本文以數值模擬來探討奈米流體流經均勻加熱圓管與徑向流的紊流強制對流的問題。所採用的奈米流體為銅-水以及氧化鋁-水混合液。數值模擬主要考慮的參數為：雷諾數、粒子體積濃度、熱通量 與奈米粒子粒徑。紊流流場的模擬，分別採用低雷諾數模式與標準 模式來求解圓管流與徑向流。本文中對於均勻加熱圓管所採用的理論模式與參考文獻的實驗數據作數值預測值的確認，平均紐賽數之數值預測值與實驗值的最大誤差在10%內。
數值模擬結果顯示，奈米流體的熱傳效率相當顯著，於圓管流中， 濃度1%與濃度2%銅-水奈米流體相較於純水約分別有15%、30%的熱傳增益；而在徑向流流場，濃度0.5%與濃度1%氧化鋁-水奈米流體約分別有16%、40%的熱傳增益。熱傳係數隨著粒子體積濃度與雷諾數Re的增加而提高。此外，固定粒子體積濃度，在純水中所加入粒子的粒徑越小，得到的熱傳係數越大。而就氧化鋁-水與銅-水兩種奈米流體而言，銅-水奈米流體的熱傳增益優於氧化鋁-水。另一方面，由奈米流體阻力係數的結果顯示，加入少量的奈米顆粒並不會造成明顯的壓降，因此相較於純流體，使用低濃度的奈米流體並不需耗費更大的輸入功率來推動。

In this study, the problem of turbulent forced convection flow of nanofluids has been investigated numerically for two particular geometrical configurations, namely a uniformly heated tube and radial flow. Both water-Cu and water-Al2O3 nanofluids are discussed. The numerical simulations are undertaken for the parameters：the Reynolds number Re, the volume concentration , the constant heat flux and the particle diameter. The turbulent governing equations are solved with the Low Reynolds number turbulence model for tube flow and the Standard turbulence model for radial flow, respectively. The theoretical model developed for tube flow is validated by comparing the numerical predictions with available experimental data in the literature, and the numerical results show that the averaged Nusselt numbers are reasonably predicted with a maximum discrepancy within 10%.
The present study indicates that in the tube flow, with the use of volume fraction 1% and 2% water/Cu nanofluids, the thermal enhancement can achieve 15%、30% compared with pure fluid. As for the radial flow, volume fraction 0.5% and 1% water/alumina nanofluids can result in 16%、40% thermal enhancement, respectively. The heat transfer coefficient increases with the increase of the particle concentration and Reynolds number. Besides, the inclusion of smaller particles into water can produce a more considerable augmentation of the heat transfer coefficient at the fixed particle volume concentration. Among the mixtures studied, the water/Cu nanofluid appears to offer a better heat transfer enhancement than water/Al2O3. On the other hand, the friction factor of the nanofluids is discussed, and it seems that no significant augmentation in pressure drop for the dilute nanofluid is found. Compared with the use of water, it will not cost more input power to make the dilute nanofluids flow.

Brinkman, H.C. The viscosity of concentrated suspensions and solutions, J. Chem. Phys 20, 571-581, 1952.
Buongiorno, J.. Convective transport in nanofluids. Journal of heat transfer. 128, 240-250, 2006
Choi, S.U.S. Enhancing thermal conductivity of fluids with nanoparticles, ASME Publications FED-Vol. 231/MD 66, 99-105. , 1995
Choi, S.U.S., Zhang, Z.G., Yu, W., Lockwood, F.E., Grulke, E.A. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett. 79, 2252., 2001
Eastman, J.A., Choi, U.S.S., Li, G., Soyez, L.J., Thompson, R.J., Di Melfi. Novel thermal properties of nanostructured materials, Mater. Sci. Forum 312-314, 629-634, 1999
Einstein, A.. Investigation on the theory of Brownian movement, Dover, New York, 1956
Jang, S.P., Choi, S.U.S.. The role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl. Phys. Lerr. 84, 4316-4318, 2004
Jang, S.P., Choi, S.U.S.. Cooling performance of a microchannel heat sink with nanofluids. Applied Thermal Engineering. 26, 2457-2463, 2006
Kittel, C., 1969. Thermal Physics, John Wiley & Sons, New York
Lee, S., Choi, S.U.S.. Application of metallic nanoparticle suspensions in advanced cooling systems. Recent Advances in Solids/Structures and Application of Metallic Materials, L. Shinpyo, eds., PVP-Vol. 342/MD-vol. 72, ASME, New York, 227–234. , 1996
Lee, S., Choi, S.U.S., Li, S., Eastman, J.A.. Measuring thermal conductivity of fluids containing oxide nanoparticles. J Heat Transfer 121, 280-289, 1999
Li, J., Li, Z. Wang, B.. Experimental viscosity measurements for copper oxide nanoparticle suspensions. Tsinghua science and technology. 2, 198-201, 2002
Maiga, S.E.B., Palm, S.J., Nguyen, C.T., Roy, G., Galanis, N.. Heat transfer enhancement by using nanofluids in forced convection flows, International Journal of Heat and Fluid Flow 26, 530–546. , 2005
Nnanna, A.G.A., Fistrovich, T., Malinski, K., Choi, S.U.S.. Thermal transport phenomena in buoyancy-driven nanofluids, in: Proceedings of ASME IMECE04, 571-578. , 2004
Pak, B.C., Cho, Y.I.. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer 11, 151-170, 1998
Palm, S. J., Roy, G., Nguyen, C. T.. Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature-dependent properties. Applied Thermal Engineering. 26, 2209-2218, 2006
Prasher Ravi, Song David, Wang Jinlin. Measurements of nanofluids viscosity and its implications for thermal applications. Applied Physics Letters. 89, 133108, 2006
Putra, N., Roetzel, W., Das, S.K.. Natural convection of nanofluids, Heat Mass Transfer 39, 775-784, 2003
Roy, G., Nguyen, C.T., Lajoie, P.R.. Numerical investigation of laminar flow heat transfer in a radial flow cooling system with use of nanofluids. Super Lattices Microstruct. 35, 497-511, 2004

Sohn, C.W., Chen, M.M.. Microconvective thermal conductivity in disperse two phase mixtures as observed in a low velocity Couette flow experiment. J. Therrmophys. Heat Transfer 103,45-51, 1981
Wang, X., Xu, X., Choi, S.U.S.. Thermal conductivity of nanoparticle-fluid mixture, J. Thermophys. Heat Transfer 13, 474-480, 1999
Xuan, Y., Li, Q.. Heat transfer enhancement of nanofluids, Int J. Heat and Fluid Flow. 21, 58-64, 2000
Xuan, Y.M., Li, Q.. Investigation on convective heat transfer and flow features of nanofluids. J. Heat Transfer 125, 151-155, 2003
Xuan, Y., Roetzel, W.. Conceptions for heat transfer correlation of nanofluids. Int. J. of Heat and Mass Transfer, 43: 3701-3707. , 2000
陶文銓, 「數值熱傳學」, 西安交通大學出版社, 1988