Stanton number

$\backslash mathrm\{St\}\; =\; \backslash frac\{h\}\{G\; c\_p\}\; =\; \backslash frac\{h\}\{\backslash rho\; u\; c\_p\}$

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:

:$\backslash mathrm\{St\}\; =\; \backslash frac\{\backslash mathrm\{Nu\}\}\{\backslash mathrm\{Re\}\backslash ,\backslash mathrm\{Pr\}\}$

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).

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.

$\backslash mathrm\{St\}\_m\; =\; \backslash frac\{\backslash mathrm\{Sh\_L\}\}\{\backslash mathrm\{Re\_L\}\backslash ,\backslash mathrm\{Sc\}\}${{Cite book|title=Fundamentals of heat and mass transfer.|date=2011|publisher=Wiley|others=Bergman, T. L., Incropera, Frank P.|isbn=978-0-470-50197-9|edition=7th|location=Hoboken, NJ|oclc=713621645}}

$\backslash mathrm\{St\}\_m\; =\; \backslash frac\{h\_m\}\{\backslash rho\; u\}$

where

• $St\_m$ is the mass Stanton number;
• $Sh\_L$ is the Sherwood number based on length;
• $Re\_L$ is the Reynolds number based on length;
• $Sc$ is the Schmidt number;
• $h\_m$ is defined based on a concentration difference (kg s⁻¹ m⁻²);
• $u$ is the velocity of the fluid

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:

$\backslash Delta\_2\; =\; \backslash int\_0^\backslash infty\; \backslash frac\{\backslash rho\; u\}\{\backslash rho\_\backslash infty\; u\_\backslash infty\}\; \backslash frac\{T\; -\; T\_\backslash infty\}\{T\_s\; -\; T\_\backslash infty\}\; d\; y$

Then the Stanton number is equivalent to

$\backslash mathrm\{St\}\; =\; \backslash frac\{d\; \backslash Delta\_2\}\{d\; x\}$

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

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

$\backslash mathrm\{St\}\; =\; \backslash frac\{C\_f\; /\; 2\}\{1\; +\; 12.8\; \backslash left(\; \backslash mathrm\{Pr\}^\{0.68\}\; -\; 1\; \backslash right)\; \backslash sqrt\{C\_f\; /\; 2\}\}$

where

$C\_f\; =\; \backslash frac\{0.455\}\{\backslash left[\; \backslash mathrm\{ln\}\; \backslash left(\; 0.06\; \backslash mathrm\{Re\}\_x\; \backslash right)\; \backslash right]^2\}$

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

{{Reflist|refs=

{{cite book|last1=Bird|first1=R. Byron |last2=Stewart|first2=Warren E. |last3=Lightfoot|first3=Edwin N. |title=Transport Phenomena|url=https://books.google.com/books?id=L5FnNlIaGfcC&pg=PA428|year=2006|publisher=John Wiley & Sons|isbn=978-0-470-11539-8|page=428}}

{{cite journal|last1=Ackroyd|first1=J. A. D.|title=The Victoria University of Manchester's contributions to the development of aeronautics|journal=The Aeronautical Journal|volume=111|issue=1122|year=2016|pages=473–493|issn=0001-9240|doi=10.1017/S0001924000004735|s2cid=113438383|url=http://www.raes.org.uk/pdfs/3164COLOUR.pdf|archive-url=https://web.archive.org/web/20101202210527/http://www.raes.org.uk/pdfs/3164COLOUR.pdf|archive-date=2010-12-02}}

{{cite book|last=Hall|first=Carl W. |title=Laws and Models: Science, Engineering, and Technology|url=https://books.google.com/books?id=EEhpsf6L09gC&pg=PA424|year=2018|publisher=CRC Press|isbn=978-1-4200-5054-7|pages=424–}}

{{cite book|last1=Kays|first1=William |last2=Crawford|first2=Michael |last3=Weigand|first3=Bernhard |title=Convective Heat & Mass Transfer |url=https://books.google.com/books?id=hiEmjxP6hQkC|year=2005|publisher=McGraw-Hill|isbn=978-0-07-299073-7}}

{{Cite web |title=Reynolds number |last=Crawford |first=Michael E. |work=TEXSTAN |date=September 2010 |access-date=2019-08-26 |url= http://www.texstan.com/ef1.php |publisher=Institut für Thermodynamik der Luft- und Raumfahrt - Universität Stuttgart }}

{{cite book|last=Lienhard|first=John H. |title=A Heat Transfer Textbook|url=https://books.google.com/books?id=P8iV6IjNtI8C&pg=PA313|date= 2011|publisher=Courier Corporation|isbn=978-0-486-47931-6|page=313}}

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