Unsteady Rayleigh-Bénard Convection of Nanoliquids in Enclosures

Rayleigh-B´enard convection of a nanoliquid in shallow, square and tall enclosures is studied using the Khanafer-Vafai-Lightstone single-phase model. The thermophysical properties of water, copper, copper-oxide, alumina, silver and titania at 3000 K under stagnant conditions that are collected from literature are used in calculating thermophysical properties of water-based nanoliquids. Phenomenological laws and mixture theory are used for calculating thermophysical properties. Free-free, rigid-rigid and rigid-free boundary conditions are considered in the study. Intractable Lorenz model for each boundary combination is derived and then reduced to the tractable Ginzburg-Landau model. The amplitude thus obtained is used to quantify the heat transport in terms of Nusselt number. Addition of nanoparticles is shown not to alter the influence of the nature of boundaries on the onset of convection as well as on heat transport. Amongst the three enclosures considered, it is found that tall and shallow enclosures transport maximum and minimum energy respectively. Enhancement of heat transport due to nanoparticles in the three enclosures is found to be in the range 3% - 11%. Comparison of results in the case of rigid-rigid boundaries is made with those of an earlier work and good agreement is found. The study has limitations in the sense that thermophysical properties are calculated by using various quantities modelled for static condition.

Authors:

• P. G. Siddheshwar
• B. N. Veena

Keywords:

• Enclosures
• free-free
• rigid-rigid and rigid-free boundaries
• Ginzburg-Landau model
• Lorenz model.

References:

[1] E. Abu-Nada and A. J. Chamkha, Effect of nanofluid variable properties
on natural convection in enclosures filled with a CuO-EG water
nanofluid, Int. J. Therm. Sci., 49, pp. 2339-2352, 2010.
[2] H. C. Brinkman, The viscosity of concentrated suspensions and
solutions, J. Chem. Phys., 20, pp. 571-571, 1952.
[3] J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Trans.,
128, pp. 240-250, 2006.
[4] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford
University Press, London, 1961.
[5] S. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids
with nanoparticles, D. A. Siginer and H. P. Wang (Eds.), Development
and applications of Non-Newtonian flows”, ASME, FED, 231 MD, 66,
pp. 99-105, 1995.
[6] M. Corcione, Rayleigh-B´enard convection heat transfer in nanoparticle
suspensions, Int. J. Heat Fluid Flow, 32, pp. 65-77, 2011.
[7] S. K. Das, N. Putra, P. Thiesen and W. Roetzel, Temperature dependence
of thermal conductivity enhancement for nanofluids, ASME J. Heat
Trans., 125, pp. 567-574, 2003.
[8] J. A. Eastman, S. U. S. Choi, S. Li, W. Yu and L. J. Thompson,
Anomalously increased effective thermal conductivities of ethylene
glycol-bases nanofluids containing copper nanoparticles, Appl. Phys.
Lett., 78, pp. 718-720, 2001.
[9] B. Elhajjar, G. Bachir, A. Mojtabi, C. Fakih and M. C. Charrier-Mojtabi,
Modeling of Rayleigh-B´enard natural convection heat transfer in
nanofluids, C. R. Mecanique, 338, pp. 350-354, 2010.
[10] R. L. Hamilton and O. K. Crosser, Thermal conductivity of
heterogeneous two-component systems, Ind. Eng. Chem. Fund., 1, pp.
187-191, 1962.
[11] R. Y. Jou and S. C. Tzeng, Numerical research of nature convective heat
transfer enhancement filled with nanofluids in rectangular enclosures,
Int. Comm. Heat Mass Trans., 33, pp. 727-736, 2006.
[12] K. Khanafer, K. Vafai and M. Lightstone, Buoyancy driven heat transfer
enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J.
Heat Mass Trans., 46, pp. 3639-3653, 2003.
[13] H. Masuda, A. Ebata, K. Teramae and N. Hishinuma, Alteration of
thermal conductivity and viscosity of liquid by dispersing ultra fine
particle, Netsu Bussei, 7, pp. 227-233, 1993.
[14] M. Nagata, Bifurcations at the Eckhaus points in two-dimensional
Rayleigh-B´enard convection, Phys. Rev. E, 52, pp. 6141-6145, 1995.
[15] H. M. Park, Rayleigh-B´enard convection of nanofluids based on the
pseudo-single-phase continuum model, Int. J. Therm. Sci., 90, pp.
267-278, 2015.
[16] P. G. Siddheshwar, C. Kanchana, Y. Kakimoto and A. Nakayama,
Steady finite-amplitude Rayleigh-B´enard convection in nanoliquids using
a two-phase model: Theoretical answer to the phenomenon of enhanced
heat transfer, ASME J. Heat Trans., 139, pp. 012402-012411, 2017.
[17] P. G. Siddheshwar, and N. Meenakshi, Amplitude equation and heat
transport for Rayleigh-B´enard convection in Newtonian liquids with
nanoparticles, Int. J. Appl. Comp. Math., 2, pp. 1-22, 2016.
[18] R. K. Tiwari and M. K. Das, Heat transfer augmentation in a two-sided
lid-driven differentially heated square cavity utilizing nanofluids, Int. J.
Heat Mass Trans., 50, pp. 2002-2018, 2007.