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TheStanton number (St), is adimensionless number that measures the ratio of heat transferred into a fluid to thethermal capacity of fluid. The Stanton number is named afterThomas Stanton (engineer) (1865–1931).^{[1][2]: 476} It is used to characterizeheat transfer in forcedconvection flows.

${\displaystyle \mathrm{S}\mathrm{t}=\frac{h}{G{c}_p}=\frac{h}{\rho u{c}_p}}$

where

• h =convectionheat 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'sNusselt,Reynolds, andPrandtl numbers:

${\displaystyle \mathrm{S}\mathrm{t}=\frac{\mathrm{N}\mathrm{u}}{\mathrm{R}\mathrm{e}\mathrm{P}\mathrm{r}}}$

where

• Nu is theNusselt number;
• Re is theReynolds number;
• Pr is thePrandtl number.^[3]

The Stanton number arises in the consideration of the geometric similarity of the momentumboundary layer and the thermal boundary layer, where it can be used to express a relationship between theshear force at the wall (due toviscous drag) and the total heat transfer at the wall (due tothermal diffusivity).

Using the heat-mass transfer analogy, a mass transfer St equivalent can be found using theSherwood number andSchmidt number in place of the Nusselt number and Prandtl number, respectively.

${\displaystyle {\mathrm{S}\mathrm{t}}_m=\frac{\mathrm{S}{\mathrm{h}}_{\mathrm{L}}}{\mathrm{R}{\mathrm{e}}_{\mathrm{L}}\mathrm{S}\mathrm{c}}}$^[4]

${\displaystyle {\mathrm{S}\mathrm{t}}_m=\frac{h_m}{\rho u}}$^[4]

where

• ${\displaystyle S{t}_m}$ is the mass Stanton number;
• ${\displaystyle S{h}_L}$ is the Sherwood number based on length;
• ${\displaystyle R{e}_L}$ 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⁻¹ m⁻²);
• ${\displaystyle u}$ 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:^[5]

${\displaystyle {\mathrm{\Delta }}_2={\int }_0^{\mathrm{\infty }}\frac{\rho u}{{\rho }_{\mathrm{\infty }}{u}_{\mathrm{\infty }}}\frac{T-T_{\mathrm{\infty }}}{T_s-T_{\mathrm{\infty }}}dy}$

Then the Stanton number is equivalent to

${\displaystyle \mathrm{S}\mathrm{t}=\frac{d{\mathrm{\Delta }}_2}{dx}}$

for boundary layer flow over a flat plate with a constant surface temperature and properties.^[6]

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]

${\displaystyle \mathrm{S}\mathrm{t}=\frac{C_f/2}{1+12.8\left({\mathrm{P}\mathrm{r}}^{0.68}-1\right)\sqrt{C_f/2}}}$

where

${\displaystyle C_f=\frac{0.455}{{\left[\mathrm{l}\mathrm{n}\left(0.06{\mathrm{R}\mathrm{e}}_x\right)\right]}^2}}$

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

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

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