有限厚度的Marangoni對流邊界層問題的解析近似解

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基金項目:

國家自然科學基金資助項目(No.50476083)

Analytical approximate solution to the boundary layer flow of finite thickness Marangoni convection

1. School of Applied Science, University of Science and Technology Beijing, Beijing 100083, China;
2. School of Science, Beijing Institute of Civil Engineering and Architecture, Beijing 100044, China;
3. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China

摘要: 討論了由不同溫度介質的界面張力梯度而誘導的有限厚度Marangoni對流的邊界層問題.假設界面張力是溫度的平方函數,下表面保持恒溫,上表面的溫度是水平距離的線性函數.通過坐標變換和巧妙引入小參數對速度和溫度邊界層控制方程組攝動漸進展開,得到了問題的解析近似解.研究了Marangoni數和Prandtl數對速度、溫度邊界層的影響,對相應的流動特性進行了探討.
- Marangoni對流 /
- 邊界層 /
- 近似解 /
- 漸進展開
Abstract: Marangoni convection induced by surface tension gradient along the liquid of finite thickness was researched. It is assumed that the surface tension is a quadratic function of temperature, the under surface temperature is constant, and the super surface temperature is a linear function of horizontal distance. The Marangoni convection boundary layer problem was solved by an efficient transformation and asymptotic expansion technique, and the analytical approximate solution to this Marangoni convection was obtained. The effects of Marangoni number and Prandtl number on the velocity and temperature boundary layers were discussed and the associated transfer mechanism was analyzed in detail.
- Marangoni convection /
- boundary layer /
- approximate solution /
- asymptotic expansion