International Scientific Journal


A two-phase model based on the double-diffusive approach is used to perform a numerical study on natural convection of water-based nanofluids in differentially-heated horizontal semi-annuli, assuming that Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum, and energy for the nanofluid, and continuity for the nanoparticles, is solved by the way of a computational code which incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient, all based on a wide number of literature experimental data. The pressure-velocity coupling is handled through the SIMPLE-C algorithm. Numerical simulations are executed for three different nanofluids, using the diameter and the average volume fraction of the suspended nanoparticles, the cavity size, the average temperature, and the temperature difference imposed across the cavity, as independent variables. It is found that the impact of the nanoparticle dispersion into the base liquid increases remarkably with increasing the average temperature, whereas, by contrast, the other controlling parameters have moderate effects. Moreover, at temperatures of the order of room temperature or just higher, the heat transfer performance of the nanofluid is significantly affected by the choice of the solid phase material.
PAPER REVISED: 2017-03-16
PAPER ACCEPTED: 2017-05-22
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 6, PAGES [2643 - 2660]
  1. Abu-Nada, E., et al., Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids, Int. Comm. Heat Mass Transfer, 35 (2008), pp. 657665
  2. Abu-Nada, E., Effects of variable viscosity and thermal conductivity of Al2O3-water nanofluid on heat transfer enhancement in natural convection, Int. J. Heat Fluid Flow, 30 (2009), pp. 679690
  3. Abu-Nada, E., Effects of variable viscosity and thermal conductivity of CuO-water nanofluid on heat transfer enhancement in natural convection: mathematical model and simulation, J. Heat Transfer, 132 (2010), 052401
  4. Sheikholeslami, M., et al., Natural convection heat transfer in a nanofluid filled semi-annulus enclosure, Int. Comm. Heat Mass Transfer, 39 (2012), pp. 565-574
  5. Yu, Z. T., et al., A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a horizontal concentric annulus, Int. J. Heat Mass Transfer, 55 (2012), pp. 1141-1148
  6. Parvin, S., et al., Thermal conductivity variation on natural convection flow of water-alumina nanofluid in an annulus, Int. J. Heat Mass Transfer, 55 (2012), pp. 5268-5274
  7. Ashorynejad, H. R., et al., Magnetic field effects on natural convection flow of a nanofluid in a horizontal cylindrical annulus using Lattice Boltzmann method, Int. J. Thermal Sciences, 64 (2013), pp. 240-250
  8. Sheikholeslami, M., et al., Effect of a magnetic field on natural convection in an inclined half-annulus enclosure filled with Cu-water nanofluid using CVFEM, Advanced Power Technology, 24 (2013), pp. 980-991
  9. Corcione, M., et al., A two-phase numerical study of buoyancy-driven convection of alumina-water nanofluids in differentially-heated horizontal annuli, Int. J. Heat Mass Transfer, 65 (2013), pp. 327-338
  10. Sheikhzadeh, G. A., et al., Laminar natural convection of Cu-water nanofluid in concentric annuli with radial fins attached to the inner cylinder, Heat Mass Transfer, 49 (2013), pp. 391-403
  11. Sheikholeslami, M., et al., Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer, Energy, 75 (2014), pp. 400-410
  12. Sheikholeslami, M., et al., Thermal management for free convection of nanofluid using two phase model, J. Mol. Liq., 194 (2014), pp. 179-187
  13. Arbaban, M., et al., Enhancement of laminar natural convective heat transfer in concentric annuli with radial fins using nanofluids, Heat Mass Transfer, 51 (2015), pp. 353-362
  14. Fallah, K., et al., Simulation of natural convection heat transfer using nanofluid in a concentric annulus, Int. J. Thermal Sciences, Doi reference: 10.2298/TSCI150118078F , (2015),
  15. Bezi, S., et al., Enhancement of natural convection heat transfer using different nanoparticles in an inclined semi-annular enclosure partially heated from above, High Temp., 53 (2015), pp. 99-117
  16. Seyyedi, S. M., et al., Natural convection heat transfer under costant heat flux wall in a nanofluid filled annulus enclosure, Ain Shams Eng. J., 6 (2015), pp. 267-280
  17. Oglakkaya, F. S., et al., MHD natural convection in a semi-annulus enclosure filled with water-based nanofluid using DRBEM, Eng. Anal. Bound. Elem., 71 (2016), pp. 151-163
  18. Zhang, C., et al., Unsteady natural convection heat transfer of nanofluid in an annulus with sinusoidally heated source, Num. Heat Transfer, 69 (2016), pp. 97-108
  19. Sheikholeslami, M., et al., Electrohydrodynamic free convection heat transfer of a nanofluid in a semi-annulus enclosure with a sinusoidal wall, Num. Heat Transfer, 69 (2016), pp. 781-793
  20. Maxwell, J. C., A Treatise on Electricity and Magnetism, 3rd ed., Dover, New York, 1954
  21. Brinkman, H. C., The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 20 (1952), pp. 571
  22. McNab, G. S., et al., Thermophoresis in liquids, J. Colloid Interface Science, 44 (1973), pp. 339-346
  23. Buongiorno, J., Convective transport in nanofluids, J. Heat Transfer, 128 (2006), pp. 240-250
  24. Das, S. K., et al., Pool boiling characteristics of nano-fluids, Int. J. Heat Mass Transfer, 46 (2003), pp. 851-862
  25. Prasher, R., et al., Measurements of nanofluid viscosity and its implications for thermal applications, Appl. Phys. Lett., 89 (2006), 133108
  26. He, Y., et al., 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
  27. Chen, H., et al., Rheological behaviour of ethylene glycol based titania nanofluids, Chem. Phys. Lett., 444 (2007), pp. 333-337
  28. Chevalier, J. et al., Rheological properties of nanofluids flowing through microchannels, Appl. Phys. Lett., 91 (2007), pp. 233103
  29. Cabaleiro, D., et al., Characterization and measurements of thermal conductivity, density and rheological properties of zinc oxide nanoparticles dispersed in (ethane-1,2-diol + water) mixture, J. Chem. Thermodynamics, 58 (2013), pp. 405-415
  30. Einstein, A., Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen (in German), Ann. Phys., 17 (1905), pp. 549-560
  31. Corcione, M., et al., Enhanced natural convection heat transfer of nanofluids in enclosures with two adjacent walls heated and the two opposite walls cooled, Int. J. Heat Mass Transfer, 88 (2015), pp. 902-913
  32. Corcione, M., Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids, Energy Convers. Management, 52 (2011), pp. 789-793
  33. Keblinski, P., et al., Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), Int. J. Heat Mass Transfer, 45 (2002), pp. 855-863
  34. Corcione, M., et al., Two-phase mixture modeling of natural convection of nanofluids with temperature-dependent properties, Int. J. Thermal Sciences, 71 (2013), pp. 182-195
  35. Ghanbarpour, M., et al., Thermal properties and rheological behavior of water based Al2O3 nanofluid as a heat transfer fluid, Exp. Thermal Fluid Science, 53 (2014), pp. 227-235
  36. Akilu, S., et al., A review of thermophysical properties of water based composite nanofluids, Renew. Sustain. Energy Rev., 66 (2016), pp. 654-678
  37. Pak, B. C., et al., Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer, 11 (1998), pp. 151-170
  38. Zhou, S. Q., et al., Measurement of the specific heat capacity of water-based Al2O3 nanofluid, Appl. Phys. Lett., 92 (2008), 093123
  39. Van Doormaal, J. P., et al., Enhancements of the simple method for predicting incompressible fluid flows, Num. Heat Transfer, 11 (1984),pp. 147-163
  40. Patankar, S. V., et al., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat Mass Transfer, 15 (1972), pp. 1787-1797
  41. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publ. Co., Washington, DC, 1980
  42. Leonard, B. P., A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comp. Meth. Appl. Mech. Eng., 19 (1979), pp. 59-78
  43. Kuehn, T. H., et al., An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders, J. Fluid Mech., 74 (1976), pp. 695-719
  44. Phanikumar, M. S., et al., Numerical analysis of unsteady thermosolutal convection over a horizontal isothermal circular cylinder, Num. Heat Transfer, 33 (1998), pp. 673-700
  45. Putra, N., et al., Natural convection of nano-fluids, Heat Mass Transfer, 39 (2003),pp. 775-784
  46. Chang, B. H., et al., Natural convection of microparticle suspensions in thin enclosures, Int. J. Heat Mass Transfer, 51 (2008), pp. 1332-1341
  47. Hu, Y., et al., Experimental and numerical study of natural convection in a square enclosure filled with nanofluid, Int. J. Heat Mass Transfer, 78 (2014), pp. 380-392
  48. Wen, D. et al., Formulation of nanofluids for natural convective heat transfer applications, Int. J. Heat Fluid Flow, 26 (2005), pp. 855-864

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence