本研究針對一採用熱管熱交換器為散熱系統主體的密閉電子裝置進行理論與數值分析，此散熱系統目標解熱瓦數為500W，容器外部採自然對流，內部採強制對流散熱。本研究主要分為四部分，其一為先行驗證現存之最佳幾何尺寸估算程序與最佳間距經驗公式是否適用於多通道均溫鰭片。分析結果顯示最佳幾何尺寸計算流程所得之結果求出鰭片厚度過薄，並不符合工程應用需求所以不予以採用。而多通道雖然有較強的煙囪效應，但因為同時也有較強的側向進氣，兩相抵消之下發現單通道最佳間距經驗公式使用於多通道並無太大誤差。第二部分則針對自然對流加鰭片管進行分析，此部分對單排管與雙排管各別進行計算，結果顯示單排管在固定鰭片面積的情形下，增加鰭片長度會有較佳的散熱效果。其原因為鰭片下緣有較薄的熱邊界層，因此會有較佳的熱擴散率，比起增加鰭片高度，增加鰭片長度能更有效的提高鰭片散熱效率；雙排加熱管部分則針對上層多下層少及上層少下層多的排列方式進行分析，結果顯示上層多下層少的排列方式會有較佳的散熱率，原因為此排列方式能提供較大的浮力，引入更多外部低溫空氣，增加通道內熱對流係數。第三部分則是針對內部強制對流進行初步估算，利用現有之經驗式推算熱沉與穿管鰭片之幾何尺寸。然而本研究模型較為複雜，現有之經驗式會低估所需壓降，因此本計算使用數值方法做更為準確的估算。最後一部分則是系統整合，統整外部自然對流與內部強制對流之設計，估算出整體系統的幾何尺寸。研究發現上下游熱管散熱量並不一致，上游熱管與環境有較大溫差，因此會有較大的散熱量。本研究使用迭代方法交互驗證外部自然對流與內部強制對流散熱量，以此方法估算每根熱管的散熱量百分比。本研究也針對機殼外部輻射與自然對流散熱進行分析，結果顯示機殼外部約可提供5%的散熱量。

In this study, the cooling system for high-power closed electronic devices using a heat pipe exchanger was investigated by numerical and theoretical methods. The cooling system employs natural convection outside the container, while the forced convection was managed inside. The target of the cooling rate is 500 W. This dissertation includes four main parts. The first part is to examine the existing optimum-spacing empirical formula and complete the geometry optimization process. The results show that the fin thickness calculated by the optimization process is too thin to be adopted in engineering applications. For optimum spacing verification, although fin arrays with multiple channels provided stronger chimney effect, it is counteracted by strengthened side flow effect. The resultant optimum spacing approximates that of a single channel. The second part is to analyze on finned heat pipe array. For the single-row finned heat pipe array with fixed fin area, extending the fin length, instead of extending the fin height, can better enhance heat transfer. The reason for this is that the boundary layer is thinnest near the bottom edge of the fin, so that long fins with a low height is more favorable for heat transfer. For the double-row finned heat pipe array, the arrangement with more heat pipes on the upper row provides stronger buoyancy to yield higher heat transfer. The third part is to estimate the forced convection using existing empirical formula for parallel flow. However, the present geometry is more complicated so that the formula underestimates pressure drops. To amend this problem, numerical method is used to analyze the flow characteristics inside the tubed fin channels. The last part is on the system integration for the heat pipe exchanger operating under natural convection outside and forced convection inside, to achieve proper geometric design. An iteration process is applied to calculate individual heat fluxes of different heat pipes. It is found that the heat pipes at the downstream transport less heat because of the cooled flow. In addition, the heat loss outside the electronic device due to natural convection and radiation is calculated to be about 5% of the total heat transfer rate.

[1] H. Shabgard, M.J. Allen, N. Sharifi, S.P. Benn, A. Faghri, T.L. Bergman, Heat pipe heat exchangers and heat sinks: Opportunities, challenges, applications, analysis, and state of the art, Int. J..Heat Mass Transfer 89 (2015) 138–158.
[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] 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.
[4] N. Kayansayan, Thermal characteristics of fin-and-tube heat exchanger cooled by natural convection, Exp. Therm. Fluid Sci. (1993) 7:177–188.
[5] C.S. Wang, M.M. Yovanovich, J.R. Culham, Modeling natural convection from horizontal isothermal annular heat sinks, ASME J. Electr. Packag. 121 (1999) 44–49.
[6] 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.
[7] W. Elenbaas, Heat dissipation of parallel plates by free convection, Physica 9. (1942) l–28.
[8] 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.
[9] 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.
[10] A. Brown, Optimum dimensions of uniform annular fins, Int. J. Heat Mass Transfer 8 (1965) 665–662.
[11] J. M. Littlefield, J.E. Cox, Optimization of annular fins on a horizontal tube, Heat Mass Transfer 7 (1974) 87–93.
[12] E. Hahne, D. Zhu, Natural convection heat transfer on finned tubes in air, Int. J. Heat Mass Transfer 37 (1) (1994) 59–63.
[13] 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.
[14] R. Katsuki, T. Shioyama, C. Iwaki, Study on free convection heat transfer in a finned tube array, Int. J. Air-Cond. Refrig. 23 (2015) 1550007 (9 pp).
[15] S.-C. Wong, W.-Y. Lee, Numerical study on the natural convection from horizontal finned tubes with small and large fin temperature variations, Int. J. Therm. Sci. 138 (2019) 116-123.
[16] 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.
[17] 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.
[18] A. Bejan, E. Sciubba, The optimal spacing of parallel plates cooled by forced convection, Int. J. Heat Mass Transfer 35 (1992) 3259-3264.
[19] Handbook of Fluent, ANSYS, Inc., 2015.
[20] D.R. Chenoweth, S. Paolucci, Natural convection in an enclosed vertical air layer with large horizontal temperature differences, J. Fluid Mech. 169 (1986) 173–210.
[21] J. Hernández, B. Zamora, Effects of variable properties and non-uniform heating on natural convection flows in vertical channels, Int. J. Heat Mass Transfer 48 (2005) 793–807.
[22] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, Fundamental of Heat and Mass Transfer, 7th Ed, Wiley, 2013.
[23] S.-C. Wong, S.-H. Chu, M.-H. Ai, Revisit on natural convection from vertical isothermal plate arrays II—3-D plume buoyancy effects, Int. J. Therm. Sci., 2018, in revision.
[24] Y.-C. Chan, W.-K. Lin, A novel quick Qmax test method and experimental investigation of heat pipes, HT2005-72379, Proc. 2005 ASME Summer Heat Transfer Conference, July 17-22, CA, USA
[25] C.-C Wang, K.-Y Chi, Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, part Ⅰ: new experimental data, Int. J. Heat and Mass Transfer 43(2000) 2681-2691
[26] C.-C Wang, K.-Y Chi, C.-J Chang, Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, partⅡ: correlation, Int. J. Heat and Mass Transfer 43(2000) 2693-2700
[27] 葉家興，機殼開孔對電腦CPU之熱沉鰭片的自然對流與熱輻射的影響，國立清華大學動機系碩士論文，2014