PIERS ONLINE, VOL. 5, NO. 3, 2009 231

Thermal Conductivity of Nanofluid with Magnetic

T.-H. Tsai1, L.-S. Kuo1, P.-H. Chen1, and C.-T. Yang2 1Department of Mechanical Engineering, National Taiwan University, Taiwan 2Department of Mechanical and Computer-aided Engineering, St. John’s University, Taiwan

Abstract— The thermal conductivities of Fe3O4 and Al2O3 nanofluids with the viscous base fluid composed by various fluids are investigated in this study. In order to change the of mixed fluid, the volumetric fractions between two fluids in the mixed fluid are varied. Measured values of of nanofluids gradually approach the values predicted by Maxwell equation with increasing the viscosity. Our measured results demonstrate that Brownian motion of suspended magnetic particles could be an important factor that enhances the thermal conduc- tivity of nanofluids, but it has little effect for suspended Al2O3 nanoparticles. It also indicates that the conduction part of prediction model can be obtained from Maxwell prediction.

1. INTRODUCTION Due the applications of suspended nanoparticles in a base fluid, the thermal properties of nanofluids have been continually studied in the last decade. Various nanoparticles and base fluids are applied to fabricate different kind of nanofluids. Former experimental data have shown that nanofluids have higher thermal conductivity than that predicted by the conventional models like Maxwell model [1– 11]. However, the conventional models did not consider the effects associated with Brownian motion. This may cause the underestimation to the thermal conductivity of nanofluids. New models included the effects associated with Brownian motion are hotly investigated in the recent years [11–23]. Some prior studies have indicated that the enhancement of thermal conductivity which directly results from collisions between nanoparticles is not obvious, and the dominant factor of the en- hancement in thermal conductivity is the convection-like behavior which indirectly results from Brownian motion [12, 14, 16, 22]. Most new models divide the effective thermal conductivity, keff , into the conduction part, kconduction , which stands for the thermal conductivity due to differences of composition of nanoflu- ids and convection part, kconvection , which stand for the thermal conductivity due to the effects associated with Brownian motion.

keff = kconduction + kconvection (1) However, for the conduction part, some models are based on parallel path of conduction [22, 23] and other models are based on Maxwell prediction [13, 20]. They do not provide a consistent and convincing predict model for the conduction part of all nanofluids. This study tries to clarify the model of conduction part on the enhancement of thermal con- ductivity with nanoparticles in a base fluid at different values of viscositiy. According to the Einstein-Stokes’s equation, the Brownian diffusion coefficient, DB, is the function of temperature, diameter of and viscosity of fluid:

kBT DB = (2) 3πµdp where kB is Boltzmann constant, T is temperature, µ is viscosity of nanofluids, and dp is diameter of nanoparticles. The Brownian diffusion coefficient will decrease with increasing the viscosity of nanofluids, and the effect of Brownian motion or convectionlike behavior will be weakened. Then the thermal conductivity of convection part should decrease and the thermal conductivity of conduction part will be measured solely in the experiment.

2. EXPERIMENTAL SECTION

In this study, Al2O3 water-based nanofluid and Fe3O4 oil-based nanofluid are investigated. For the Al2O3 water-based nanofluid, two kinds of viscous base fluids, the compound of water and EG and PIERS ONLINE, VOL. 5, NO. 3, 2009 232 the compound of EG and Glycerol, are used. The measured of water, EG and glycerol are 1cP, 16.8cP and 937cP, respectively. Figure 1(a) shows the viscosity of the water-EG base fluid as a function of volume fraction of EG at 25◦C. Figure 1(b) shows the viscosity of the EG- glycerol base fluid as a function of volume fraction of glycerol at 25◦C. The viscosities of both base fluids grow exponentially when the volume fraction of EG or glycerol increases. Al2O3 of average diameter of 13 nm is used as nanoparticles dispersed in water-EG or EG-glycerol base fluid. Al2O3 nanoparticles are purchased from the Yong-Zhen technomaterial CO., LTD. For the Fe3O4 oil-based nanolfuid, diesel oil and PDMS are used to form viscous base fluid. The viscosity of diesel oil and PDMS are 4.188cP and 5500cP, respectively. Figure 1(c) shows the viscosity of the base fluid as a function of volume fraction of PDMS at 25◦C. The viscosity of the base fluid grows exponentially when the volume fraction of PDMS increases. Fe3O4 of average diameter of 10 nm used in this study is fabricated by co-precipitation method. The chemical reaction formula is expressed as: 2+ 3+ − F e + 2F e + 8OH → F e3O4 + 4H2O The thermal conductivity of such nanofluids is measured by the thermal hot wire method at 25◦C.

Figure 1: Measured values of viscosity of the mixed base fluid versus volume fraction of (a) EG (b) glycerol (c) PDMS at 25◦C.

3. RESULTS AND DISCUSSION

Figure 2 shows the thermal conductivity ratio of Al2O3 nanofluid versus the viscosity of base fluid with 2% volume fraction of Al2O3 nanoparticles. The experimental results do not have regularities in thermal conductivity. It may result from that the commercial nanoparticles are dry powder and cannot be dispersed in the base fluid well. The aggregation causes the unstable thermal conductivity ratio of nanofluid.

Figure 2: Thermal conductivity ratio of Al2O3 nanofluids versus viscosity of base fluid: (a) water-EG base fluid, (b) EG-glycerol base fluid.

Figure 3 shows the effect of viscosity of base fluid on the thermal conductivity ratio, knano/kbf and kMaxwell/kbf , of nanofluids with 1% and 2% volume fraction of Fe3O4 nanoparticles. The pa- rameters, knano and kbf , denote the thermal conductivity of nanofluids and base fluid, respectively. PIERS ONLINE, VOL. 5, NO. 3, 2009 233

The predicted thermal conductivity of nanofluid, kMaxwell, is determined by the Maxwell equation, given by kp + 2kbf + 2(kp − kbf )φ keff = (3) kp + 2kbf − (kp − kbf )φ where kp is thermal conductivity of nanoparticles, kbf is thermal conductivity of base fluid, and φ is volume fraction of nanoparticles.

Figure 3: Effect of viscosity of base fluid on thermal conductivity ratio of nanofluids: (a) knano/kbf , (b) knano/kMaxwell.

With the low viscous base fluid (4.188cP), the thermal conductivity ratio (knano/kbf ) of nanoflu- ids is higher than that predicted by the Maxwell equation. The highest enhancement of thermal conductivity is 8.75% at 2.24% volume fraction of Fe3O4 nanoparticles. And knano/kMaxwell are 1.007 and 1.021 at 1.12% and 2.24% volume fraction of Fe3O4 nanoparticles, respectively. The ex- perimental results indicate that Brownian motion and the convectionlike behavior are much active and cause the observable enhancement of thermal conductivity in the low viscous base fluid. With the high viscous base fluid (140.4cP), the thermal conductivity ratio (knano/kbf ) of nanoflu- ids becomes the same as that predicted by the Maxwell equation. Measured values of knano/kMaxwell in the high viscous fluid are 1 at 1.12% and 2.24% volume fraction of Fe3O4 nanoparticles. At this situation, high viscosity of nanofluids makes Brownian motion and the convectionlike behavior dis- appear. The measured thermal conductivity of nanofluids only presents the conduction part which Maxwell equation predicts. The experimental results with the extra high viscous base fluid (648cP) are almost identical to those in the high viscous base fluid (140.4cP).

4. CONCLUSIONS

For the Al2O3 nanofluid, the unstable thermal conductivity may result from the aggregation. For the Fe3O4 nanofluid, high viscosity of base fluid weakens Brownian motion of suspended nanoparti- cles. Our experimental results with various viscosities of base fluids indicate that Brownian motion of suspended nanoparticles is one of important factors to enhance the thermal conductivity of nanofluids. In such a highly viscous fluid, Maxwell equation gives a good prediction on the thermal conductivity of nanofluids without Brownian motion of suspended nanoparticles, and the conduc- tion part of prediction model can be obtained from Maxwell prediction, i.e., kconduction = kMaxwell.

REFERENCES 1. Lee, S., S. U. S. Choi, and J. A. Eastman, “Measuring thermal conductivity of fluids containing oxide nanoparticles,” J. Heat Transfer, Vol. 121, No. 2, 280–289, 1999. 2. Wang, X., X. Xu, and S. U. S. Choi, “Thermal conductivity of nanoparticle-fluid mixture,” J. Thermophys. Heat Transfer, Vol. 13, No. 4, 474–480, 1999. 3. Xuan, Y. and Q. Li, “Heat transfer enhancement of nanofluids,” Int. J. Heat Fluid Flow, Vol. 21, No. 1, 58–64, 2000. 4. Eastman, J. A., S. U. S. Choi, S. Li, W. Yu, and L. J. Thompson, “Anomalously increased effective thermal conductivities of -based nanofluids containing copper nanopar- ticles,” Appl. Phys. Lett., Vol. 78, No. 6, 718–720, 2001. PIERS ONLINE, VOL. 5, NO. 3, 2009 234

5. Xie, H., J. Wang, T. Xi, Y. Liu, F. Ai, and Q. Wu, “Thermal conductivity enhancement of suspensions containing nanosized alumina particles,” J. Appl. Phys., Vol. 91, No. 7, 4568–4572, 2002. 6. Das, S. K., N. Putta, P. Thiesen, and W. Roetzel, “Temperature dependence of thermal conductivity enhancement for nanofluids,” J. Heat Transfer, Vol. 125, No. 4, 567–574, 2003. 7. Patel, H. E., S. K. Das, T. Sundararagan, A. S. Nair, B. Geoge, and T. Pradeep, “Thermal conductivities of naked and monolayer protected metal nanoparticle based nanofluids: Mani- festation of anomalous enhancement and chemical effects,” Appl. Phys. Lett., Vol. 83, No. 14, 2931–2933, 2003. 8. Hong, T. K., H. S. Yang, and C. J. Choi, “Study of the enhanced thermal conductivity of Fe nanofluids,” J. Appl. Phys., Vol. 97, No. 6, 064311, 2005. 9. Murshed, S. M. S., K. C. Leong, and C. Yang, “Enhanced thermal conductivity of TiO2 — water based nanofluids,” Int. J. Therm. Sci., Vol. 44, No. 4, 367–373, 2005. 10. Hwang, Y., H. S. Park, J. K. Lee, and W. H. Jung, “Thermal conductivity and lubrication characteristics of nanofluids,” Curr. Appl. Phys., Vol. 6, Supplement 1, e67–e71, 2006. 11. Li, C. H. and G. P. Peterson, “Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids),” J. Appl. Phys., Vol. 99, No. 8, 084314, 2006. 12. Keblinski, P., S. R. Phillpot, S. U. S. Choi, and J. A. Eastman, “Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids),” Int. J. Heat Mass Transfer, Vol. 45, No. 4, 855–863, 2002. 13. Koo, J. and C. Kleinstreuer, “A new thermal conductivity model for nanofluids,” J. Nanopart. Res., Vol. 6, No. 6, 577–588, 2004. 14. Jang, S. P. and S. U. S. Choi, “Role of Brownian motion in the enhanced thermal conductivity of nanofluids,” Appl. Phys. Lett., Vol. 84, No. 21, 4316–4318, 2004. 15. Prasher, R., P. Bhattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett., Vol. 94, 025901, 2005. 16. Evans, W., J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett., Vol. 88, No. 9, 093116, 2006. 17. Keblinski, P. and J. Thomin, “Hydrodynamic field around a Brownian particle,” Phys. Rev. E, Vol. 73, 010502, 2006. 18. Prasher, R., P. E. Phelan, and P. Bhattacharya, “Effect of aggregation kinetics on the thermal conductivity of nanoscale colloidal solutions (nanofluid),” Nano. Lett., Vol. 6, No. 7, 1529–1534, 2006. 19. Buongiorno, J., “Convective transport in nanofluids,” J. Heat Transfer, Vol. 128, No. 3, 240– 250, 2006. 20. Prasher, R., P. Bhattacharya, and P. E. Phelan, “Brownian-motion-based convective- conductive model for the effective thermal conductivity of nanofluids,” J. Heat Transfer, Vol. 128, No. 6, 588–595, 2006. 21. Prakash, M. and E. P. Giannelis, “Mechanism of heat transport in nanofluids,” J. Comput. Aided Mater. Des., Vol. 14, No. 1, 109–117, 2007. 22. Jang, S. P. and S. U. S. Choi, “Effects of various parameters on nanofluid thermal conductivity,” J. Heat Transfer, Vol. 129, No. 5, 617–623, 2007. 23. Patel, H. E., T. Sundararajan, and S. K. Das, “A cell model approach for thermal conductivity of nanofluids,” J. Nanopart. Res., Vol. 10, No. 1, 87–97, 2008.