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邊界層

邊界層示意圖,圖中可看出由層流演變為紊流的過程

邊界層,又称附面层是一個流體力學名詞,表示流體中緊接著管壁或其他固定表面的部份。邊界層是由黏滯力產生的效應,和雷諾數Re有關。

一般提到的邊界層是指速度的邊界層。在邊界層外,流體的速度接近定值,不隨位置而變化。在邊界層內,在固定表面上流速為0,距固定表面越遠,速度會趨近一定值。

流體速度及自由速度

邊界層厚度

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若流體的速度為為該點和固定表面的距離,而流體在不受黏滯力影響的速度為自由速度,則可依下式定義邊界層厚度(也稱作速度邊界層厚度),即速度到達99%自由速度的位置:

邊界層厚度越小,邊界層內速度的變化率越大,可以視為速度的擴散率越大。

不可壓縮流中,位移厚度displacement thickness)δ*或δ1可以用以下的方式定義:

而在可壓縮流中對應的定義如下(為流體密度):

位移厚度可視為若流體沒有黏滯力,其速度為自由速度,若其流量(可壓縮流中為質量流量)和原來流場的流量相同,流體可以減少的厚度。位移厚度可以量度在一流場中,因黏滯力而減少的流量。

以類似的方式可以定義動量厚度momentum thickness)θ或δ2

動量厚度可視為若流體沒有黏滯力,其速度為自由速度,若其總動量和原來流場的動量相同,流體可以減少的厚度。

熱傳的邊界層厚度

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熱傳導中也有熱的邊界層。熱邊界層厚度定義和邊界層厚度類似,是從邊界到溫度為99%原始流體溫度位置的距離。 熱的邊界層厚度越小,表示熱傳的效果越好。

熱傳的邊界層厚度及速度邊界層厚度的關係由普兰特尔数Pr控制。若 Pr=1,兩者厚度相同;若Pr> 1,熱傳邊界層厚度較薄,熱傳的效果較好;若 Pr < 1,熱傳邊界層厚度較厚,熱傳的效果較差(如空氣)。

參考文獻

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  • A.D. Polyanin and V.F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, Boca Raton - London, 2004. ISBN 1-58488-355-3
  • A.D. Polyanin, A.M. Kutepov, A.V. Vyazmin, and D.A. Kazenin, Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, Taylor & Francis, London, 2002. ISBN 0-415-27237-8
  • Herrmann Schlichting, Klaus Gersten, E. Krause, H. Jr. Oertel, C. Mayes "Boundary-Layer Theory" 8th edition Springer 2004 ISBN 3-540-66270-7
  • John D. Anderson, Jr, "Ludwig Prandtl's Boundary Layer", Physics Today, December 2005
  • Anderson, John. Fundamentals of Aerodynamics 2nd edition. Toronto: McGraw-Hill. 1991: 711–714. ISBN 0-07-001679-8. 
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邊界層
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