Unsteady Rayleigh-Bénard Convection of Nanoliquids in Enclosures
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32870
Unsteady Rayleigh-Bénard Convection of Nanoliquids in Enclosures

Authors: P. G. Siddheshwar, B. N. Veena


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.

Keywords: Enclosures, free-free, rigid-rigid and rigid-free boundaries, Ginzburg-Landau model, Lorenz model.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1130533

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 823


[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.