本研究以逆算法搭配實驗溫度量測值探討不同鰭片間距、鰭片大小、邊界條件及加熱功率下，垂直單管環狀鰭管式熱交換器之熱傳特性與流動特性。由於鰭片上的熱傳係數為不均勻的分布，故將鰭片劃分成數個小區域，結合有限差分法、最小平方法及實驗溫度量測值之逆算法來預測鰭片之熱傳係數。為了驗證其準確性，本文使用商用軟體ANSYS進行數值模擬與本文逆算法所得之逆算值做比較，探討不同流動模式與網格劃分對於不同物理模型的適用度。
結果顯示在模擬中選擇Zero equation紊流模式所求得的結果較符合實驗量測溫度與逆向方法結果。在穩態模擬中，隨著鰭片面積的增加，鰭片的平均熱傳係數會降低。隨著鰭片間距的增加，鰭片的平均熱傳係數會增加，不過上升幅度有趨於平緩的趨勢。在不同的邊界條件下，開放式邊界條件之平均熱傳係數會大於封閉式邊界條件。隨著加熱功率的上升，鰭片平均熱傳係數亦會跟著上升;於暫態模擬中，鰭片之平均熱傳係數會隨著時間的前進而緩緩上升，當模擬趨於穩態時，鰭片之熱傳係數將維持一個定值。所求得熱傳係數之逆算結果配合實驗與模擬來與先前結果或其他相關文獻之經驗公式相比較。

The present study applies the inverse method and computational fluid dynamics (CFD) software along with experimental method to predict the heat transfer and fluid characteristics of vertical annular finned tube heat exchanger. The effects of some physical parameters such as fin spacing, fin diameter, boundary condition, heating power are examined. Due to the heat transfer coefficient on the fin is non-uniform, so the fin is divided into several sub-regions. Later, the inverse method applied finite difference method in conjunction with the least-squares scheme and the experimental data to estimate the heat transfer coefficient on the fins. Simulation in this study can be divide into transient analysis and steady state analysis. Furthermore, how to choose the appropriate flow model and the effect of the grid point are also investigated. In order to verify the reliability of the predicted result, the present study also compares with other relevant literature and CFD simulation packages. The result show that Zero equation is more suitable for this study than laminar and standard k-ε turbulence flow model. The correlation for Nusselt number has been developed for open system and it shows a good agreement between the empirical formula and the predicted result.

[1] J. R. Senapati, S. K. Dash, and S. Roy, "Numerical investigation of natural convection heat transfer from vertical cylinder with annular fins," International Journal of Thermal Sciences, vol. 111, pp. 146-159, 2017.
[2] S. Nada, "Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated rectangular finned base plate," International Journal of Heat and Mass Transfer, vol. 50, pp. 667-679, 2007.
[3] Ş. Yildiz and H. Yüncü, "An experimental investigation on performance of annular fins on a horizontal cylinder in free convection heat transfer," Heat and Mass Transfer, vol. 40, pp. 239-251, 2004.
[4] N. Kayansayan, "Thermal characteristics of fin-and-tube heat exchanger cooled by natural convection," Experimental Thermal and Fluid Science, vol. 7, pp. 177-188, 1993.
[5] F. Xu, J. C. Patterson, and C. Lei, "An experimental study of the unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity," International Journal of Heat and Fluid Flow, vol. 29, pp. 1139-1153, 2008.
[6] V. T. Morgan, "The overall convective heat transfer from smooth circular cylinders," in Advances in heat transfer, vol. 11: Elsevier, 1975, pp. 199-264.
[7] S. W. Churchill and H. H. Chu, "Correlating equations for laminar and turbulent free convection from a horizontal cylinder," International Journal of Heat and Mass Transfer, vol. 18, pp. 1049-1053, 1975.
[8] T. Tsubouchi and H. Masuda, "Natural convection heat transfer from horizontal cylinders with circular fins," in International Heat Transfer Conference 4, 1970, vol. 17: Begel House Inc.
[9] C. Leung, S. Probert, and M. Shilston, "Heat exchanger design: optimal uniform separation between rectangular fins protruding from a vertical rectangular base," Applied Energy, vol. 19, pp. 287-299, 1985.
[10] J. R. Senapati, S. K. Dash, and S. Roy, "Numerical investigation of natural convection heat transfer over annular finned horizontal cylinder," International Journal of Heat and Mass Transfer, vol. 96, pp. 330-345, 2016.
[11] A. Kumar, J. B. Joshi, A. K. Nayak, and P. K. Vijayan, "3D CFD simulations of air cooled condenser-II: Natural draft around a single finned tube kept in a small chimney," International Journal of Heat and Mass Transfer, vol. 92, pp. 507-522, 2016.
[12] A. Elatar, M. A. Teamah, and M. A. Hassab, "Numerical study of laminar natural convection inside square enclosure with single horizontal fin," International Journal of Thermal Sciences, vol. 99, pp. 41-51, 2016.
[13] S. Baskaya, M. Sivrioglu, and M. Ozek, "Parametric study of natural convection heat transfer from horizontal rectangular fin arrays," International Journal of Thermal Sciences, vol. 39, pp. 797-805, 2000.
[14] F. Harahap, E. Rudianto, and I. M. E. Pradnyana, "Measurements of steady-state heat dissipation from miniaturized horizontally-based straight rectangular fin arrays," Heat and Mass Transfer, vol. 41, pp. 280-288, 2005.
[15] J. R. Senapati, S. K. Dash, and S. Roy, "3D numerical study of the effect of eccentricity on heat transfer characteristics over horizontal cylinder fitted with annular fins," International Journal of Thermal sciences, vol. 108, pp. 28-39, 2016.
[16] H. T. Chen and J. C. Chou, "Investigation of natural-convection heat transfer coefficient on a vertical square fin of finned-tube heat exchangers," International Journal of Heat and Mass Transfer,vol. 49, pp. 3034-3044, 2006.
[17] H. T. Chen and W. L. Hsu, "Estimation of heat transfer coefficient on the fin of annular-finned tube heat exchangers in natural convection for various fin spacings," International Journal of Heat and Mass Transfer, vol. 50, pp. 1750-1761, 2007.
[18] H. T. Chen, Y. J. Chiu, C. S. Liu, and J. R. Chang, "Numerical and experimental study of natural convection heat transfer characteristics for vertical annular finned tube heat exchanger," International Journal of Heat and Mass Transfer, vol. 109, pp. 378-392, 2017.
[19] E. Sparrow, A. Haji-Sheikh, and T. Lundgren, "The inverse problem in transient heat conduction," Journal of Applied Mechanics, vol. 31, pp. 369-375, 1964.
[20] S. Sunil, J. R. N. Reddy, and C. Sobhan, "Natural convection heat transfer from a thin rectangular fin with a line source at the base—a finite difference solution," Heat and Mass Transfer, vol. 31, pp. 127-135, 1996.
[21] N. Ainajem and M. Ozisik, "A direct analytical approach for solving linear inverse heat conduction problems," ASME Transactions Journal of Heat Transfer, vol. 107, pp. 700-706, 1985.
[22] H. Ay, J. Jang, and J. N. Yeh, "Local heat transfer measurements of plate finned-tube heat exchangers by infrared thermography," International Journal of Heat and Mass Transfer, vol. 45, pp. 4069-4078, 2002.
[23] J. V. Beck, B. Litkouhi, and C. S. Clair Jr, "Efficient sequential solution of the nonlinear inverse heat conduction problem," Numerical Heat Transfer, Part A Applications, vol. 5, pp. 275-286, 1982.
[24] C. H. Huang, I. C. Yuan, and H. Ay, "An experimental study in determining the local heat transfer coefficients for the plate finned-tube heat exchangers," International Journal of Heat and Mass Transfer, vol. 52, pp. 4883-4893, 2009.
[25] J. Jang, "The development of high efficiency air-cooled steam condenser for the power plant. Report of National Council Science," NSC 92-2622-E006-146, Taiwan2004.
[26] A. Bejan, Convection Heat Transfer. John wiley & sons, 2013.
[27] F. Saboya and E. Sparrow, "Local and average transfer coefficients for one-row plate fin and tube heat exchanger configurations," Journal of Heat Transfer, vol. 96, pp. 265-272, 1974.
[28] E. Rosman, P. Carajilescov, and F. Saboya, "Performance of one-and two-row tube and plate fin heat exchangers," Journal of Heat Transfer, vol. 106, pp. 627-632, 1984.
[29] V. S. Arpaci, S. H. Kao, and A. Selamet, Introduction to Heat Transfer. Prentice Hall, 1999.
[30] Q. Chen and W. Xu, "A zero-equation turbulence model for indoor airflow simulation," Energy and Buildings, vol. 28, pp. 137-144, 1998.
[31] B. E. Launder and D. B. Spalding, "The numerical computation of turbulent flows," in Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion: Elsevier, 1983, pp. 96-116.
[32] 賴詩婷，矩形鰭片陣列於具開孔矩形外殼內之熱傳特性研究，國立成功大學機械工程學系，碩士論文，2012。
[33] 胡坤，ANSYS CFD 疑難問題實例詳解，人民郵電出版社，2017。