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Research Papers: Micro/Nanoscale Heat Transfer

Steady Finite-Amplitude Rayleigh–Bénard Convection in Nanoliquids Using a Two-Phase Model: Theoretical Answer to the Phenomenon of Enhanced Heat Transfer

[+] Author and Article Information
P. G. Siddheshwar

Professor
Department of Mathematics,
Bangalore University,
Bangalore 560056, India
e-mail: pgsiddheshwar@bub.ernet.in

C. Kanchana

Department of Mathematics,
Bangalore University,
Bangalore 560056, India
e-mail: kanchanac@bub.ernet.in

Y. Kakimoto

Associate Professor
Department of Mechanical Engineering,
Shizuoka University,
3-5-1 Johoku, Naka-Ku,
Hamamatsu 432-8561, Japan
e-mail: tykakim@ipc.shizuoka.ac.jp

A. Nakayama

Professor
Department of Mechanical Engineering,
Shizuoka University,
3-5-1 Johoku, Naka-Ku,
Hamamatsu 432-8561, Japan;
School of Civil Engineering and Architecture,
Wuhan Polytechnic University,
Wuhan 430023, China
e-mail: tmanaka@ipc.shizuoka.ac.jp

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 8, 2015; final manuscript received August 6, 2016; published online September 13, 2016. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 139(1), 012402 (Sep 13, 2016) (8 pages) Paper No: HT-15-1330; doi: 10.1115/1.4034484 History: Received May 08, 2015; Revised August 06, 2016

Rayleigh–Bénard convection in liquids with nanoparticles is studied in the paper considering a two-phase model for nanoliquids with thermophysical properties determined from phenomenological laws and mixture theory. In the absence of nanoparticle-modified thermophysical properties as used in the paper, the problem is essentially binary liquid convection with Soret effect. The base liquids chosen for investigation are water, ethylene glycol, engine oil, and glycerine, and the nanoparticles chosen are copper, copper oxide, silver, alumina, and titania. Using data on these 20 nanoliquids, our theoretical model clearly explains advanced onset of convection in nanoliquids in comparison with that in the base liquid without nanoparticles. The paper sets to rest the tentativeness regarding the boundary condition to be chosen in the study of Rayleigh–Bénard convection in nanoliquids. The effect of thermophoresis is to destabilize the system and so is the effect of other parameters arising due to nanoparticles. However, Brownian motion effect does not have a say on onset of convection. In the case of nonlinear theory, the five-mode Lorenz model is derived under the assumptions of Boussinesq approximation and small-scale convective motions, and using it enhancement of heat transport due to the presence of nanoparticles is clearly explained for steady-state motions. Subcritical motion is shown to be possible in all 20 nanoliquids.

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References

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Figures

Grahic Jump Location
Fig. 1

Physical configuration

Grahic Jump Location
Fig. 2

Variation of thermal Rayleigh number, Rnl, with wave number, κ, for water–titania nanoliquid

Grahic Jump Location
Fig. 3

Variation of thermal Nusselt number, Nunl, with thermal Rayleigh number, Rnl, for water-based nanoliquids

Grahic Jump Location
Fig. 4

Variation of Nunl with Rnl for ethylene glycol-based nanoliquids

Grahic Jump Location
Fig. 5

Variation of Nunl with Rnl for engine oil-based nanoliquids

Grahic Jump Location
Fig. 6

Variation of Nunl with Rnl for glycerine-based nanoliquids

Grahic Jump Location
Fig. 7

Contour plot of stream function for ethylene-glycol–silver nanoliquid

Grahic Jump Location
Fig. 8

Contour plot of stream function for water–titania nanoliquid

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