以數值方法去探討傾斜的圍場內，關於熱毛細力在靠近角落區域的穩態對流現象。介紹固定的轉換式，在液態裡解質量、動量、能量方程式，而在固態區解能量方程式，去預測自由表面遭受入射能量影響所造成的形狀，結果提供了固體液體的介面所引起的波紋、邊緣凹陷、氣洞等等缺陷分析，有了更進一步的看法。

The steady thermocapillary motion in shallow enclosures is studied. Two different configurations, imposed heat flux and differentially heated side walls, are considered. A numerical simulation of the problem in the imposed heat flux case is made. The Pressure Correction Method is used to treat the pressure velocity coupling, in particular, the SIMPLER approximation. The discretization is made using central differences along with an appropriate non-uniform grid. The computed results show the streamlines and temperature field in different Marangoni number, Prandtl number, Capillary number and aspect ratio

謝 誌…………………………………………………………….i
英文摘要………………………………………………………….ii
摘 要…………………………………………………………….iii
目 錄…………………………………………………………….iv
圖 目 錄………………………………………………………….vi
第一章 序論
1.1 研究動機及目的………………………………………..1
1.2 文獻回顧………………………………………………..2
第二章 方程式及推導
2.1 Nomenclature…………………………………………..5
2.2 方程式………………………………………………….6
2.2-1 統御方程式……………………………………………8
2.2-2 無因次化………………………………………………8
2.2-3 有限差分法（final difference）………………………9
2.3 邊界條件……………………………………………...21
第三章 實驗目的、設備及方法…………………………………24
第四章 結果與討論……………………………………………….27
第五章 結論……………………………………………………….30
參考文獻…………………………………………………………….31
圖…………………………………………………………………….34
附錄一
座標轉換……………………………………………………….43
傅利葉半幅展開……………………………………………….44

Chang, C. E., and Wilcox, W. R., 1976, "Analysis of Surface Tension Driven Flow in Floating Zone Melting," International J. Heat and Mass Transfer, Vol. 19, pp. 355-366.
Canright, D., 1994, "Thermocapillary Flow near a Cold Wall," Physics of Fluids, Vol. 6, pp. 1415-1424.
Carpenter, B. M., and Homsy, G. M., 1989, "Combined Buoyant-Thermocapillary Flow in a Cavity," J. Fluid Mechanics, Vol. 207, pp. 121-132.
Chan,C.,Mazumder,J.,and Chen,M.M.,1984,"A Two-Dimensional Transient Modelfor Convection in Laser Melted Pools," Metallurgical Transactions, Vol.15A, pp.2175-2184
Chang, C. E., and Wilcox, W. R., 1976, "Analysis of Surface Tension Driven Flow in Floating Zone Melting," International J. Heat and Mass Transfer, Vol. 19, pp. 355-366.
Chen, M. M., 1987, "Thermocapillary Convection in Materials Processing," in Interdisciplinary Issues in Materials Processing and Manufacturing, edited by S. K. Samanta, R. Komanduri, R. McMeeking, M. M. Chen, and A. Tseng, ASME, New York, pp. 541-558.
Cowley, S. J., and Davis, S. H., 1983, "Viscous Thermocapillary Convection at High Marangoni Number,"J. Fluid Mechanics, Vol. 135, pp. 175-188.
Giedt, W. H., Wei, X.-C., and Wei, S.-R., 1984,"Effect of Surface Convection on Stationary GTA Weld Zone Temperatures," Welding J., Vo1.63, pp.376-s-383-s.
Heiple, C. R., and Roper, J. R., 1982,"Mechanism for Minor Element Effect on GTA Fusion Zone Geometry," Welding J., Vo1.61, pp.97-s-102-s.
Kamotani, Y., Chao, L., Ostrach, S., and Zhang, H., 1995, "Effects of g Jitter on Free-Surface Motion in a Cavity," J. Spacecraft and Rockets, Vol. 32, pp. 177-183.
Kamotani, Y., Ostrach, S., and Pline, A., 1994, "Analysis of Velocity Data Taken in Surface Tension Driven Convection Experiment in Microgravity," Physics of Fluids, Vol. 6, pp. 3601- 3609.
Kamotani, Y., and Platt, J., 1992, "Effect of Free Surface Shape on Combined Thermocapillary and Natural Convection," J. Thermophysics and Heat Transfer Vol. 6, pp. 72 1 -726.
Kanouff, M., and Greif, R., 1992, "The Unsteady Development of a GTA Weld Pool," International J. Heat and Mass Transfer, Vol. 35, pp. 967-979.