本研究使用COMSOL Multiphysics探討在奈米尺度下電磁波對金屬加熱之鎔化問題。電磁波照射在金屬表面產生能量損失造成金屬加熱及熔化。鎔化金屬的流動以及表面形狀變化受到表面張力、熱毛細力與勞倫之力作用影響。鎔化的金屬表面變型過程以相位場方法決定，並以兩相流模型考慮不同材料性質相位變化。

This study investigated the heating of metal irradiated by electromagnetic wave in nanoscale, using COMSOL Multiphysics. Energy losses are responsible for heating and melting of metal. The flow of molten regime in metal is driven by surface tension, thermocapillary and Lorentz forces. Surface deformation of molten regime is determined by phase-field method. Two-phase flow model accounts for distinct properties.

學位論文審定書 i
中文摘要 ii
Abstract iii
目錄 iv
圖次 v
符號說明 vi
第一章 緒論 1
1.1 研究背景及動機 1
1.2 文獻回顧 2
1.3 有限元素法 4
1.4 論文架構 4
第二章 研究方法 5
2.1 兩相流、相位場法 5
2.2 電磁波之波動方程式 7
2.3 質量守恆方程式 8
2.4 動量守恆方程式 8
2.5 複數型式之波印廷定理 12
2.6 能量方程式 15
第三章 模型設定 17
3.1 幾合模型 17
3.2 網格設置 18
3.3 初始設定與邊界條件 19
3.4 流體性質 21
第四章 結果與討論 23
第五章 結論 33
參考文獻 34

[1] Cary, Howard B; Scott C. Helzer, Modern Welding Technology. Upper Saddle River, New Jersey: Pearson Education, 2005. pp.5-6
[2] Y. M. Lin and F. G. Shi, Minimization of Welding-induced Alignment Distortion in Butterfly Laser Module Packages: A Study of Laser Pulse Shape, Optical Engineering, 2007. Vol. 46
[3] C. R. Heiple and J. R. Roper, Mechanism for Minor Element Effect on GTA Fusion Zone Geometry, J. Welding, Vol.61, 1982. pp.97-s-102-s
[4] S. Kuo and Y.H. Wang, Weld Pool Convection and Its Effect, J. Welding, Vol. 65, 1986. pp-63-s-70-s
[5] A. Paul and T. Debroy, Free Surface Flow and Heat Transfer in Conduction Mode Laser Welding, Meral. Trans. Vol.19B, 1988. pp.851-858
[6] F. Kong, H. Zhang and G. Wang, Numerical Simulation of Transient Multiphase Field during Hybrid Plasma Laser deposition Manufacturing, J. Heat Transfer, Vol.130, 2008. NO.112101, pp.1-7
[7] Conny Lampa, John Powell and Alexander F H Kaplan, An analytical thermodynamic model of laser welding, J.O. Physics D: Applied Physics, 1997. pp.1293-1299
[8] R.W. Wood, 1902, Philos. Mag. 4396
[9] Eli Jerby, Incremental metal-powder solidification by localized microwave-heating and its potential for additive manufacturing, Additive Manufacturing, 2015. pp.53-66
[10] Nathan Ida. ,1999, Engineering Electromagnetics, Springer, pp.759-760
[11] R. W. Wood, Philos. Mag. 4,396 (1902)
[12] U. Fano, 1941, J. Opt. Soc. Am. 31,213
[13] 邱國斌、蔡定平 (2006)，物理雙月刊28卷第2期，pp.472-485
[14] H. Raether, Surface Plasmons (Springer, New York, 1998)
[15] A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, 2005, Phys. Reports 408, 131
[16] Li Gi-Rong, “The effect of surface plasmon irradiated by electromagnetic field on transport processes near a surface’’, Department of Mechanical and Electro-Mechanical Engineering (National Sun Yet-sen University, 2015), pp. 8 – pp.15.
[17] S. Osher and N. Paragios, 2003, “Geometric level set methods in imaging, vision, and graphics.” Springer- Verlag. New York.
[18] H. Emmerich, 2003, “The diffuse interface approach in materials science”, Springer-Verlag. New York.
[19] J. S. Rowlinson, 1979, Translation of J.D. van der Waals’ “The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density”. Journal of Statistical Physics, Vol.20, No.2
[20] P. Yue and J. J. Feng, 2004, “A diffuse-interface method for simulating two-phase flows of complex fluids”, J. Fluid Mech, Vol. 515, pp.293-317.
[21] P. C. Hohenberg and B. I. Halperin, 1977, “Theory of dynamic critical phenomena”, Rev. Mod. Phy. Vol. 49, pp.435-479.
[22] D. Jacqmin, 1999, “Calculation of two-phase Navier–Stokes flows using Phase-Field modeling”, Journal of Computational Physics, 155, pp.96-127
[23] M. Verschueren, F. N. Van De Vosse and H. E. H. Meijer, 2001: “Diffuse-interface modolling of thermocapillary flow instabilities in a Hele-Shaw cell”, J. Fluid Mech., Vol. 434, pp.153-166.
[24] Kaplan, A., 1994. “A model of deep penetration laser welding based on calculation of the keyhole profile.” Journal of Physics D: Applied Physics, 27(9), 1805-1814.
[25] Xu et al., 2011. Adaptive volumetric heat source models for laser beam and laser + pulsed GMAW hybrid welding processes. Int. Journal of Advanced Manufacturing Technology 57, 245-255.

[26] Chen, X., Wang, H.X., 2003. Prediction of the laser-induced plasma characteristics in laser welding: a new modelling approach including a simplified keyhole model. Journal of Physics D: Applied Physics 36(13), 1634-1643.
[27] Cho, J.H., Na, S.J., 2009. Three-dimensional analysis of molten pool in GMA-laser hybrid welding. Welding Journal 88, 35s-43s.
[28] Dasgupta, A.K., Mazumder, J., Li, P., 2007. Physics of zinc vaporization and plasma absorption during CO2 laser welding. Journal of Applied Physics 102, 053108.
[29] Pang, S., Chen, L., Zhou, J., Yin, Y., Chen, T., 2011. A three-dimensional sharp interface model for self-consistent keyhole and weld pool dynamics in deep penetration laser welding. Journal of Physics D: Applied Physics 44, 025301.
[30] Comsol: CFD Module Users Guide, (2014).