Document Type : Original Research Paper

**Authors**

Mechanical Engineering Department, University of Technology Babol, Babol, I.R. Iran

**Abstract**

The effects of Single Walled Carbon Nanotube (SWCNT) on mixed convection in a cavity are investigated numerically. The problem is studied for different Richardson numbers (0.1-10), volume fractions of nanotubes (0-1%), and aspect ratio of the cavity (0.5-2.5) when the Grashof number is equal to 103. The volume fraction of added nanotubes to Water as base fluid are lowers than 1% to make dilute suspensions. The Study presents a numerical treatment based on LBM to model convection heat transfer of Carbon nanotube based nanofluids. A theoretical model is used for effective thermal conductivity of the nanofluid containing Carbon nanotubes. This model covers different phenomena of energy transport in nanofluids. Also, an analytical model is applied for effective viscosity of the nanofluid which includes the Brownian effect and other physical properties of nanofluids. Results show that adding a low value of SWCNT to the base fluid led to significant enhancement of convection heat transfer. Make a comparison between the obtained results and other published papers shows that Carbon nanotubes enhances the rate of convection heat transfer better than other nanoparticles.

**Keywords**

[1] F.D.S. Marquis , L.P.F. Chibante: Improving the heat transfer of nanofluids and nano lubricants with Carbon nanotubes, JOM Res. Summary Carbon Nanotubes, December (2005).

[2] R.K. Tiwari, M.K. Das: Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer, 50 (2007) 2002-2018.

[3] J.A. Eastman, S.U.S Choi, S. Li, W. Yu, L.J. Thompson: Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Appl. Phys. Lett., 78 (2001) 718-724.

[4] H. Xie, J. Wang, T. Xi, Y. Liu, F. Ai: Thermal conductivity enhancement of suspensions containing nanosized alumina particles, J. Appl. Phys., 10 (2002) 4568-4572.

[5] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke: Anomalous thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett., 79 (2001) 2252-2256.

[6] H. Xie, H.W. Youn, M. Choi: Nanofluids containing multi-walled Carbon nanotubes and their enhanced thermal conductivities, J. Appl. Phys., 94 (2003) 4967-4973.

[7] U.S. Choi: Enhancing thermal conductivity of fluids with nanoparticles, Developments and application of non-Newtonian flows, ASME J. Heat Transfer, 66 (1995) 99-105.

[8] K. Khanafer, K. Vafai, M. Lightstone: Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer, 46 (2003) 3639-3653.

[9] I. Gherasim, G. Roy, C.T. Nguyen, D. Vo-Ngoc: Experimental investigation of nanofluids in confined laminar radial flows, Int. J. Therm. Sci., 48 (2009) 1486-1493.

[10] H. Saleh, R. Roslan ,I. Hashim: Natural convection heat transfer in a nanofluid-filled trapezoidal enclosure, Int. J. Heat Mass Transfer, 54 (2011) 194-201.

[11] S. Mirmasoumi ,A. Behzadmehr: Numerical study of laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model, Appl. Therm. Eng., 28 (2008) 717-727.

[12] O. Ghaffari, A. Behzadmehr: Investigation of the effect of nanoparticles mean diameter on turbulent mixed convection of a nanofluid in a horizontal curved tube using a two phase approach, Transport Phenomena in Nano and Micro Scales, 1 (2013) 64-74.

[13] A.K. Santra, S. Sen, N. Chakraborty: Study of heat transfer augmentation in a differentially heated square cavity using copper-water nanofluid, Int. J. Therm. Sci., 47 (2008) 1113-1122.

[14] M. Izadi, A. Behzadmehr, D. Jalali-Vahida: Numerical study of developing laminar forced convection of a nanofluid in an annulus, Int. J. Therm. Sci., 48 (2009) 2119-2129.

[15] S. Iijima, T. Ichihashi: Single-shell Carbon nanotubes of 1-nm diameter, Nature, 363 (1993) 603- 605.

[16] E. T. Thostenson, Z. Ren and T.W. Chou: Advances in the science and technology of Carbon nanotubes and their composites: a review, Compos. Sci. Technol., 61 (2001) 1899-1912.

[17] S. Berber, Y.K. Kwon, D. Tomanek: Unusually high thermal conductivity of Carbon nanotubes, Phys. Rev. Lett., 84 (2000) 4613-4616.

[18] P. Kim, L. Shi, A. Majumdar, P.L. Mceuen, Thermal transport measurements of individual multi walled nanotubes, Phys. Rev. Lett., 87 (2001) 215502-215505.

[19] A. Gavili, T. Dallali Isfahani, J. Sabbaghzadeh: The variation of heat transfer in a two-sided lid-driven differentially heated square cavity with nanofluids containing Carbon nanotubes for physical properties of fluid dependent on temperature, Int. J. Numer. Meth. Fluids, 68 (3) (2011) 302-323.

[20] A. Mohamad, Applied Lattice Boltzmann Method for Transport Phenomena, Momentum, Heat and Mass Transfer, Sure, Calgary, 2007.

[21] M. Jafari, M. Farhadi, K. Sedighi, E. Fattahi: Lattice Boltzmann simulation of mixed convection in an inclined cavity with a wavy wall, Heat Transfer-Asian Research, 41 (5) (2012) 371-387.

[22] E. Fattahi, M. Farhadi, K. Sedighi: Natural Convection and Entropy Generation in L-Shaped Enclosure Using Lattice Boltzmann Method, Transport Phenomena in Nano and Micro Scales, 1 (2013) 1-18.

[23] M. Aghajani Delavar, M. Farhadi, K. Sedighi: Numerical simulation of direct methanol fuel cells using lattice Boltzmann method, Int. J. Hydrog. Energy, 35 (2010) 9306-9317.

[24] E.J. Javaran, S.A.G. Nassab, S. Jafari: Thermal analysis of a 2-D heat recovery system using porous media including lattice Boltzmann simulation of fluid flow, Int. J. Therm. Sci., 49 (2010) 1031-1041.

[25] E. Fattahi, M. Farhadi, K. Sedighi, H. Nemati: Lattice Boltzmann simulation of natural convection heat transfer in nanofluids, Int. J. Therm. Sci., 52 (2012) 137-144.

[26] M. Jafari, M. Farhadi, K. Sedighi: Effect of Wavy Wall on Convection Heat Transfer of Water-Al2O3 Nanofluid in a Lid-driven Cavity Using Lattice Boltzmann Method, Int. J. Engine. - Transaction (A), 25 (2012) 168-180.

[27] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi: Lattice Boltzmann simulation of nanofluid in lid-driven cavity, Int. Commun. Heat Mass Transfer, 37 (2010) 1528-1534.

[28] E. Abu-Nadaa, A.J. Chamkhac: Mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid, Eur. J. Mech. B/Fluids, 29 (2010) 472-482.

[29] F. Talebi, A.H. Mahmoudi, M. Shahi: Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid, Int. Commun. Heat Mass Transfer, 37 (2010) 79-90.

[30] J. Sabbaghzadeh and S. Ebrahimi: Effective of thermal conductivity of nanofluids containing cylindrical nanoparticles, Int. J. of Nanosci., 6 (2007) 45-49.

[31] N. Masoumi, N. Sohrabi and A. Behzadmehr, A new model for calculating the effective viscosity of nanofluids, J. Phys. D: Appl. Phys., 42 (2009) 055501 (6pp).

[32] Y. He, C. Qi, Y. Hu, B. Qin, Y. Ding: Lattice Boltzmann simulation of alumina-water nanofluid in a square cavity, Nanoscale Research Letters, 6 (2011) 184-192.

[33] Y. Xuan , W. Roetzel: Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer, 43 (19) (2000) 3701-3707.

[34] R. Prasher, E.P. Phelan: Brownian motion based convective-conductive model for the effective thermal conductivity of nanofluids, ASME J. Heat Transfer, 128 (2006) 588-593.

[35] Y. Ding, H. Alias, D. Wen, R. A. Williams: Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids), Int. J. Heat and Mass Transfer, 49 (2006) 240-250.

[36] A. Einstein: Investigations on the Theory of the Brownian movement, Dover, New York, (1959), p. 64.

[37] M. K. Moallemi, K.S. Jang: Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity, Int. J. Heat Mass Transfer, 35 (1992) 1881-1892.

Winter and Spring 2014

Pages 14-28