本文應用數值方法對具有外部流之橢圓管外的紊流薄膜凝結進行分析。為了簡化數學模型以利於計算，在橢圓的幾何形體上並非使用圓形的極座標(r,θ)來進行運算，而是採用以橢圓偏心率表示之橢圓座標，在方程式的運算上應用了庫爾本類比(Colburn Analogy)來預估汽液界面之摩擦阻力再藉此估算出剪應力，並且使用Kato之紊流模式結合Myong之紊流普朗特數來建立紊流渦流擴散率，外部流場則是採用potential flow theory，而在數值運算的方法上則是採用具高收斂性的二分法(Bisection Method)。
此外，本文將統御方程式進行無因次化後可以透過橢圓偏心率、福祿數、界面剪力參數、普朗特數以及過冷效應等無因次參數，分析紊流薄膜凝結的薄膜厚度、速度分布、溫度梯度及溫度分布、局部熱傳率還有平均熱傳率，了解參數與結果間的關係，並在偏心率為零之圓管特例與相關文獻對比，藉此對方法的可行性以及結果的準確性進行驗證。
而從研究結果中可以了解，液膜膜厚會隨著過冷效應參數、普朗特數以及福祿數的增加而上升，但會因為偏心率的提高而減少。局部熱傳率則是隨著福祿數、普朗特數以及界面剪力參數的提高而上升，但會隨著過冷效應數參數的增加而減少。而平均熱傳率則是隨著界面剪力參數、福祿數以及普朗特數的提高而上升，但會隨著橢圓偏心率以及過冷效應參數的提高而減少。

This research analyzes the problem of turbulent film condensation on the elliptical tube with external flow. To simplify the mathematical model, the coordinates are represented by the ellipse eccentricity, and the Colburn analogy is used to estimate the frictional resistance. And use Kato's turbulent model and Myong's turbulent Prandtl number model to establish the eddy diffusivity, and the external flow uses the potential flow, and the numerical method is Bisection Method which have high convergence and haven’t initial value problem. And investigate the condensation film thickness, velocity distribution, temperature gradient, temperature distribution, local and mean heat transfer coefficient by ellipse eccentricity, Froude number, interfacial shear parameter, Prandtl number, and sub-cooling parameter. Show the relationship between the parameter and result, and verify the accuracy of the model by comparing it with related research.
The results show that the film thickness gets higher by the higher sub-cooling parameter, Prandtl number, Froude number, and interfacial shear parameter, lower ellipse eccentricity. The local heat transfer coefficient gets higher by the Froude number, Prandtl number, and interfacial shear parameter, the lower sub-cooling parameter. The mean heat transfer coefficient gets higher by the interfacial shear parameter, Froude number, and Prandtl number, the lower ellipse eccentricity and the sub-cooling parameter. And the present study has a high similarity with past studies.

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