本研究利用尺寸因次分析預測在低功率電子束或雷射焊接過程中受馬里哥尼(熱毛細)流影響的熔區形狀。本研究因使用雷射或電子束當作入射能量，所以熔池中沒有洞之產生，也不包含電磁力量。因馬里哥尼數和雷諾數有104之多，所以可以採用尺寸因次分析技巧以估算不同區熱邊界層和黏滯層。本研究使用電腦計算出的結果發現熔池形狀、熔池表面流體速度和熔池表面溫度分佈可由馬里哥尼數、Prandtl數、入射能量、Peclet數、Biot數以及固體到液體的熱傳導率來決定。本研究不但對於機械加工方面有莫大幫助，並且凡關於低能量熔化的過程都能使用本研究的結果去預測熔池形狀、表面流體速度及表面溫度分佈⋯等。

In this study, shapes of the molten region and transport processes affected by thermocapillary convection in melting or welding pool irradiated by a low-power-density beam are determined from a scale analysis. A low-power-density-beam heating implies no deep and narrow cavity or keyhole taking place in the pool. In this work, the complicated flow pattern in the pool is influenced by an unknown shape of solid-liquid interface, and interactions between the free surface layer, corner regions, and boundary layer with phase transition on the solid-liquid interface. Since Prandtl number is much less than unity while Marangoni and Reynolds number can be more than in melting metals, an appropriate scaling mass, momentum, and energy transport subject to a force balance between viscous stress and surface tension gradient on the free surface account for distinct thermal and viscous boundary layers in these regions of different length, velocity, and temperature scales. The results find that shapes of the fusion zone, free surface velocity and temperature profiles are determined by Marangoni, 104
i
Prandtl, beam power, Peclet, and Biot numbers, and solid-to-liquid thermal conductivity ratio. The predications agree with numerical computations.

目錄 英文摘要 i 中文摘要 iii 圖目錄 iv 表目錄 v 符號說明 vi 第一章 緒論 1 1-1 相關文獻回顧 1 1-2 研究動機及目的 4 第二章 系統模型 5 2-1 理論分析 5 2-1.1 尺寸因次分析 7 2-2 模擬方式 13 第三章 結果與討論 15 3-1 模擬結果 15 3-2 不同表面張力係數模擬結果之比較 22
第四章 結論 25 附錄一 26 附錄二 37 參考文獻 41

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