# 斯坦頓數

${\displaystyle St={\frac {h}{Gc_{p}}}={\frac {h}{\rho uc_{p}}}}$

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

## 質傳

${\displaystyle \mathrm {St} _{m}={\frac {\mathrm {Sh} }{\mathrm {Re} \,\mathrm {Sc} }}}$

${\displaystyle \mathrm {St} _{m}={\frac {h_{m}}{\rho _{m}u}}}$

• ${\displaystyle St_{m}}$ 為質傳的斯坦頓數
• ${\displaystyle Sh}$ 為舍伍德数
• ${\displaystyle Re}$ 為雷諾數
• ${\displaystyle Sc}$ 為施密特數
• ${\displaystyle h_{m}}$ 是依濃度差來定義（kg s−1 m−2
• ${\displaystyle u}$ 為流體速度
• ${\displaystyle \rho _{m}}$ 為通量中物質的密度

## 邊界層流

${\displaystyle \Delta _{2}=\int _{0}^{\infty }{\frac {\rho u}{\rho _{\infty }u_{\infty }}}{\frac {T-T_{\infty }}{T_{s}-T_{\infty }}}dy}$

${\displaystyle \mathrm {St} ={\frac {d\Delta _{2}}{dx}}}$

### Reynolds-Colburn類比的相關性

${\displaystyle \mathrm {St} ={\frac {C_{f}/2}{1+12.8\left(\mathrm {Pr} ^{0.68}-1\right){\sqrt {C_{f}/2}}}}}$

${\displaystyle C_{f}={\frac {0.455}{\left[\mathrm {ln} \left(0.06\mathrm {Re} _{x}\right)\right]^{2}}}}$

## 參考資料

1. ^ The Victoria University of Manchester’s contributions to the development of aeronautics
2. ^ Bird, Stewart, Lightfoot. Transport Phenomena. New York: John Wiley & Sons. 2007: 428. ISBN 978-0-470-11539-8.