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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). It is used to characterize heat transfer in forced convection flows.

Formula

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

where

• h = convection heat transfer coefficient
• G = mass flux of the fluid
• ρ = density of the fluid
• c_p = specific heat of the fluid
• u = velocity of the fluid

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

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

where

• Nu is the Nusselt number;
• Re is the Reynolds number;
• Pr is the Prandtl number.

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).

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.

${\displaystyle \mathrm {St} _{m}={\frac {\mathrm {Sh_{L}} }{\mathrm {Re_{L}} \,\mathrm {Sc} }}}$

${\displaystyle \mathrm {St} _{m}={\frac {h_{m}}{\rho u}}}$

where

• ${\displaystyle St_{m}}$ is the mass Stanton number;
• ${\displaystyle Sh_{L}}$ is the Sherwood number based on length;
• ${\displaystyle Re_{L}}$ is the Reynolds number based on length;
• ${\displaystyle Sc}$ is the Schmidt number;
• ${\displaystyle h_{m}}$ is defined based on a concentration difference (kg s m);
• ${\displaystyle u}$ 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 (or excess) in the boundary layer due to heat transfer from a planar surface. If the enthalpy thickness is defined as:

${\displaystyle \Delta _{2}=\int _{0}^{\infty }{\frac {\rho u}{\rho _{\infty }u_{\infty }}}{\frac {T-T_{\infty }}{T_{s}-T_{\infty }}}dy}$

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.

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

${\displaystyle \mathrm {St} ={\frac {C_{f}/2}{1+12.8\left(\mathrm {Pr} ^{0.68}-1\right){\sqrt {C_{f}/2}}}}}$

where

${\displaystyle C_{f}={\frac {0.455}{\left^{2}}}}$

See also

Strouhal number, an unrelated number that is also often denoted as ${\displaystyle \mathrm {St} }$.

References

1. Hall, Carl W. (2018). Laws and Models: Science, Engineering, and Technology. CRC Press. pp. 424–. ISBN 978-1-4200-5054-7.
2. Ackroyd, J. A. D. (2016). "The Victoria University of Manchester's contributions to the development of aeronautics" (PDF). The Aeronautical Journal. 111 (1122): 473–493. doi:10.1017/S0001924000004735. ISSN 0001-9240. S2CID 113438383. Archived from the original (PDF) on 2010-12-02.
3. Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2006). Transport Phenomena. John Wiley & Sons. p. 428. ISBN 978-0-470-11539-8.
4. ^ Fundamentals of heat and mass transfer. Bergman, T. L., Incropera, Frank P. (7th ed.). Hoboken, NJ: Wiley. 2011. ISBN 978-0-470-50197-9. OCLC 713621645.{{cite book}}: CS1 maint: others (link)
5. Crawford, Michael E. (September 2010). "Reynolds number". TEXSTAN. Institut für Thermodynamik der Luft- und Raumfahrt - Universität Stuttgart. Retrieved 2019-08-26.
6. Kays, William; Crawford, Michael; Weigand, Bernhard (2005). Convective Heat & Mass Transfer. McGraw-Hill. ISBN 978-0-07-299073-7.
7. Lienhard, John H. (2011). A Heat Transfer Textbook. Courier Corporation. p. 313. ISBN 978-0-486-47931-6.

• Dimensionless numbers of fluid mechanics
• Dimensionless numbers of thermodynamics
• Eponymous numbers
• Eponyms in physics
• Fluid dynamics