本研究以數值方法模擬加鰭片水平管的鰭片不均溫性對自然對流熱傳的影響，在固定0.5 mm鰭片厚度下透過改變鰭片外徑、管徑、鰭片間距、及鰭片材料來探討鰭片不均溫性與鰭片各項參數的相互影響。模擬結果顯示，當鰭片較為均溫(鋁鰭片)時，隨著管徑越小，總散熱量越大；當鰭片較為不均溫(不鏽鋼鰭片)時，隨著管徑越大，鰭片散熱通量增加使得總散熱量越大。鰭片不均溫性及管徑也會對最佳鰭片間距造成影響，若將現有最佳間距經驗式套用在大管徑及不均溫的加鰭片水平管會有顯著誤差。在自然對流的浮力熱流作用下，鰭片上的溫度與熱對流係數皆呈非軸對稱分布，當採用不鏽鋼鰭片時，隨著鰭片外徑增大，不鏽鋼鰭片的溫度及熱對流係數的不均勻性均較鋁鰭片劇烈，在管上方的鰭片區域甚至可發生負值的局部熱對流係數。因此，當採用現有加鰭片水平管之鰭片效率的軸對稱理論方法來估算高不均溫性的不鏽鋼鰭片時，會產生顯著的誤差，但使用簡易的面積修正法可將誤差縮小。本研究顯示鰭片的不均溫性與管徑大小均對加鰭片水平管的自然對流熱傳有顯著影響。

This study numerically investigates the thermal performance of non-isothermal finned horizontal tube under natural convection. The parameters considered include fin diameter, fin spacing, fin material and tube diameter, with fin thickness fixed at 0.5 mm. The effect of the temperature uniformity is found to affect the total heat output of the finned tube. The computational results show that when the fin temperature is relatively uniform (aluminum fins), the total heat output becomes greater for a smaller tube diameter; on the contrary, when the fin temperature is non-uniform (stainless-steel fins), the total heat output becomes greater for a larger tube diameter. The uniformity of fin temperature, and tube diameter as well, would affect the optimum fin spacing. Consequently, applying the empirical optimum-spacing formula available in the literature leads to notable discrepancies for the cases with non-isothermal fins or large tube diameters. Under natural convection, the distributions of temperature and heat transfer coefficient on the fins deviate from being axisymmetric due to the buoyancy flow. For stainless-steel fins, the non-uniformities of fin temperature and heat transfer coefficient are far more serious than for aluminum fins. On the non-uniform fins, the region above the tube could be distributed with negative local heat transfer coefficients. In calculating the fin efficiencies of highly non-uniform fins, the axisymmetric theoretical methods in the literature may yield significant errors. The present results indicate that both temperature uniformity and tube diameter are highly influential to the thermal performance of finned horizontal tube.

目錄 V
圖表目錄 VI
符號表 IX
第一章 緒論 1
1.1前言 1
1.2文獻回顧與基礎原理 1
1.3 研究動機與目的 7
第二章 理論基礎與模型建構 14
2.1數學模型 14
2.1.1 The Boussinesq Model 14
2.1.2統御方程式 14
2.1.3邊界條件 15
2.2數值方法 16
2.2.1速度與壓力求解方式 17
2.2.2其餘離散化方程式 17
2.2.3相關參數 17
2.3模擬參數 18
2.4流固耦合計算之網格建立 18
第三章 結果與討論 23
3.1鰭片不均溫性對鰭片最佳間距的影響 23
3.2在不同鰭片外徑及鰭片材料下的鰭片熱傳特性 25
3.3 不同鰭片材料與管徑對熱傳的影響 26
3.4非軸對稱不均溫鰭片的效率計算 27
第四章 結論與未來方向 41
參考文獻 42

[1] H. Ye, B. Li, H. Tang, J. Zhao, C. Yuan, G. Zhang, Design of vertical fin arrays with heat pipes used for high-power light-emitting diodes, Microelectronics Reliability 54 (2014) 2448–2455.
[2] A. Samba , H. Louahlia-Gualous , S. Le Masson , D. Nörterhäuser, Two-phase thermosyphon loop for cooling outdoor telecommunication equipments, Appl. Therm. Eng. 50 (2013) 1351–1360.
[3] J.A. Edwards, J.B. Chaddock, An experimental investigation of the radiation and free-convection heat transfer from a cylindrical disk extended surface, Trans. Am. Soc. Heat. Refrig. Air-Condit. Eng. 69 (1963) 313–322.
[4] W. Elenbaas, Heat dissipation of parallel plates by free convection, Physica 9. (1942) l–28.
[5] T. Tsubouchi, M. Masuda, Natural convection heat transfer from horizontal cylinders with circular fins, in: Proc. 6th Int. Heat Transfer Conf., Paper NC 1.10 Paris, 1970.
[6] N. Kayansayan, Thermal characteristics of fin-and-tube heat exchanger cooled by natural convection, Exp. Therm. Fluid Sci. (1993) 7:177–188.
[7] Ş. Yildiz, H. Yűncű, An experimental investigation on performance of annular fins on a horizontal cylinder in free convection heat transfer, Heat Mass Transfer 40 (2004) 239–251.
[8] A. Brown, Optimum dimensions of uniform annular fins, Int. J. Heat Mass Transfer 8 (1965) 665–662.
[9] K. Laor, H. Kalman, Performance and optimum dimensions of different cooling fins with a temperature-dependent heat transfer coefficient, Int. J. Heat Mass Transfer 39 (1996) 1993–2003.
[10] J. M. Littlefield, J.E. Cox, Optimization of annular fins on a horizontal tube, Heat Mass Transfer 7 (1974) 87–93.
[11] E. Hahne, D. Zhu, Natural convection heat transfer on finned tubes in air, Int. J. Heat Mass Transfer 37 (1) (1994) 59–63.
[12] H.-T. Chen, W.-L. Hsu, Estimation of heat transfer coefficient on the fin of annular-finned tube heat exchangers in natural convection for various fin spacings, Int. J. Heat Mass Transfer 50 (2007) 1750–1761.
[13] J. R. Senapati, S. K. Dash, S. Roy, Numerical investigation of natural convection heat transfer over annular finned horizontal cylinder, Int. J. Heat Mass Transfer 95 (2016) 330–345.
[14] T. Saitoh, T. Sajiki, K. Maruhara, Bench mark solutions to natural convection heat transfer problem around a horizontal circular cylinder, Int. J. Heat Mass Transfer 36 (1993) 1251–1259.
[15] T. H. Kuehn, R. J. Goldstein, Numerical solution to the Navier-Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder, Int. J. Heat Mass Transfer 23 (1980) 971–979.
[16] A. Bejan, Convection Heat Transfer, 3th Ed., John Wiley & Sons., 2004
[17] Handbook of Fluent, ANSYS, Inc., 2015.
[18] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, 1980.
[19] C. S. Wang, M. M. Yovanovich, J. R. Culham, General model for natural convection: Application to annular-fin heat sinks, ASME Journal of Electronic Packaging 121 (1) (1999) 44–49.