本文以數值方法模擬47 nm- Al2O3/water奈米流體流動與熱傳現象，將奈米流體視為單相，探討三種情況：徑向流冷卻系統、微流道熱沉與垂直式方腔。針對徑向流系統，使用基於控制體積法的商用軟體CFD-ACE V2004進行模擬；對於微流道熱沉與垂直式方腔，則使用晶格波茲曼法進行數值計算。
關於奈米流體在徑向流冷卻系統的熱傳特性，與文獻中多數的研究趨勢一致，即熱傳係數隨雷諾數與粒子分率的增加而提高，然而系統壓降的增益受粒子分率的影響更為顯著。當固定幫浦功率，在較低熱通量下(q〞≦3900 W/m2)奈米流體表現不如純水，然而當加熱量提高，奈米流體熱傳率將高於純水。固定PPrel=0.5，4% Al2O3/water奈米流體在加熱量q〞=16000 W/m2與q〞=34000 W/m2所得到的平均紐賽數增益分別為4%與10%；熱阻值則減少2.3%與7%。
關於奈米流體在微流道熱沉的熱傳表現，探討兩種情況：單一流道與共軛熱傳系統，所模擬的雷諾數較低(2≦Re≦16)，計算所得的平均紐賽數為奈米流體熱傳導係數的函數，其範圍為0.6≦Nu≦13。一如預期，結果顯示平均紐賽數隨雷諾數與粒子體積分率的增加而提高，且奈米流體溫度分布較純水更為均勻。
關於奈米流體在垂直式方腔的熱傳表現，與文獻中多數的數值研究趨勢一致，結果顯示平均紐賽數隨萊利數與粒子體積分率的增加而提高。在相同萊利數下奈米流體的平均紐賽數高於純水；然而在相同溫差下，由於奈米流體黏滯係數明顯高於純水，因此熱傳率較純水為低。此外，在微流道與自然對流的數值結果皆發現使用不同奈米流體物性模型所得到的平均紐賽數差異甚為明顯。再者，此部分數值結果已與文獻中的研究數據比對驗證，顯示晶格波茲曼法是精確的且可應用於求解工程問題。

In the present study, mathematical modeling is performed to simulate the flow and heat transfer features of 47 nm- Al2O3/water nanofluids using a single phase approach. Three practical cases are carried out, including radial flow cooling system, microchannel heat sink and vertical square enclosure. The control volume method based commercial software CFD-ACE V2004 is adopted to investigate the radial flow system while the lattice Boltzmann method (LBM) is introduced to examine both microchannel heat sink and vertical square enclosure.
For the thermal performance of nanofluids in the radial flow cooling system, results show the same trend as revealed in most of the published works that the heat transfer coefficient increases with the increase of the Reynolds number and the nanoparticle volume fraction, though the increase in pressure drop is more significantly associated with the increase of particle concentration. Under a fixed pumping power the nanofluid shows no higher heat transfer rate than water at heat flux q〞≦3900 W/m2, while as the heat flux increases the enhancement using a nanofluid becomes more remarkable. For 4% Al2O3/water mixture at PPrel=0.5, the average Nusselt number increases by about 4% and 10% respectively as the heat flux q〞=16000 W/m2 and q〞=34000 W/m2 is applied, while the thermal resistance can be reduced by 2.3% and 7%.
For the thermal performance of nanofluids in the microchannel heat sink, single channel flow and conjugate heat transfer problem are taken into consideration. Simulations are conducted at low Reynolds numbers (2≦Re≦16). The computed average Nusselt number, which is associated with the thermal conductivity of nanofluid, is in the range of 0.6≦Nu≦13. Results indicate, as expected, that the average Nusselt number increases with the increase of Reynolds number and particle volume concentration. The fluid temperature distribution is more uniform with the use of nanofluid than that of pure water.
For the thermal performance of nanofluids in a vertical square enclosure, results show the same trend as revealed in most of the published numerical works that the average Nusselt number increases with the increase of Rayleigh number and particle volume concentration. The average Nusselt number with the use of nanofluid is higher than the use of water under the same Rayleigh number. However, the heat transfer rate of the nanofluid takes on a lower value than water at a fixed temperature difference across the enclosure mainly due to the significant enhancement of dynamic viscosity. Furthermore, great deviations of computed Nusselt numbers using different models associated with the physical properties of a nanofluid are revealed for both microchannel heat sink and vertical square enclosure. The present results are well validated with the works available in the literature and consequently LBM is robust and promising for practical applications.

Abu Nada, E., Masoud, Z., Oztop, H.F., Campo, A., Effects of nanofluid variable properties on natural convection in enclosures, International Journal of Thermal Sciences 49 (2010) 479–491.
Abu Nada, E., Oztop, H.F., Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid, International Journal of Heat and Fluid Flow 30 (2009) 669–678.
Ali, F.M., Yunus, W.M., Moksin, M.M., Talib, Z.A., The effect of volume fraction concentration on the thermal conductivity and thermal diffusivity of nanofluids: numerical and experimental, Review of Scientific Instruments 81 (2010) 074901.
Andrianova, I.S., Samoilov, O.Ya., Fisher, I.Z., Thermal conductivity and structure of water, Journal of Structural Chemistry 8 (1967) 736–739.
Angue Mintsa, H., Roy, G., Nguyen, C.T., Doucet, D., New temperature dependent thermal conductivity data for water-based nanofluids, International Journal of Thermal Sciences 48 (2009) 363–371.
Batchelor, G.K., The effect of Brownian motion on the bulk stress in a suspension of spherical particles, Journal of Fluid Mechanics 83 (1977) 97–117.
Beck, M.P., Yuan, Y., Warrier, P., Teja, A.S., The thermal conductivity of alumina nanofluids in water, ethylene glycol, and ethylene glycol + water mixtures, Journal of Nanoparticle Research 12 (2010) 1469–1477.
Bhattacharya, P., Samanta, A.N., Chakraborty, S., Numerical study of conjugate heat transfer in rectangular microchannel heat sink with Al2O3/H2O nanofluid, Heat and Mass Transfer 45 (2009) 1323–1333.
Brinkman, H.C., The viscosity of concentrated suspensions and solutions, Journal of Chemical Physics 20 (1952) 571–581.
Chang, C., Liu, C.H., Lin, C.A., Boundary conditions for lattice Boltzmann simulations with complex geometry flows, Computers and Mathematics with applications 58 (2009) 940–949.
Chang, C.C., Yang, Y.T., Yen, T.H., Chen, C.K., Numerical investigation into thermal mixing efficiency in Y-shaped channel using Lattice Boltzmann method and field synergy principle, International Journal of Thermal Sciences 48 (2009) 2092–2099.
Chein, R., Chuang, J., Experimental microchannel heat sink performance studies, International Journal of Thermal Sciences 46 (2007) 57–66.
Chen, H., Ding, Y., He, Y., Tan, Ch., Rheological behavior of ethylene glycol based titania nanofluids, Chemical Physics Letters 444 (2007) 333–337.
Chen, S., Doolen, G.D., Lattice Boltzmann model for fluid flows, Annual Review of Fluid Mechanics 30 (1998) 329–364.
Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, ASME, FED-231/MD-66 (1995) 99–105.
Chon, C.H., Kihm, K.D., Lee, S.P., Choi, S.U.S., Empirical correlation finding the role of temperature and particle size for nano-fluid (Al2O3) thermal conductivity enhancement, Applied Physics Letters 87 (2005) 153107.
Corcione, M., Heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the sidewalls, International Journal of Thermal Sciences 49 (2010) 1536–1546.
Das, S.K., Choi, S.U.-S., Patel, H.E., Heat transfer in nanofluids – a review, Heat Transfer Engineering 37 (2006) 3–19.
Das, S.K., Putra, N., Thiesen, P., Roetzel, W., Temperature dependence of thermal conductivity enhancement for nanofluids, ASME Journal of Heat Transfer 125 (2003) 567–574.
Das, S.K., Putra, N., Roetzel, W., Pool boiling characteristics of nano-fluids, International Journal of Heat and Mass Transfer 46 (2003) 851–862.
De Vahl Davis, G., Natural convection of air in a square cavity, a benchmark numerical solution, International Journal for Numerical Methods in Fluids 3 (1962) 249–264.
Ding, Y., Alias, H., Wen, D., Williams, R.A., Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids), International Journal of Heat and Mass Transfer 49 (2005) 240–250.
Duangthongsuk, W., Wongwises, S., An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime, International Journal of Heat and Mass Transfer 53 (2010) 334–344.
Eastman, J.A., Choi, S.U.-S., Li, S., Soyez, G., Thompson, L.J., Di-Melfi, R.J., Novel thermal properties of nanostructured materials, Journal of Metastable Nanocrystalline Materials 2 (1999) 629–634.
Eastman, J.A., Choi, U.S., Li, S., Thompson, L.J., Lee, S., Enhanced thermal conductivity through the development of nanofluids, Materials Research Society Symposium – Proceedings, vol. 457, Materials Research Society, Pittsburgh, PA, USA, Boston, MA, USA (1997) 3–11.
Eastman, J.A., Choi, S.U.S., Li, S., Yu, W., Thompson, L.J., Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Applied Physics Letters 78 (2001) 718–720.
Ebrahimi, S., Sabbaghzadeh, J., Lajevardi, M., Hadi, I., Cooling performance of a microchannel heat sink with nanofluids containing cylindrical nanoparticles (carbon nanotubes), Heat and Mass Transfer 46 (2010) 549–553.
Eckert, E., Drake, R., Analysis of Heat and Mass Transfer McGraw-Hill, New York (1972).
Einstein, A., Investigation on The Theory of Brownian Movement, Dover, New York (1956).
Elison, B., Webb, B.W., Local heat transfer to impinging liquid jets in the initially laminar, transitional, and turbulent regimes, International Journal of Heat and Mass Transfer 37 (1994) 1207–1216.
Feng, Y., Kleinstreuer, C., Nanofluid convective heat transfer in a parallel-disk system, International Journal of Heat and Mass Transfer 53 (2010) 4619–4628.
Fox, R.W., McDonald, A.T., Pritchard, P.J., Introduction to Fluid Mechanics, 6th ed., Wiley, New York, 2004.
Frankel, N.A., Acrivos, A., On the viscosity of a concentrate suspension of solid particle, Chemical Engineering Science 22 (1967) 847–853.
Garimella, S.V., Nenaydykh, B., Nozzle-geometry effects in liquid jet impingement heat transfer, International Journal of Heat and Mass Transfer 39 (1996) 2915–2923.
Ghasemi, B., Aminossadati, S.M., Periodic natural convection in a nanofluid-filled enclosure with oscillating heat flux, International Journal of Thermal Sciences 49 (2009) 1–9.
Ghasemi, B., Aminossadati, S.M., Natural convection heat transfer in an inclined enclosure filled with a water–CuO nanofluid, Numerical Heat Transfer, Part A: Applications 55 (2009) 807–823.
Ghasemi, B., Aminossadati, S.M., Brownian motion of nanoparticles in a triangular enclosure with natural convection, International Journal of Thermal Sciences 49 (2010) 931–940.
Gherasim, I., Roy, G., Nguyen, C.T., Vo-Ngoc, D., Experimental investigation of nanofluids in confined laminar radial flows, International Journal of Thermal Sciences 48 (2009) 1486–1493.
Gherasim, I., Roy, G., Nguyen, C.T., Vo-Ngoc, D., Heat transfer enhancement and pumping power in confined radial flows using nanoparticle suspensions (nanofluids), International Journal of Thermal Sciences 50 (2011) 369–377.
Goldstein, R.J., Sobolik, K.A., Sool, W.S., Effect of entrainment on the heat transfer to a heated circular air jet impinging on a flat surface, Transactions of the ASME 112 (1990) 608–611.
Graham, A.L., On the viscosity of suspensions of solid spheres, Applied Scientific Research 37 (1981) 275–286.
Grunau, D., Chen, S., Eggert, K., A lattice Boltzmann model for multiphase fluid flows, Physics of Fluids A 5 (1993) 2557–2562.
Guo, Z., Zhao, T.S., Lattice Boltzmann model for incompressible flows through porous media, Physical Review E 66 (2002) 036304.
Hamilton, R.L., Crosser, O.K., Thermal conductivity of heterogeneous two-component systems, Industrial and Engineering Chemistry Fundamentals 1 (1962) 182–191.
Han, K., Feng, Y.T., Owen, D.R.J., Coupled lattice Boltzmann and discrete element modelling of fluid–particle interaction problems, Computers and Structures 85 (2007) 1080–1088.
He, X., Zou, Q., Luo, L.S., Dembo, M., Analytic solution of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model, Journal of Statistical Physics 87 (1997) 115–136.
Herwig, H., Mahulikar, S.P., Variable property effects in single-phase incompressible flows through microchannels, International Journal of Thermal Sciences 45 (2006) 977–981.
Ho, C.J., Chen, M.W., Li, Z.W., Numerical simulation of natural convection of nanofluid in a square enclosure: effect due to uncertainties of viscosity and thermal conductivity, International Journal of Heat and Mass Transfer 51 (2008) 4506–4516.
Ho, C.J., Liu, W.K., Chang, Y.S., Lin, C.C., Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: An experimental study, International Journal of Thermal Sciences 49 (2010) 1345–1353.
Ho, C.J., Wei, L.C., Li, Z.W., An experimental investigation of forced convective cooling performance of a microchannel heat sink with Al2O3/water nanofluid, Applied Thermal Engineering 30 (2010) 96–103.
Hojjat, M., Etemad, S.Gh., Bagheri, R., Thibault, J., Thermal conductivity of non-Newtonian nanofluids: Experimental data and modeling using neural network, International Journal of Heat and Mass Transfer 54 (2011) 1017–1023.
Hou, S., Zou, Q., Chen, S., Doolen, G., Cogley, A.C., Simulation of cavity flow by lattice Boltzmann method, Journal of Computational Physics 118 (1995) 329–347.
Hwang, K.S., Lee, J.H., Jang, S.P., Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity, International Journal of Heat and Mass Transfer 50 (2007) 4003–4010.
Incropera, F.P., Dewitt, D.P., Fundamentals of Heat and Mass Transfer, 4th ed. Wiley, New York (1996).
Izadi, M., Behzadmehr, A., Jalali-Vahida, D., Numerical study of developing laminar forced convection of a nanofluid in an annulus, International Journal of Thermal Sciences 48 (2009) 2119–2129.
Jang, S.P., Choi, S.U.S., Role of Brownian motion in the enhanced thermal conductivity of nanofluids, Applied Physics Letters 84 (2004) 4316–4318.
Jang, S.P., Choi, S.U.S., Cooling performance of a microchannel heat sink with nanofluids, Applied Thermal Engineering 26 (2006) 2457–2463.
Jang, S.P., Choi, S.U.S., Effects of various parameters on nanofluid thermal conductivity, Journal of Heat Transfer 129 (2007) 617–623.
Jou, R.Y., Tzeng, S.C., Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures, International Communications in Heat and Mass Transfer 33 (2006) 727–736.
Kahveci, K., Buoyancy driven heat transfer of nanofluids in a tilted enclosure, Journal of Heat Transfer 132 (2010) 062501.
Kakaç, S., Pramuanjaroenkij, A., Review of convective heat transfer enhancement with nanofluids, International Journal of Heat and Mass Transfer 52 (2009) 3187–3196.
Keblinski, P., Phillpot, S.R., Choi, S.U.S., Eastman, J.A., Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), International Journal of Heat and Mass Transfer 45 (2002) 855–863.
Khanafer, K., Vafai, K., Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer 46 (2003) 3639–3653.
Khiabani, R.H., Joshi, Y., Aidun, C.K., Heat transfer in microchannels with suspended solid particles: lattice-Boltzmann based computations, Journal of Heat Transfer 132 (2010) 041003.
Ko, G.H., Heo, K., Lee, K., Kim, D.S., Kim, C., Sohn, Y., Choi, M., An experimental study on the pressure drop of nanofluids containing carbon nanotubes in the horizontal tube, International Journal of Heat and Mass Transfer 50 (2007) 4749–4753.
Koo, J., Kleinstreuer, C., A new thermal conductivity model for nanofluids, Journal of Nanoparticles Research 6 (2004) 577–588.
Koo, J., Kleinstreuer, C., Laminar nanofluid flow in micro-heat sinks, International Journal of Heat and Mass Transfer 48 (2005) 2652–2661.
Krane, R.J., Jessee, J., Some detailed field measurements for a natural convection flow in a vertical square enclosure, Proceedings of the First ASME-JSME Thermal Engineering Joint Conference 1 (1983) 323–329.
Lallave, J.C., Rahman, M.M., Kumar, A., Numerical analysis of heat transfer on a rotating disk surface under confined liquid jet impingement, International Journal of Heat and Fluid Flow 28 (2007) 720–734.
Lee, S., Choi, S.U.S., Li, S., Eastman, J.A., Measuring thermal conductivity of fluids containing oxide nanoparticles, Journal of Heat Transfer 121 (1999) 280–289.
Lee, S.W., Park, S.D., Kang, S., Bang, I.C., Kim, J.H., Investigation of viscosity and thermal conductivity of SiC nanofluids for heat transfer applications, International Journal of Heat and Mass Transfer 54 (2011) 433–438.
Li, Z.G., Huai, X.L., Tao, Y.J., Chen, H.Z., Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Applied Thermal Engineering 27 (2007) 2803–2814,.
Li, J.M., Li, Z.L., Wang, B.X., Experimental viscosity measurements for copper oxide nanoparticle suspensions, Tsinghua Science and Technology 7 (2002) 198–201.
Li, C.H., Peterson, G.P., Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids), Journal of Applied Physics 99 (2006) 084314.
Li, C.H., Peterson, G.P., Experimental studies of natural convection heat transfer of Al2O3/DI water nanoparticle suspensions (nanofluids). Advances in Mechanical Engineering 2010 (2010) Article ID 742739.
Lim, C.Y., Shu, C., Niu, X.D., Chew, Y.T., Application of lattice Boltzmann model to simulate microchannel flows, Physics of Fluids 14 (2002) 2299–2308.
Liu, X., Lienhard, J.H., Lombara, J.S., Convective heat transfer by impingement of circular liquid jets, Journal of Heat Transfer 113 (1991) 571–582.
Lotfi, R., Saboohi, Y., Rashidi, A.M., Numerical study of forced convective heat transfer of Nanofluids: Comparison of different approaches, International Communications in Heat and Mass Transfer 37 (2010) 74–78.
Lundgren, T.S., Slow flow through stationary random beds and suspensions of spheres, Journal of Fluid Mechanics 51 (1972) 273–299.
Ma, C.F., Gan, Y.P., Tian, Y.C., Lei, D.H., Gomi, T., Liquid jet impingement heat transfer with or without boiling, Journal of Thermal Science 2 (1993) 32–49.
Maiga, S.E.B., Nguyen, C.T., Galanis, N., Roy, G., Heat transfer behaviours of nanofluids in a uniformly heated tube, Superlattices and Microstructures 35 (2004) 543–557.
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 (2005) 530–546.
Markatos, N.C., Pericleous, K.A., Laminar and turbulent natural convection in an enclosed cavity. International Journal of Heat and Mass Transfer 27 (1984) 772–775.
Masoumi, N., Sohrabi, N., Behzadmehr, A., A new model for calculating the effective viscosity of nanofluids, Journal of Physics D: Applied Physics 42 (2009) 055501.
Maxwell, J. C., Electricity and Magnetism, 1st Ed., Clarendon Press, Oxford, England, 1873.
Min, J.Y., Jang, S.P., Kim, S.J., Effect of tip clearance on the cooling performance of a microchannel heat sink, International Journal of Heat and Mass Transfer 47 (2004) 1099–1103.
Mochizuki, S., Yang, W.J., Local heat transfer performance and mechanisms in radial flow between parallel disks, Journal of Thermophysics and Heat Transfer 1 (1987) 112–116.
Morini, G.L., Scaling effects for liquid flows in micro-channels, Heat Transfer Engineering 27 (2006) 64–73.
Namburu, P.K., Das, D.K., Tanguturi, K.M., Vajjha, R.S., Numerical study of turbulent flow and heat transfer characteristics of nanofluids considering variable properties, International Journal of Thermal Sciences 48 (2009) 290–302.
Namburu, P.K., Kulkarni, D.P., Misra, D., Das, D.K., Viscosity of copper oxide nanoparticles dispersed in ethylene glycol and water mixture, Experimental Thermal and Fluid Science 32 (2007) 397–402.
Nguyen, C.T., Desgranges, F., Roy, G., Galanis, N., Maré, T., Boucher, S., Angue Mintsa, H., Temperature and particle-size dependent viscosity data for water-based nanofluids-hysteresis phenomenon, International Journal of Heat and Fluid Flow 28 (2007) 1492–1506.
Nnanna, A.G.A., Experimental model of temperature-driven nanofluid, ASME Journal of Heat Transfer 129 (2007) 697–704.
Ogut, E.B., Natural convection of water-based nanofluids in an inclined enclosure with a heat source, International Journal of Thermal Sciences 48 (2009) 2063–2073.
Özerinç, S., Kakaç, S., YazIcIoǧlu, A.G., Enhanced thermal conductivity of nanofluids: a state-of-the-art review, Microfluidics and Nanofluidics 8 (2010) 145–170.
Oztop, H.F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow 29 (2008) 1326–1336.
Pak, B.C., Cho, Y.I., Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Experimental Heat Transfer 11 (1998) 151–170.
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 (2006) 2209–2218.
Patel, H.E., Das, S.K., Sundararagan, T., Nair, A.S., Geoge, B., Pradeep, T., Thermal conductivities of naked and monolayer protected metal nanoparticle based nanofluids: Manifestation of anomalous enhancement and chemical effects, Applied Physics Letters 83 (2003) 2931–2933.
Paul, G., Chopkar, M., Manna, I., Das, P.K., Techniques for measuring the thermal conductivity of nanofluids: a review, Renewable and Sustainable Energy Reviews 14 (2010) 1913–1924.
Phuoc, T.X., Massoudi, M., Experimental observations of the effects of shear rates and particle concentration on the viscosity of Fe2O3 deionized water nanofluids, International Journal of Thermal Sciences 48 (2009) 1294–1301.
Popa, C.V., Fohanno, S., Nguyen, C.T., Polidori, G., On heat transfer in external natural convection flows using two nanofluids, International Journal of Thermal Sciences 49 (2010) 901–908.
Prasher, R., Song, D., Wang, J., Measurements of nanofluid viscosity and its implications for thermal applications, Applied Physics Letters 89 (2006) 133108.
Putnam, S.A., Cahill, D.G., Braun, P.V., Ge, Z., Shimmin, R.G., Thermal conductivity of nanoparticle suspensions, Journal of Applied Physics 99 (2006) 084308.
Putra, N., Roetzel, W., Das, S.K., Natural convection of nano-fluids, Heat and Mass Transfer 39 (2003) 775–784.
Rea, U., McKrell, T., Hu, L.W., Buongiorno, J., Laminar convective heat transfer and viscous pressure loss of alumina–water and zirconia–water nanofluids, International Journal of Heat and Mass Transfer 52 (2009) 2042–2048.
Roy, G., Nguyen, C.T., Lajoie, P.-R., Numerical investigation of laminar flow and heat transfer in a radial flow cooling system with the use of nanofluids, Superlattices and Microstructures 35 (2004) 497–511.
Saad, N.R., Douglas, J.M., Mujumdar, A.S., Prediction of heat transfer under an axisymmetric laminar impinging jet, Industrial and Engineering Chemistry Fundamental 16 (1977) 148–154.
Sahoo, B.C., Vajjha, R.S., Ganguli, R., Chukwu, G.A., Das, D.K., Determination of rheological behavior of aluminum oxide nanofluid and development of new viscosity correlations, Petroleum Science and Technology 27 (2009) 1757–1770.
Santra, A.K., Sen, S., Chakraborty, N., Study of heat transfer augmentation in a differentially heated square cavity using copper–water nanofluid, International Journal of Thermal Sciences 47 (2008) 1113–1122.
Santra, A.K., Sen, S., Chakraborty, N., Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates, International Journal of Thermal Sciences 48 (2009) 391–400.
Shah, R.K., London, A.L., Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data. New York: Academic (1978).
Shi, Y., Zhao, T.S., Guo, Z.L., Thermal lattice Bhatnagar–Gross–Krook model for flows with viscous heat dissipation in the incompressible limit, Physical Review E 70 (2004) 066310.
Shu, C., Peng, Y., Chew, Y.T., Simulation of natural convection in a square cavity by Taylor series expansion and least square-based lattice Boltzmann method, International Journal of Modern Physics C 13 (2002) 1399–1414.
Singh, D., Timofeeva, E., Yu, W., Routbort, J., France, D., Smith, D., Lopez-Cepero, J.M., An investigation of silicon carbide-water nanofluid for heattransfer applications, Journal of Applied Physics 105 (2009) 064306.
Succi, S., Vergassola, M., Benzi, R., Lattice Boltzmann scheme for two-dimensional magnetohydrodynamics, Physical Review A 43 (2001) 4521–4524.
Sundar, L.S., Sharma, K.V., Turbulent heat transfer and friction factor of Al2O3 Nanofluid in circular tube with twisted tape inserts, International Journal of Heat and Mass Transfer 53 (2010) 1409–1416.
Toh, K.C., Chen, X.Y., Chai, J.C., Numerical computation of fluid flow and heat transfer in microchannels, Applied Thermal Engineering 25 (2005) 1472–1487.
Tuckerman, D.B., Heat transfer microstructures for integrated circuits, Ph.D. thesis, Stanford University, 1984.
Tuckerman, D.B., Pease, R.F.W., High-performance heat sinking for VLSI, IEEE Electron Device Letters, EDL 2 (1981) 126–129.
Wang, X.S., Dagan, Z., Jili, L.M., Heat transfer between a circular free impinging jet and a solid surface with non-uniform wall temperature or wall heat flux-1. solution for the stagnation region, International Journal of Heat and Mass Transfer 32 (1989) 1351–1360.
Wang, X.Q., Mujumdar, A.S., Heat transfer characteristics of nanofluids: a review, International Journal of Thermal Sciences 46 (2007) 1–19.
Wang, J., Wang, M., Li, Z., A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer, International Journal of Thermal Sciences 46 (2007) 228–234.
Wang, X., Xu, X., Choi, S.U.S., Thermal conductivity of nanoparticle–fluid mixture, Journal of Thermophysics and Heat Transfer 13 (1999) 474–480.
Wen, D., Ding, Y., Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions, International Journal of Heat and Mass Transfer 47 (2004) 5181.
Wen, D., Ding, Y., Formulation of nanofluids for natural convective heat transfer applications, International Journal of Heat and Fluid Flow 26 (2005) 855–864.
Xuan, Y., Conception for enhanced mass transport in binary nanofluids, Heat and Mass Transfer 46 (2009) 277–279.
Xuan, Y., Li, Q., Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer 125 (2003) 151–155.
Xuan, Y., Li, Q., Hu, W., Aggregation structure and thermal conductivity of nanofluids, AIChE Journal 49 (2003) 1038–1043.
Xuan, Y.M., Roetzel, W., Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer 43 (2000) 3701–3707.
Xuan, Y.M., Yao, Z.P., Lattice Boltzmann model for nanofluids, Heat and Mass Transfer 41 (2005) 199–205.
Yan, Y.Y., Zu, Y.Q., Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder – a LBM approach, International Journal of Heat and Mass Transfer 51 (2008) 2519–2536.
Yang, C.H., Chang, C., Lin, C.A., A direct forcing immersed boundary method based lattice Boltzmann method to simulate flows with complex geometry, CMC –Computers, Materials, & Continua 11 (2009) 209–228.
Yoo, D.H., Hong, K.S., Yang, H.S., Study of thermal conductivity of nanofluids for the application of heat transfer fluids, Thermochimica Acta 455 (2007) 66–69.
Yu, W., Choi, S.U.S., The role of interfacial layers in the enhanced thermal of nanofluids: a renovated Maxwell model, Journal of Nanoparticle Research 5 (2003) 167–171.
Yu, W.H., France, D.M., Routbort, J.L., Choi, S.U.S., Review and comparison of nanofluid thermal conductivity and heat transfer enhancements, Heat Transfer Engineering 29 (2008) 432–460.
Zeinali Heris, S., Etemad, S.Gh., Nasr Esfahany, M., Experimental investigation of oxide nanofluids laminar flow convective heat transfer, International Communications in Heat and Mass Transfer 33 (2006) 529–535.
Zhang, X., Gu, H., Fujii, M., Experimental study on the effective thermal conductivity and thermal diffusivity of nanofluids, International Journal of Thermophysics 27 (2006) 569–580.
Zou, Q., He, X., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids 9 (1997) 1591–1598.