Stanton number

Physical key figure
Surname	Stanton number
Formula symbol	${\displaystyle {\mathit {St}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {St}}={\frac {\alpha }{v\cdot \rho \cdot c}}}$
${\displaystyle \alpha }$ Heat transfer coefficient ${\displaystyle v}$ speed ${\displaystyle \rho }$ density ${\displaystyle c}$ Specific heat capacity
Named after	Thomas Edward Stanton
scope of application	convective heat transfer

The dimensionless Stanton number is a measure of the relative cooling intensity during the heat transfer by means of a flow onto a wall or a body. It is named after the British engineer Thomas Edward Stanton (1865–1931). Basically, the larger the Stanton number, the faster the process. If a sample is placed in an oven and then the temperature of the oven is increased, if the Stanton number is low, the temperature of the sample will only slowly follow the oven temperature. In the case of a high Stanton number, the temperature of the sample quickly follows the oven temperature. The temperature increase of the sample is linear after a certain time (for a high Stanton number) or after an infinite time (for a low Stanton number). ${\displaystyle {\mathit {St}}}$

definition

The Stanton number can be composed of other dimensionless quantities . It is the ratio of the Nusselt number to the product of the Reynolds and Prandtl numbers :

${\displaystyle {\mathit {St}}={\frac {\mathit {Nu}}{{\mathit {Re}}\cdot {\mathit {Pr}}}}={\frac {\text{Dynamik des Prozesses}}{\text{Fähigkeit, Energie zu speichern}}}}$

Alternatively, the Stanton number can be expressed in terms of dimensions and understood as the ratio of the total heat transferred to the convectively transported heat:

${\displaystyle {\mathit {St}}={\frac {\alpha }{v\cdot \rho \cdot c}}={\frac {\alpha \cdot A\cdot (\vartheta _{\mathrm {u,a} }-\vartheta _{\mathrm {a} })}{\rho \cdot c\cdot V\cdot w}}}$

With

• Heat transfer coefficient ${\displaystyle \alpha \left(\mathrm {\tfrac {W}{m^{2}\cdot K}} \right)}$
• Speed ​​of the flowing fluid ${\displaystyle v}$ ${\displaystyle \left(\mathrm {\tfrac {m}{s}} \right)}$
• Density of the flowing fluid ${\displaystyle \rho }$ ${\displaystyle \left(\mathrm {\tfrac {kg}{m^{3}}} \right)}$
• Specific heat capacity of the flowing fluid ${\displaystyle c}$ ${\displaystyle \left(\mathrm {\tfrac {J}{kg\cdot K}} \right)}$
• Heating rate ${\displaystyle w={\frac {\Delta \vartheta }{t}}\left(\mathrm {\tfrac {^{\circ }C}{s}} \right)}$
• Volume of the body ${\displaystyle V}$ ${\displaystyle \left(\mathrm {m^{3}} \right)}$
• Initial ambient temperature (° C) ${\displaystyle \vartheta _{\mathrm {u,a} }}$
• Initial body temperature (° C) ${\displaystyle \vartheta _{\mathrm {a} }}$
• Area of the body ${\displaystyle A}$ ${\displaystyle \left(\mathrm {m^{2}} \right).}$

The Stanton number can also be used to describe oscillating processes. It is then provided with the index for the angular frequency (not for the heating rate): ${\displaystyle \omega }$

${\displaystyle St_{\omega }={\frac {\alpha \cdot A}{\omega \cdot \rho \cdot c\cdot V}}}$

With

• Angular frequency ${\displaystyle \omega ={\frac {2\pi }{T}}\left(\mathrm {\tfrac {1}{s}} \right).}$

The sample from the above example would not be placed in an oven, but exposed to the outside temperature. The temperature curve of the sample would not be linear after a long time, but would oscillate permanently.

Individual evidence

1. ^ Josef Kunes: Dimensionless Physical Quantities in Science and Engineering . Elsevier, 2012, ISBN 0-12-391458-2 , pp. 201 ( limited preview in Google Book search).