^{}Mechanical Engineering Department, University of Kashan, Kashan, I.R. Iran

Abstract

Flow field and heat transfer of a nanofluid, whose non-Newtonian behavior has been demonstrated in the laboratory, in a square enclosure have been numerically modeled and investigated. To estimate the viscosity of nanofluid, experimental data of Hong and Kim, 2012 have been used, and a new model has been proposed. Finally, the obtained results have been compared to those of Newtonian behavior. The results obtained by the numerical simulation indicate that the average Nusselt number with non-Newtonian behavior has a value less than the Newtonian behavior. Also for the case in which the nanofluid is non-Newtonian, the buoyancy force is often insignificant, and forced convection dominates. By adding the nanoparticles, the average Nusselt number for the non-Newtonian nanofluid increases, but for the Newtonian nanofluid, depending on the dominant of natural or forced convection in the flow, it decreases or increases, respectively. On the other hand, with increasing the Reynolds number, the heat transfer rate increases for both Newtonian and non-Newtonian fluid at any constant Grashof number, while with increasing of Grashof number at a given temperature difference and a constant Reynolds number, the heat transfer rate increases and decreases in Newtonian and non-Newtonian nanofluids, respectively.

[1] X. Wang, S.U.S. Choi: Thermal conductivity of nanoparticle–fluid mixture, J. of Thermophysics Heat Transfer 13 (1999) 474–480.

[2] J. Chevalier, O. Tillement, F. Ayela: Rheogical properties of nanofluids flowing through microchannels, Appl. Phy. Lett 91 (2007) 233103.

[3] B. Aladag, S. Halelfadl, N. Doner, T. Maré, S. Duret, P. Estellé: Experimental investigations of the viscosity of nanofluids at low temperatures, Appl. Energy 97 (2012) 876–880.

[4] K. Kwak, C. Kim: Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol, Korea–Australia Rheology J 17 (2005) 35–40.

[5] H. Chang, C.S. Jwo, C.H. Lo, T.T. Tsung, M.J. Kao, H.M. Lin, Rheology of CuO nanoparticle suspension prepared by ASNSS, Rev. on Adv. Materials Sci 10 (2005) 128–132.

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

[7] J. Hong, D. Kim: Effects of aggregation on the thermal conductivity of alumina/water nanofluids, Thermochimica Acta 542(2012) 28-32.

[8] N. Putra, W. Roetzel, S.K. Das: Natural convection of nano-fluids, Heat and Mass Transfer 39 (2003) 775–784.

[9] D. Wen, Y. Ding, Natural convective heat transfer of suspensions of titanium dioxide nanoparticles (nanofluids), IEEE Transactions on Nanotechnology 5 (2006) 220–227.

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

[11] M.M. Cross Rheology of non-Newtonian fluids, a new flow equation for pseudoplastic systems, J. of Colloid Sci 20 (1965) 417-437.

[12] H. Ozoe, S. Churchill, Hydrodynamic stability and natural convection in Ostwald-De Waele and Ellis fluids: the development of a numerical solution, AIChE J 18 (1972) 1196-1207.

[13] G.B. Kim, J.M. Hyun, H.S. Kwak, Transient buoyant convection of a power-law non-Newtonian fluid in an enclosure, Int. J. of Heat and Mass Transfer 46 (2003) 3605-3617.

[14] N. Ouertatani, N. Ben Cheikh, B. Ben Beyaa, T. Lilia, T., A. Campo, Mixed convection in a double lid-driven cubic cavity, Int. J. of Therm. Sci 48 (2009) 1265–1272.

[15] R. Iwatsu, J. Hyun, K. Kuwahara, Mixed convection in a driven cavity with a stable vertical temperature gradient, Int. J. of Heat and Mass Transfer 36 (1993) 1601–1608

[16] K. Khanafer, A.J. Chamkha, Mixed convection flow in a lid-driven enclosure filled with a fluid-saturated porous medium, Int. J. of Heat and Mass Transfer 42 (1999) 2465–2481.

[17] O. Aydin, Aiding and opposing mechanisms of mixed convection in a shearand buoyancy-driven cavity, Int. Commun.in Heat and Mass Transfer 26 (1999) 1019–1028.

[18] M.A.R. Sharif, Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Appl. Therm. Engin 27 (2007) 1036–1042.

[19] K.M. Khanafer, A.M. Al-Amiri, I. Pop, Numerical simulation of unsteady mixed convection in a driven cavity, using an externally excited sliding lid, Eurpean J. of Mechanics B/Fluids 26 (2007) 669–687.

[20] M.M. Abdelkhalek, Mixed convection in a square cavity by a perturbation technique, Computer and Material Sci 42 (2008) 212–219.

[21] M.A. Waheed, Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate, Int. J. of Heat and Mass Transfer 52 (2009) 5055–5063.

[22] O. Aydin, W.J. Yang, Mixed convection in cavities with a locally heated lower wall and moving sidewalls, Numerical Heat Transfer 37 (2000) 695–710.

[23] H.F. Oztop, I. Dagtekin, Mixed convection in two sided lid driven differentially heated square cavity, Int. J. of Heat and Mass Transfer 47 (2004) 1761–1769.

[24] W.J. Luo, R.J. Yang,Multiple fluid flow and heat transfer solutions in a two sided lid-driven cavity, Int. J. of Heat and Mass Transfer 50 (2007) 2394–2405.

[25] F. Gurcan, Effect of the Reynolds number on streamline bifurcations in a double-lid-driven cavity with free surfaces, Computer & Fluids 32 (2003) 1283–1298.

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

[27] M. Muthtamilselvan, P. Kandaswamy, J. Lee, Heat transfer enhancement of copper–water nanofluids in a lid-driven enclosure, Commun. in Nonlinear Sci. and Numerical Simulation 15 (2010) 1501–1510.

[28] H.C. Brinkman, The viscosity of concentrated suspensions and solution, J. Chem. Phy 20 (1952) 571–581.

[29] N. Ait Messaoudene, A. Horimek, C. Nouar, B. Benaouda-Zouaoui, Laminar mixed convection in an eccentric annular horizontal duct for a thermodependent non-Newtonian fluid, Int. J. Heat Mass Transfer 54 (2011) 4220-4234.

[30] A. Mahdy, Soret and Dufour effect on double diffusion mixed convection from a vertical surface in a porous medium saturated with a non-Newtonian fluid, J. Non-Newtonian Fluid Mechanics165 (2010) 568-575.

[31] Ahmed M. Salem, Mohamed Abd El-Aziz, Emad M. Abo-Eldahab, Ibrahim Abd-Elfatah, Effect of variable density on hydromagnetic mixed convection flow of a non-Newtonian fluid past a moving vertical plate, Commun. Nonlinear Sci. Num. Simulation 15(6) (2010) 1485-1493

[32] R.B. Bird, W.E. Stewert, E.N. Lightfoot: Transport Phenomena, John Wiley & Sons, Singapore, 1960.

[33] K. Khanafer, K. Vafai, A critical synthesis of thermophysical characteristics of nanofluids, Int. J. of Heat and Mass Transfer 54 (2011) 4410–4428.

[34] A. Barnes, Handbook of Elementary Rheology, Howard University of Wales, Institute of Non-Newtonian Fluid Mechanics, Aberystwyth 2000.

[35] Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. of Heat and Mass Transfer 43 (2000) 3701–3707.

[36] H.E. Patel, T. Sundarrajan, T., Pradeep, A. Dasgupta, N. Dasgupta, S.K. Das, A micro-convection model for thermal conductivity of nanofluid, Pramana J. of Phy 65 (2005) 863–869.

[37] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980.

[38] A.J. Chamkha, E. Abu-Nada, Mixed convection flow in single and doublelid driven square cavities filled with water–Al2O3 nanofluid: Effect of viscosity models, European J. Mechanics B/Fluids 36 (2012) 82-96.

[39] S.Z. Heris, S.Gh. Etemad, M.N. Esfahany, Experimental investigation of oxide nanofluids laminar flow convective heat transfer, Int. Commun. in Heat Mass Transfer 33 (2006) 529–535.