Stanton number

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

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).

Mass Transfer[edit]

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

  • St_m is the mass Stanton number;
  • Sh is the Sherwood number;
  • Re is the Reynolds number;
  • Sc is the Schmidt number;
  • is defined based on a concentration difference (kg s−1 m−2);
  • is the component density of the species in flux.

Boundary Layer Flow[edit]

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 [3]

Then the Stanton number is equivalent to [4]

for boundary layer flow over a flat plate with a constant surface temperature and properties.

Correlations using Reynolds-Colburn Analogy[edit]

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 [5]

where

References[edit]

  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. 
  3. ^ Reynolds Number
  4. ^ Kays, Crawford, Weigand (2005). Convective Heat and Mass Transfer. McGraw-Hill. 
  5. ^ Lienhard, Lienhard (2012). A Heat Transfer Texbook. Phlogiston Press.