International Scientific Journal


Laminar natural convection of Al2O3 + H2O nanofluids inside square cavities differentially heated at sides is studied numerically. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum and energy transfer governing equations. Assuming that the nanofluid behaves like a single-phase fluid, these equations are the same as those valid for a pure fluid, provided that the thermophysical properties appearing in them are the nanofluid effective properties. The thermal conductivity and dynamic viscosity of the nanofluid are calculated by means of a couple of empirical equations based on a wide variety of experimental data reported in the literature. The other effective properties are evaluated by the conventional mixing theory. Simulations are performed for different values of the nanoparticle volume fraction in the range 0-0.06, the diameter of the suspended nanoparticles in the range 25-100 nm, the temperature of the cooled sidewall in the range 293-313 K, the temperature of the heated sidewall in the range 298-343 K, and the Rayleigh number of the base fluid in the range 103-107. All computations are executed in the hypothesis of temperature-dependent effective properties. The main result obtained is the existence of an optimal particle loading for maximum heat transfer, that is found to increase as the size of the suspended nanoparticles is decreased, and the nanofluid average temperature is increased.
PAPER REVISED: 2012-01-31
PAPER ACCEPTED: 2012-05-02
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THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Issue 2, PAGES [591 - 608]
  1. Khanafer, K., Vafai, K., Lightstone, M., Buoyancy-driven heat transfer enhancement in a twodimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer, 46 (2003), pp. 3639- 3653
  2. Jou, R.-Y., Tzeng, S.-C., Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures, Int. Comm. Heat Mass Transfer, 33 (2006), pp. 727-736
  3. Oztop, H. F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow, 29 (2008), pp. 1326-1336
  4. Abu-Nada, E., Oztop, H. F., Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid, Int. J. Heat Fluid Flow, 30 (2009), pp. 669-678
  5. Kahveci, K., Buoyancy driven heat transfer of nanofluids in a tilted enclosure, J. Heat Transfer, 132 (2010), p. 062501
  6. Kefayati, GH. R., Hosseinizadeh, S. F., Gorji, M., Sajjadi, H., Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid, Int. Comm. Heat Mass Transfer, 38 (2011), pp. 798-805
  7. Lai, F.-H., Yang, Y.-T., Lattice Boltzmann simulation of natural convection heat transfer of Al2O3/water nanofluids in a square enclosure, Int. J. Thermal Sciences, 50 (2011), pp. 1930- 1941
  8. Abu-Nada, E., Masoud, Z., Oztop, H. F., Campo, A., Effects of nanofluid variable properties on natural convection in enclosures, Int. J. Thermal Sciences, 49 (2010), pp. 479-491
  9. Lin, K. C., Violi A., Natural convection heat transfer of nanofluids in a vertical cavity: Effects of non-uniform particle diameter and temperature on thermal conductivity, Int. J. Heat Fluid Flow, 31 (2010), pp. 236-245
  10. Abu-Nada E., Chamkha A. J., Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO-EG-Water nanofluid, Int. J. Thermal Sciences, 49 (2010), pp.2339- 2352
  11. Maxwell-Garnett, J. C., A Treatise on Electricity and Magnetism, 3rd ed., Dover, New York, USA, 1954.
  12. Brinkman, H. C., The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 20 (1952), p. 571
  13. Hamilton, R. L., Crosser, O. K., Thermal conductivity of heterogeneous two component systems, Ind. Eng. Chem. Fundam., 1 (1962), pp. 187-191
  14. Bruggemann, D. A. G., Berechnung Verschiedener Physikalischer Konstanten von Heterogenen Substanzen, I. Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus Isotropen Substanzen, Ann. Phys., 24 (1935), pp. 636-679
  15. Eapen, J., Williams, W. C., Buongiorno, J., Hu, L.-W., Yip, S., Rusconi, R., Piazza, R. , Meanfield versus microconvection effects in nanofluid thermal conduction. Phys. Rev. Lett., 99 (2007), paper No. 095901
  16. Buongiorno, J., et al., A benchmark study on the thermal conductivity of nanofluids, J. Appl. Phys., 106 (200), paper No. 094319
  17. Das, S. K., Putra, N., Thiesen, P., Roetzel, W., Temperature dependence of thermal conductivity enhancement for nanofluids, J. Heat Transfer, 125 (2003), pp. 567-574
  18. Li, C. H., Peterson, G. P., Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids), J. Appl. Phys., 99 (2006), paper No. 084314
  19. Yu, W., Xie, H., Chen, L., Li, Y., Investigation on the thermal transport properties of ethylene glycol-based nanofluids containing copper nanoparticles, Powder Tecnology, 197 (2010), pp. 218-221
  20. Chen, H., Ding, Y., Tan, C., Rheological behaviour of nanofluids, New Journal of Physics, 9 (2007), paper No. 367
  21. Chen, H., Ding, Y., He, Y., Tan, C., Rheological behaviour of ethylene glycol based titania nanofluids, Chem. Phys. Lett., 444 (2007), pp. 333-337
  22. Chevalier, J., Tillement, O., Ayela, F., Rheological properties of nanofluids flowing through microchannels, Appl. Phys. Lett., 91 (2007), paper No. 233103
  23. Einstein, A., Eine neue Bestimmung der Molekuldimension, Ann. Phys., 19 (1906), pp. 289-306
  24. Einstein, A., Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Molekuldimension, Ann. Phys., 34 (1911), pp. 591-592
  25. Putra, N., Roetzel, W., Das, S. K., Natural convection of nano-fluids, Heat Mass Transfer, 39 (2003), pp. 775-784
  26. Nnanna, A. G. A., Experimental model of temperature-driven nanofluid, J. Heat Transfer, 129 (2007), pp. 697-704
  27. Ho, C. J., Liu, W. K., Chang, Y. S., Lin, C. C., Natural convection heat transfer of aluminawater nanofluid in vertical square enclosures: An experimental study, Int. J. Thermal Sciences, 49 (2010), pp. 1345-1353
  28. Corcione, M., Heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the sidewalls, Int. J. Thermal Sciences, 49 (2010), pp. 1536- 1546
  29. Chang, B. H., Mills, A. F., Hernandez, E., Natural convection of microparticle suspensions in thin enclosures, Int. J. Heat Mass Transfer, 51 (2008), pp. 1332-1341
  30. Williams, W., Buongiorno, J., Hu, L.-W., Experimental investigation of turbulent convective heat transfer and pressure loss of alumina/water and zirconia/water nanoparticle colloids (nanofluids) in horizontal tubes, J. Heat Transfer, 130 (2008), 042412
  31. Sommers, A. D., Yerkes, K. L., Experimental investigation into the convective heat transfer and system-level effects of Al2O3-propanol nanofluid, J. Nanopart. res., 12 (2009), pp. 1003-1014
  32. Rea, U., McKrell, T., Hu, L.-W., Buongiorno, J., Laminar convective heat transfer and viscous pressure loss of alumina-water and zirconia-water nanofluids, Int. J. Heat Mass Transfer, 52 (2009), pp. 2042-2048
  33. Das, S. K., Putra, N., Roetzel, W., Pool boiling characteristics of nano-fluids, Int. J. Heat Mass Transfer, 46 (2003), pp. 851-862
  34. Prasher, R., Song, D., Wang, J., Phelan, P., Measurements of nanofluid viscosity and its implications for thermal applications, Appl. Phys. Lett., 89 (2006), paper No. 133108
  35. He, Y., Jin, Y., Chen, H., Ding, Y., Cang, D., Lu, H., Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe, Int. J. Heat Mass Transfer, 50 (2007), pp. 2272-2281
  36. Kays, W., Crawford, M., Weigand, B., Convective Heat and Mass Transfer, 4th ed., Mc Graw- Hill Companies, Inc., New York, NY, USA, 2005.
  37. Corcione, M., Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids, Energy Conv. Manag., 52 (2011), pp. 789-793
  38. Keblinski, P., Phillpot, S. R., Choi, S. U. S., Eastman, J. A., Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), Int. J. Heat Mass Transfer, 45 (2002), pp. 855- 863
  39. Pak, B. C., Cho, Y. I., Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer, 11 (1998) pp. 151-170
  40. Xuan, Y., Roetzel, W., Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer, 43 (2000), pp. 3701-3707
  41. Van Doormaal, J. P., Raithby, G. D., Enhancements of the simple method for predicting incompressible fluid flows, Num. Heat Transfer, 11 (1984), pp. 147-163
  42. Patankar, S. V., Spalding, D. B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat Mass Transfer, 15 (1972), pp. 1787-1797
  43. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publ. Co., Washington, DC, USA, 1980.
  44. Leonard, B. P., A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comp. Meth. in Appl. Mech. Engng., 19 (1979), pp. 59-78
  45. de Vahl Davis, G., Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Num. Meth. Fluids, 3 (1983), pp. 249-264
  46. Mahdi, H. S., Kinney, R. B., Time-dependent natural convection in a square cavity: application of a new finite volume method, Int. J. Num. Meth. Fluids, 11 (1990), pp. 57-86
  47. Hortmann, M., Peric, M., Scheuerer, G., Finite volume multigrid prediction of laminar natural convection: bench-mark solutions, Int. J. Num. Meth. Fluids, 11 (1990), pp. 189-207
  48. Wan, D. C., Patnaik, B. S. V., Wei, G. W., A new benchmark quality solution for the buoyancydriven cavity by discrete singular convolution, Num. Heat Transfer, 40 (2001), pp. 199-228
  49. Bejan, A., Convection Heat Transfer, 3rd ed., John Wiley & Sons, Inc., Hoboken, NJ, USA, 2004.
  50. Incropera, F. P., DeWitt, D. P., Bergman, T. L., Lavine, A. S., Fundamentals of Heat and Mass Transfer, 6th ed., John Wiley & Sons, Inc., Hoboken, NJ, USA, 2007.

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