Introduction
Natural convection has many industrial and geophysical application. Such application vary from
the circulation in a vessel of liquid in which a crystal is being grown to the convective heat loss
from a flat plate solar collector. Other uses include the natural convection cooling of nuclear fuel
in shipping flasks, electronic cooling heat transfer and thermal systems.
Natural convection heat transfer occurs in enclosures due to temperature difference and
buoyancy forces. The problem was analyzed for enclosures filled with clear fluid [8] or
nanofluid [9] and for the cases of constant temperature or constant heat flux. In recent years,
effects of non-isothermal boundary conditions on natural convection in enclosure were analyzed
by researchers due to its applications in solar systems or furnaces. In this context, Bilgen and
Ben [10] performed study on the effects of non-isothermal boundary condition on natural
convection for a rectangular cavity
The first study concerning natural convection of a nanofluid confined in a differentially heated
enclosure seems to be due to Khanafer et al. (2003). The same problem was considered by Jou
and Tzeng (2006). The Khanafer et al.’s model was used to investigate the convective heat
transfer enhancement in rectangular enclosures filled with an Al2O3–water nanofluid.
Lai et al [] pointed out that the average Nusselt number with the use of nanofluid is higher than
the use of water under the same Rayleigh number and the heat transfer rate of the nanofluid
takes on a lower value than water at a fixed temperature difference across the enclosure
mainly due to the significant enhancement of dynamic viscosity.
However, contradictory results have been noted in the experimental studies [10 e 14] that
dispersion of nanoparticles in the base fluid may result in marked reduction, instead of
enhancement, of natural convection heat transfer in enclosures. Putra et al. [10] conducted
experiments to investigate natural convective heat transfer of aqueous CuO and Al2O3
nanofluids inside a cylinder. They observed a systematic and significant deterioration in natural
convective heat transfer at Rayleigh numbers from 10 6to 10 9. The deterioration increased with
particle concentration and was more pronounced for CuO nanofluids. Wen and Ding [11]
reported that for a Rayleigh number less than 10 6, the natural convection heat transfer rate
increasingly decreases with the increase of particle fraction, particularly at low Rayleigh
numbers.
Fattahi et al () showed the effects of solid volume fraction of nanofluids on hydrodynamic and
thermal characteristics are investigated and discussed. It is found that the effects of solid
volume fraction for Cu are stronger than Al2O3.
Lattice Boltzmann method (LBM) is an ideal mesoscopic approach to solve nonlinear
macroscopic conservation equations because of its simplicity and ease for parallelization. For
incompressible isothermal flows, the LBM is found to be at least as stable, accurate and
computationally efficient, as traditional computational methods [1,2] and has achieved excellent
success in different application areas such as multiphase flow and complex fluid phenomena [3].
Mathematical model and simulation methodology
References
[8] J.A. Eastman, U.S. Choi, S. Li, W. Yu, L.J. Thompson, Anomalously increased effective
thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles, Appl.
Phys. Lett. 78 (2001) 718–720.
[9] H.F. Oztop, E. Abu-Nada, Numerical study of natural convection in partially heated
rectangular enclosure filled with nanofluids, Int. J. Heat Fluid Flow 29 (2008) 1326–1336.
[10] E. Bilgen, Y.R. Ben, Natural convection in enclosure with heating and cooling by
sinusoidal temperature profiles on one side, Int. J. Heat Mass Transfer 50
(2007) 139–150.
[] Khanafer, K., K. Vafai and M. Lightstone, “Buoyancy-Driven Heat Transfer Enhancement in a
Two-Dimensional Enclosure Utilizing Nanofluids,” Int. J. Heat Mass Transfer 46, 3639–3653
(2003).
[] Jou, R. Y. and S. C. Tzeng, “Numerical Research of Nature Convective Heat Transfer
Enhancement Filled With Nanofluids in Rectangular Enclosures,” Int. Commun. Heat Mass
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[] Feng-Hsiang Lai, Yue-Tzu Yang, Lattice Boltzmann simulation of natural
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[] C.H. Li, G.P. Peterson, Experimental studies of natural convection heat transfer of Al2O3/DI
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[] C.J. Ho, W.K. Liu, Y.S. Chang, C.C. Lin, Natural convection heat transfer of alumina-water
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[] Ehsan Fattahi, Mousa Farhadi, Kurosh Sedighi, Hasan Nemati, Lattice
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