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.

References

1.
Choi
,
S.
, and
Eastman
,
J. A.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,”
Int. Mech. Eng. Congr. Exh.
, Vol. 231, Paper No. W-31109-ENG-38.
2.
Masuda
,
H.
,
Ebata
,
A.
,
Teramae
,
K.
, and
Hishinuma
,
N.
,
1993
, “
Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra Fine Particles
,”
Netsu Bussei
,
7
(
4
), pp.
227
233
.
3.
Eastman
,
J. A.
,
Choi
,
S. U. S.
,
Li
,
S.
,
Yu
,
W.
, and
Thompson
,
L. J.
,
2001
, “
Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles
,”
Appl. Phys. Lett.
,
78
(
6
), pp.
718
720
.
4.
Das
,
S. K.
,
Putra
,
N.
,
Thiesen
,
P.
, and
Roetzel
,
W.
,
2003
, “
Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids
,”
ASME J. Heat Transfer
,
125
(
4
), pp.
567
574
.
5.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Trans.
,
128
(
3
), pp.
240
250
.
6.
Tzou
,
D. Y.
,
2008
, “
Instability of Nanofluids in Natural Convection
,”
ASME J. Heat Transfer
,
130
(
7
), p.
072401
.
7.
Tzou
,
D. Y.
,
2008
, “
Thermal Instability of Nanofluids in Natural Convection
,”
Int. J. Heat Mass Trans.
,
51
(11–12), pp.
2967
2979
.
8.
Kim
,
J.
,
Kang
,
Y. T.
, and
Choi
,
C. K.
,
2004
, “
Analysis of Convective Instability and Heat Transfer Characteristics of Nanofluids
,”
Phys. Fluids
,
16
(
7
), pp.
2395
2401
.
9.
Kim
,
J.
,
Choi
,
C. K.
,
Kang
,
Y. T.
, and
Kim
,
M. G.
,
2006
, “
Effects of Thermodiffusion and Nanoparticles on Convective Instabilities in Binary Nanofluids
,”
Nanoscale Microscale Thermophys. Eng.
,
10
(
1
), pp.
29
39
.
10.
Kim
,
J.
,
Kang
,
Y. T.
, and
Choi
,
C. K.
,
2007
, “
Analysis of Convective Instability and Heat Transfer Characteristics of Nanofluids
,”
Int. J. Refrig.
,
30
(
2
), pp.
323
328
.
11.
Bhadauria
,
B. S.
, and
Agarwal
,
S.
,
2014
, “
Convective Heat Transport by Longitudinal Rolls in Dilute Nanoliquids
,”
J. Nanofluids
,
3
(
4
), pp.
380
390
.
12.
Dhananjaya
,
Y.
,
Agarwal
,
G. S.
, and
Bhargava
,
R.
,
2011
, “
Rayleigh–Bénard Convection in Nanofluid
,”
Int. J. Appl. Math. Mech.
,
7
(
2
), pp.
61
76
.https://www.researchgate.net/publication/260785212_Rayleigh-Benard_convection_in_nanofluid
13.
Dhananjaya
,
Y.
,
Agarwal
,
G. S.
, and
Bhargava
,
R.
,
2011
, “
Thermal Instability of Rotating Nanofluid Layer
,”
Int. J. Eng. Sci.
,
49
(
11
), pp.
1171
1184
.
14.
Jawdat
,
J. M.
,
Hashim
,
I.
, and
Momani
,
S.
,
2012
, “
Dynamical System Analysis of Thermal Convection in a Horizontal Layer of Nanofluids Heated From Below
,”
Corp., Math. Prob. Eng.
,
2012
, pp.
1
13
.
15.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2009
, “
Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid
,”
Int. J. Heat Mass Trans.
,
52
(25–26), pp.
5796
5801
.
16.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2014
, “
Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model
,”
Int. J. Heat Mass Trans.
,
68
, pp.
211
214
.
17.
Yang
,
C.
,
Sano
,
Y.
,
Li
,
W.
,
Mochizuki
,
M.
, and
Nakayama
,
A.
,
2013
, “
On the Anomalous Convective Heat Transfer Enhancement in Nanofluids: A Theoretical Answer to the Nanofluids Controversy
,”
ASME J. Heat Transfer
,
135
(
5
), p.
054504
.
18.
Siddheshwar
,
P. G.
, and
Titus
,
P. S.
,
2013
, “
Nonlinear Rayleigh–Bénard Convection With Variable Heat Source
,”
ASME J. Heat Transfer
,
135
(
12
), p.
122502
.
19.
Ghasemi
,
B.
, and
Aminossadati
,
S. M.
,
2009
, “
Natural Convection Heat Transfer in an Inclined Enclosure Filled With a Water—CuO Nanofluid
,”
Numer. Heat Transfer
,
55
(
8
), pp.
807
823
.
20.
Siddheshwar
,
P. G.
, and
Meenakshi
,
N.
,
2016
, “
Amplitude Equation and Heat Transport for Rayleigh–Benard Convection in Newtonian Liquids With Nanoparticles
,”
Int. J. Appl. Comput. Math.
,
2
, pp.
1
22
.
21.
Bergman
,
T. L.
,
Lavine
,
A. S.
,
Incropera
,
F. P.
, and
Dewitt
,
D. P.
,
2006
,
Fundamentals of Heat and Mass Transfer
,
Wiley
,
New York
.
22.
Abu-Nada
,
E.
,
Masoud
,
Z.
, and
Hijazi
,
A.
,
2008
, “
Natural Convection Heat Transfer Enhancement in Horizontal Concentric Annuli Using Nanofluids
,”
Int. Commun. Heat Mass Transfer
,
35
(
5
), pp.
657
665
.
23.
Khanafer
,
K.
,
Vafai
,
K.
, and
Lightstone
,
M.
,
2003
, “
Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids
,”
Int. J. Heat Mass Trans.
,
46
(
19
), pp.
3639
3653
.
24.
Corcione
,
M.
,
2011
, “
Rayleigh–Bénard Convection Heat Transfer in Nanoparticle Suspensions
,”
Int. J. Heat Fluid Flow
,
32
(
1
), pp.
65
77
.
You do not currently have access to this content.