heat transfer coefficient
ρ = density of the fluid
c_p = specific heat of the fluid
u = speed of the fluid

It can also be represented in terms of the fluid's Nusselt, Reynolds, and Prandtl numbers:

\mathrm {St} ={\frac {\mathrm {Nu} }{\mathrm {Re} \,\mathrm {Pr} }}

where

Nu is the Nusselt number;
Re is the Reynolds number;
Pr is the Prandtl number.^[2]

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).

References

^ The Victoria University of Manchester’s contributions to the development of aeronautics
^ Bird, Stewart, Lightfoot (2007). Transport Phenomena. New York: John Wiley & Sons. p. 428. ISBN 978-0-470-11539-8.{{cite book}}: CS1 maint: multiple names: authors list (link)

[1] The Victoria University of Manchester’s contributions to the development of aeronautics

[2] Bird, Stewart, Lightfoot (2007). Transport Phenomena. New York: John Wiley & Sons. p. 428. ISBN 978-0-470-11539-8.{{cite book}}: CS1 maint: multiple names: authors list (link)

[1]

[2]