本研究以尺寸分析成功預測金屬或合金的熔化與焊接過程中，熔池形狀及熱毛細流。熔池形狀及輸送變數與熔融區的材料強度及特性息息相關。本研究假設表面張力係數為負值，意指會產生由中心向外的表面流。高Prandtl number代表熱邊界層小於動量邊界層。Marangoni number通常很高，故尺寸分析的範圍可分為︰熱區、中間區、冷區。其中冷區又分固-液交界面及固體區。結果發現冷、熱角落區域的最大及次大表面速度、最高溫度、熔池寬度、深度可以分別表示為工作變數，或Marangoni、Prandtl、Peclet、Stefan及雷射能量數的函數。尺寸分析的結果發現與實驗數據一致，且與尺寸分析方程式之不同組合相吻合。

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from scale analysis. Determination of the molten pool shape and transport variables is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative, indicating an outward surface flow, whereas high Prandtl number represents a thinner thickness of the thermal boundary layer than that of momentum boundary layer. Since Marangoni number is usually very high, the domain of scaling is divided into the hot, intermediate and cold corner regions, boundary layers on the solid-liquid interface and ahead of the melting front. The results find that the width and depth of the pool, peak and secondary surface velocity, and maximum temperatures in the hot and cold corner regions can be explicitly and separately determined as functions of working variables or Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The scaled results agree with numerical data, different combinations among scaled equations, and available experimental data.

謝誌 I
目錄 II
圖目錄 IV
符號說明 VI
中文摘要 1
英文摘要 2
第一章 緒論 3
1.1前言 3
1.2研究目的 7
1.3本文架構 8
第二章 系統模型之假設與理論 9
2.1系統模型 9
2.2系統假設與理論分析 11
第三章 結果與討論 13
3.1尺寸分析 13
3.2依據工作變數得到的輸送變數表示式 21
3.3尺寸分析結果與討論 23
第四章 結論 44
參考文獻 45

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