Número de Stanton

Se define como:

${\displaystyle \mathrm {St} ={\frac {\text{Convección de calor}}{\text{Potencia de calor almacenada}}}}$

Deducción

	1	2	3	4
Ecuaciones	${\displaystyle \mathrm {St} ={\frac {h\ d^{2}\ \Delta T}{{\dot {m}}\ c_{p}\ \Delta T}}}$	${\displaystyle {\dot {m}}={\frac {m}{t}}}$	${\displaystyle \rho ={\frac {m}{d^{2}\ L}}}$	${\displaystyle u={\frac {L}{t}}}$
Simplificando	${\displaystyle \mathrm {St} ={\frac {h\ d^{2}}{{\dot {m}}\ c_{p}}}}$
Sustituyendo	${\displaystyle \mathrm {St} ={\frac {h\ d^{2}}{(m\ /\ t)\ c_{p}}}}$
Multiplicando ${\displaystyle {\Bigl (}{\frac {L}{L}}{\Bigr )}}$	${\displaystyle \mathrm {St} ={\frac {h\ d^{2}}{(m\ /\ t)\ c_{p}}}{\Bigl (}{\frac {L}{L}}{\Bigr )}}$
Ordenando	${\displaystyle \mathrm {St} ={\frac {h}{c_{p}\ [m\ /\ (d^{2}\ L))]\ [L/t]}}}$
Sustituyendo	${\displaystyle \mathrm {St} ={\frac {h}{c_{p}\ \rho \ u}}}$

${\displaystyle \mathrm {St} ={\frac {h}{c_{p}\ \rho \ u}}}$

Deducción

	1	2	3	4
Ecuaciones	${\displaystyle \mathrm {St} ={\frac {h}{c_{p}\,\rho \,u}}}$	${\displaystyle \mathrm {Nu} ={\frac {h\ d}{k}}}$	${\displaystyle \mathrm {Re} ={\frac {\rho \ u\ d}{\mu }}}$	${\displaystyle \mathrm {Pr} ={\frac {\mu \ c_{p}}{k}}}$
Multiplicando ${\displaystyle {\Bigl (}{\frac {\mu \ k\ d}{\mu \ k\ d}}{\Bigr )}}$	${\displaystyle \mathrm {St} ={\frac {h}{c_{p}\,\rho \,u}}{\Bigl (}{\frac {\mu \ k\ d}{\mu \ k\ d}}{\Bigr )}}$
Ordenando	${\displaystyle \mathrm {St} ={\Bigl (}{\frac {h\ d}{k}}{\Bigr )}{\Bigl (}{\frac {k}{\mu \ c_{p}}}{\Bigr )}{\Bigl (}{\frac {\mu }{\rho \ u\ d}}{\Bigr )}}$
Sustituyendo	${\displaystyle \mathrm {St} ={\frac {\mathrm {Nu} }{\mathrm {Re} \ \mathrm {Pr} }}}$

${\displaystyle \mathrm {St} ={\frac {\mathrm {Nu} }{\mathrm {Re} \ \mathrm {Pr} }}}$