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斯坦頓數

斯坦頓數(Stanton number)簡稱St,是描述流體熱傳量和本身熱容量比例的無因次量。斯坦頓數得名自Thomas Edward Stanton (1865–1931)[1]。斯坦頓數可用來描述強制對流下的传热特性。

其中

斯坦頓數也可以用努塞尔数雷诺数普朗特数表示[2]

其中

斯坦頓數常用來考慮動量邊界層及熱邊界層的相似性時出現[3],可以用來表示管壁剪力(因為黏度造成)以及管壁總熱傳(因為热扩散率造成)之間的關係。

質傳

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利用熱傳及質傳類似的特性,也可以用舍伍德数施密特數取代努塞爾數和普朗特數,得到質傳的等效斯坦頓數[4]

其中

  • 為質傳的斯坦頓數
  • 為舍伍德数
  • 為雷諾數
  • 為施密特數
  • 是依濃度差來定義(kg s−1 m−2
  • 為流體速度
  • 為通量中物質的密度

邊界層流

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斯坦頓數可以用來量測平板表面附近因為熱傳造成,邊界層熱能增加或是減少的速率。若焓厚度(enthalpy thickness)定義為[5]

則斯坦頓數可以等效如下式[6]

上式是針對平板的邊界層流,且平板的溫度及特性都是相同的。

Reynolds-Colburn類比的相關性

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利用有關有粘性次層流及thermal log紊流模型的Reynolds-Colburn類比特性,可以得到以下紊流熱傳的公式[7]

其中

參考資料

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  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. 
  3. ^ [oer.pusan.ac.kr/file/download?id=215 Chapter 6. Introduction to convection]
  4. ^ BINAY K. DUTTA. PRINCIPLES OF MASS TRANSFER AND SEPERATION PROCESSES. PHI Learning Pvt. Ltd. 21 January 2007: 103–. ISBN 978-81-203-2990-4. 
  5. ^ Reynolds Number. [2019-07-15]. (原始内容存档于2020-01-31). 
  6. ^ Kays, Crawford, Weigand. Convective Heat and Mass Transfer. McGraw-Hill. 2005. 
  7. ^ Lienhard, Lienhard. A Heat Transfer Texbook. Phlogiston Press. 2012. 
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斯坦頓數
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