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.
Formula
where
- h = convection heat transfer coefficient
- ρ = density of the fluid
- cp = 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:
where
- Nu is the Nusselt number;
- Re is the Reynolds number;
- Pr is the Prandtl number.[3]
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.
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 (kg s−1 m−2);
- 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:[5]
Then the Stanton number is equivalent to
for boundary layer flow over a flat plate with a constant surface temperature and properties.[6]
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[7]
where
See also
Strouhal number, an unrelated number that is also often denoted as .
References
- ↑ Hall, Carl W. (2018). Laws and Models: Science, Engineering, and Technology. CRC Press. pp. 424–. ISBN 978-1-4200-5054-7.
- ↑ 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.
- ↑ Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2006). Transport Phenomena. John Wiley & Sons. p. 428. ISBN 978-0-470-11539-8.
- 1 2 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.
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: CS1 maint: others (link) - ↑ Crawford, Michael E. (September 2010). "Reynolds number". TEXSTAN. Institut für Thermodynamik der Luft- und Raumfahrt - Universität Stuttgart. Retrieved 2019-08-26.
- ↑ Kays, William; Crawford, Michael; Weigand, Bernhard (2005). Convective Heat & Mass Transfer. McGraw-Hill. ISBN 978-0-07-299073-7.
- ↑ Lienhard, John H. (2011). A Heat Transfer Textbook. Courier Corporation. p. 313. ISBN 978-0-486-47931-6.