本文旨在探討非牛頓紊流於熱交換機制內強制對流效應對熱交換器效能之影響。故模擬非牛頓流體於均勻等壁溫三維扭曲橢圓管紊流之強制對流數值計算，應用控制體積法以數值求解紊流強制對流下非牛頓流體在不同條件的幾何、流場、暫/穩態之三維統御方程。所得出統御方程再使用標準"k-ω" 紊流模型以求解。研究參數包含雷諾數("5000 ≤ Re ≤ 15000" )、非牛頓流體n值("0.2≤ n ≤ 1.2" )，與節距長度("96mm ≤ d ≤ 192mm" )等。
首先以參考文獻中純水於扭曲橢圓管之實驗數據作驗證，其結果相當吻合，最大誤差在3%以內，並比較不同扭曲橢圓管的節距，再進一步延伸應用至非牛頓流體的流變特性，得出了紐賽數、壓降與熱阻等參數對熱場與流場的影響。
模擬結果顯示，不同節距的扭曲橢圓管與橢圓直管相比，流體流經扭曲橢圓管時產生旋轉，造成熱傳性能的增強，雖然可以提高傳熱能力，但引起的擾動也會增加壓降。此外，以場協同原理解釋二次流對於熱傳的影響，並計算橢圓扭曲管中的積耗散率，雷諾數與n值增加與節距長度縮短時，積耗散量會增加，熱阻減少，傳熱效率較佳；但若考慮摩擦阻抗的影響，雷諾數降低時會有較高的熱性能因子。以上結論對於新型熱交換器之設計具有高附加價值與應用性。

In this article, we have investigated the effect of forced convection on the heat exchanger efficiency of non-Newtonian turbulence in the heat exchanger system. Therefore, we simulated the forced convection of a non-Newtonian fluid in a uniform three-dimensional twisted elliptical tube with uniform wall temperature are investigated using the finite volume approach. Flow resistance and heat transfer characteristics of nanofluids in the twisted elliptical tube are studied with the parameters including Reynolds number, power law index, and the twist pitch.Effects of the above-mentioned parameters on the performance of the twisted elliptical tubes are analyzed and the overall thermal-hydraulic performance is evaluated.
The simulation results show that the twisted elliptic tube with different pitches produces a rotation when the fluid flows through the twisted elliptic tube, which enhanced the heat transfer performanc. Although the heat transfer capacity can be improved, the disturbance caused by the pressure increases pressure drop.In addition, the effect of secondary flow on heat transfer is explained by the field synergy theory, and calculated the entransy dissipation rate in the elliptic twisted tube. When the Reynolds number and the n value increase and the pitch length is shortened, the entransy dissipation will increase, but the thermal resistance reduces. The overall heat transfer efficiency is better; but considering the influence of frictional impedance, there will be a higher thermal performance factor when the Reynolds number is lowered. The above conclusions have high added value and applicability for the design of the new heat exchanger.

[1] B.S. Petukhov, V.N. Popov, Theoretical calculation of heat exchange and frictional resistance in turbulent flow in tubes of an incompressible fluid with variable physical properties, High Temperature Institute, Vol.1 pp. 69–83, 1963.
[2] R.L. Webb, in: Principles of Enhanced Heat Transfer, John Wiley and Sons Inc, New York, p. 89, 1994.
[3] W.Q. Tao, Z.Y. Guo, B.X. Wang, Field synergy principle for enhancing convective heat transfer––its extension and numerical verifications, International Journal of Heat Mass Transfer‚ Vol.45 pp.3849–3856, 2002.
[4] A.E. Bergles, Advanced enhancement-third generation heat transfer technology. Experimental Thermal and Fluid Science, Vol.26 pp.335-344, 2002.
[5] A.E. Bergles, ExHFT for fourth generation heat transfer technology. Experimental Thermal and Fluid Science, Vol.26 pp.335-344, 2002
[6] R.L. Webb, A.E. Bergles, Heat transfer enhancement: second generation technology. Mechanical Engineering, Vol.115(6) pp.60-67, 1983.
[7] A.E. Bergles, Some perspectives on enhanced heat transfer second Generation heat transfer technology. ASME Journal of Heat Transfer, Vol.110 pp.1082-1096, 1988.
[8] B. Timité, C. Castelain, H. Peerhossaini, Mass transfer and mixing by pulsatile three-dimensional chaotic flow in alternating curved pipes, International Journal of Heat Mass Transfer. Vol.54 pp.3933-3950, 2011.
[9] M.Y. Wen, Flow structures and heat transfer of swirling jet impinging on a flat surface with micro-vibrations, International Journal of Heat Mass Transfer‚ Vol.48 (3) pp. 545–560, 2005.
[10] Y. Yan, H. Zhang, J. Hull, Numerical modeling of electrohydrodynamic (EHD)effect on natural convection in an enclosure, Numerical Heat Transfer‚ Part A: Appl. Vol.46 (5) pp. 453–471, 2004.
[11] N. Kasayapanand, Electrohydrodynamic enhancement of heat transfer invertical fin array using computational fluid dynamics technique, International Communications in Heat and Mass Transfer‚ Vol.35 (6) pp.762–770, 2008
[12] Z.Y. Guo, A Brief Introduction to A Novel Heat-transfer Enhancement Heat Exchanger, Internal Report, Department of EMEMKLEHTEC, Tsinghua University, Beijing, China, 2003
[13] J.F. Guo, M.T. Xu, The application of entransy dissipation theory in
optimization design of heat exchanger, Applied Thermal Engineering, 36.pp.227-235, 2012.
[14] S. Liu, A comprehensive review on passive heat transfer enhancements in pipe exchangers, 2012.
[15] 楊荔, 李志信, 扭曲橢圓管層流換熱得數值研究, 2003.
[16] L.A. Asmantas, M.A. Nemira, V.V. Trilikauskas, Coefficients of heat transfer and hydraulic drag of a twisted oval tube, Heat Transfer-Soviet Research, Vol.17 pp.103-109, 1985.
[17] Q. Si, Q. Xia, D.X. Liang, L.H. Li, Investigation of heat transfer and flow resistance on twisted tube heat exchanger, Journal of Chemical Industry and Engineering, Vol.46 pp.601–608, 1995.
[18] X.X. Zhang, G.H. Wei, Zh.F. Sang, Experimental research of heat transfer and flow friction properties in twisted tube heat exchanger, Chemical Engineering, Vol.35,pp.17–20, 2007.
[19] L. Yang, Z.X. Li, Numerical analysis of laminar flow and heat transfer in twisted elliptic tubes , Engineering Mechanics, Vol.20 pp. 143–148, 2003.
[20] S. Yang, Li. Zhang, H. Xu, Experimental study on convective heat transfer and flow resistance characteristics of water flow in twisted elliptical tubes, Applied Thermal Engineering, Vol.31 pp.2981-2991, 2011.
[21] T.J. Rennie, G.S. Raghavan, Thermally dependent viscosity and non-Newtonian flow in a double-pipe helical heat exchanger, Appl. Therm. Eng. 27, pp.862-868, 2007.
[22] A. Carezzato, M.R. Alcantara, J. Telis-Romero, C.C. Tadini, J.A.W. Gut, Non-newtonian heat transfer on a plate heat exchanger with generalized configurations., Chem. Eng. Technol. 30 pp.21-26, 2007.
[23] S.X. Gao, J.P. Hartnett, Steady flow of non-Newtonian fluids through rectangular ducts, Int Commun Heat Mass Transfer 20, pp.197-210, 1993.
[24] S.X. Gao, J.P. Hartnett, Heat transfer behavior of Reiner-Rivlin fluids in rectangular ducts, Int J Heat Mass Transfer 39:1317-24, 1996.
[25] P.Y. Chang, F.C. Chou, C.W. Tung, Heat transfer mechanism for Newtonian and non-Newtonian fluids in 2:1 rectangular ducts, Int J Heat Mass Transfer, 41:3841-56, 1998.
[26] C.R. Maia, J.B. Aparecido, L.F. Milanez, Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section, International Journal of Thermal Sciences 45, pp.1066–1072, 2006
[27] S. Shin, Y.I. Cho, Temperature effect on the non-newtonian viscosity of an aqueous polyacrylamide solution, Int. Comm. Heat Mass Transfer Vol.20 pp.831-844, 1993.
[28] L. Yang, J.L. Tian, Z. Yang, Y. Li, C.H. Fu, Y.H. Zhu, X.L. Pang, Numerical analysis of non-Newtonian rheology effect on hydrocyclone flow field, Petroleum 1 ,pp. 68-74, 2005.
[29] A. Bejan, Study of entropy generation in fundamental convective heat transfer, J. Heat Transfer – Trans. ASME, Vol. 101 (4), pp. 718–725, 1979.
[30] Z.Y. Guo, H.Y. Zhu, X.G. Liang, Entransy – a physical quantity describing heat transfer ability, International Journal of Heat and Mass Transfer, Vol. 50, pp. 2545–2556, 2007.
[31] Q. Chen, M. Wang, N. Pan et al, Optimization principles for convective heat transfer, Energy, Vol. 34 (9), pp. 1199–1206, 2009.
[32] Q. Chen, X.G. Liang, Z.Y. Guo, Entransy theory for the optimization of heat transfer - A review and update International Journal Of Heat And Mass Transfer, Vol. 63, pp.65–81, 2013.
[33] Z.Y. Guo, D.Y. Li, B.X. Wang, A novel concept for convective heat transfer enhancement, International Journal of Heat and Mass Transfer, Vo. 41, Issue 14, pp. 2221–2225, 1998.
[34] A. Bejan, Entropy Generation through Heat and Fluid Flow, Wiley, New York, pp.118–134, 1992.
[35] A. Bejan, Entropy Generation Minimization, CRC Press, Florida, pp. 47–112, 1996.
[36] A. Bejan, Study of entropy generation in fundamental convective heat transfer, J. Heat Transfer – Trans. ASME, Vol. 101 (4), pp.718–725, 1979.
[37] R.K. Shah, T. Skiepko, Entropy generation extrema and their relationship with heat exchanger effectiveness – number of transfer unit behavior for complex flow arrangements, Journal of Heat Transfer – Transaction of The. ASME, Vol. 126 (6) , pp. 994–1002, 2004
[38] 孟繼安, 基於場協同理論的縱向渦強化換熱技術及其應用,北京:清華大學, 2001.
[39] 陳群, 對流換熱過程的不可逆性及其優化,北京:清華大學, 2008.
[40] R.L. Webb‚E.R.G.Eckert, Application of rough surfaces to heat exchanger design, International Journal of Heat and Mass Transfer, Vol.15(9), pp. 1647–1658, 1972.
[41] 過增元, 梁新剛, 積-描述物體傳遞熱量能力的物理量.自然科學發展, 16(10):1288-1296, 2006.
[42] J.F. Guo, M.T. Xu, The application of entransy dissipation theory in optimization design of heat exchanger. Applied Thermal Engineering, 36. 227-235, 2012.
[43] D.C. Bogue, Entrance effects and prediction of turbulence in non-Newtonian flow, Ind. Eng. Chem, pp.874-878, 1959.
[44] J.N. Kapur, R.C. Gupta, Power-law fluid flow in the inlet length of a circular pipe, The Mathematics Seminar 3, pp.55-67, 1993.
[45] M. Collins, W.R. Schowalter, Behavior of non-Newtonian fluids in the entry region of a circular pipe, A. I. Ch. E. J. 9, pp.804-809, 1963.
[46] R.C. Gupta, Flow behaviour of power-law fluids in the entry region of a circular pipe, J. Mkt. 8, pp.207-220, 1969.
[47] R.C. Gupta, Hydrodynamic inlet region flow of power-law fluids in a circular tube, ZAMM 61, pp.299-303, 1981.
[48] Z. Matras, Z. Nowak, Laminar entry flow problem for power law fluids, Acta Mech, 48, pp.81-90, 1983.
[49] F.T. Pinho,The finite-volume method applied to computational rheology:fundamentals for stress-explicit fluids[J], e-rheo, pp:111-122, 1983.
[50] R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids 2nd edn, Vol.1, Wiley,New York, 1987.
[51] P.J. Carreau, D. Dekee, R.P. Chhabra, Rheology of Polymeric Systems: Principles and Applications , Hanser, Munich, 1997.
[52] R.B. Bird, Rev. Annu, Fluid Mech, 1976.
[53] P.J. Carreau, Rheological equations from molecular network theories, Trans. Soc. Rheolo, 1992.
[54] W. KOZICKI, C.H. CHOU, C. TIU, Non-Newtonian flow in ducts of arbitrary cross-sectional shape.
[55] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
[56] S.V. Patankar, D.B. Spalding, A calculation process for heat, mass and momentum transfer in three-dimension parabolic flows, International Journal of Heat and Mass Transfer, vol.15, pp.1787-1806, 1972.
[57] A.T. Johnson, Biological Process Engineering, Wiley,New York, 1999.