This paper studies the effect of local thermal nonequilibrium (LTNE) on the thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two temperature model has been used for the effect of LTNE among the particle and fluid phases. The boundary condition involved assumes that the nano-concentration flux is zero thereat, including the effect of thermophoresis. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series method has been used to obtain the thermal Nusselt number, whose variation with respect to various parameters has been depicted graphically.
Issue Section:
Natural and Mixed Convection
References
References
1.
Maxwell
, J. C.
, 1881
, A Treatise on Electricity and Magnetism
, 2nd ed., Vol. 1, Clarendon
, Oxford, UK
, p. 435
.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
.10.2963/jjtp.7.227
3.
Choi
, S.
, 1995
, Enhancing Thermal Conductivity of Fluids With Nanoparticles (Development and Applications of Non-Newtonian Flows, ASME FED)
,
D. A.
Siginer
and
H. P.
Wang
, eds., Vol. 231/MD Vol. 66
, pp. 99
–105
.4.
Eastman
, J. A.
,
Choi
, S. U. 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
.10.1063/1.1341218
5.
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
.10.1115/1.1571080
6.
Xie
, H.
,
Wang
, J.
,
Xi
, T.
, and
Ai
, F.
, 2002
, “Thermal Conductivity Enhancement of Suspensions Containing Nanosized Alumina Particles
,” J. Appl. Phys.
, 91
(7
), pp. 4568
–4572
.10.1063/1.1454184
7.
Eastman
, J. A.
,
Choi
, S. U. S.
,
Yu
, W.
, and
Thompson
, L. J.
, 2004
, “Thermal Transport in Nanofluids
,” Annu. Rev. Mater. Res.
, 34
, pp. 219
–246
.10.1146/annurev.matsci.34.052803.090621
8.
Buongiorno
, J.
, 2006
, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
, 128
(3
), pp. 240
–250
.10.1115/1.2150834
9.
Tzou
, D. Y.
, 2008
, “Instability of Nanofluids in Natural Convection
,” ASME J. Heat Transfer
, 130
(7
), p. 072401
.10.1115/1.2908427
10.
Tzou
, D. Y.
, 2008
, “Thermal Instability of Nanofluids in Natural Convection
,” Int. J. Heat Mass Transfer
, 51
(11–12
), pp. 2967
–2979
.10.1016/j.ijheatmasstransfer.2007.09.014
11.
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
.10.1063/1.1739247
12.
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
.10.1080/10893950500357772
13.
Nield
, D. A.
, and
Bejan
, A.
, 2006
, Convection in Porous Media
, 3rd ed., Springer
, New York
.14.
Vafai
, K.
, 2005
, Handbook of Porous Media
, 2nd ed., Taylor & Francis
, New York
.15.
Vafai
, K.
, 2010
, Porous Media: Applications in Biological Systems and Biotechnology
, Taylor & Francis, CRC
, New York
.10.1201/9781420065428
16.
Vadasz
, P.
, 2008
, Emerging Topics in Heat and Mass Transfer in Porous Media
, Springer
, New York
.10.1007/978-1-4020-8178-1
17.
Vadasz
, P.
, 2005
, “Nanofluids Suspensions: Possible Explanations for the Apparent Enhanced Effective Thermal Conductivity
,” ASME
Paper No. HT2005–72258.10.1115/HT2005-72258
18.
Vadasz
, P.
, 2006
, “Heat Conduction in Nanofluid Suspensions
,” ASME J. Heat Transfer
, 128
(5
), pp. 465
–477
.10.1115/1.2175149
19.
Kuznetsov
, A. V.
, and
Nield
, D. A.
, 2010
, “Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model
,” Transp. Porous Media
, 81
(3
), pp. 409
–422
.10.1007/s11242-009-9413-2
20.
Nield
, D. A.
, and
Kuznetsov
, A. V.
, 2009
, “Thermal Instability in a Porous Medium Layer Saturated by Nanofluid
,” Int. J. Heat Mass Transfer
, 52
(25–26
), pp. 5796
–5801
.10.1016/j.ijheatmasstransfer.2009.07.023
21.
Agarwal
, S.
,
Bhadauria
, B. S.
, and
Siddheshwar
, P. G.
, 2011
, “Thermal Instability of a Nanofluid Saturating a Rotating Anisotropic Porous Medium
,” Spec. Top. Rev. Porous Media
, 2
(1
), pp. 53
–64
.10.1615/SpecialTopicsRevPorousMedia.v2.i1.60
22.
Agarwal
, S.
,
Sacheti
, N. C.
,
Chandran
, P.
,
Bhadauria
, B. S.
, and
Singh
, A. K.
, 2012
, “Non-Linear Convective Transport in a Binary Nanofluid Saturated Porous Layer
,” Transp. Porous Media
, 93
(1
), pp. 29
–49
.10.1007/s11242-012-9942-y
23.
Rana
, P.
, and
Agarwal
, S.
, 2014, “Convection in a Binary Nanofluid Saturated Rotating Porous Layer
,” J. Nanofluids
4
(1).24.
Agarwal
, S.
, and
Bhadauria
, B. S.
, 2014, “Convective Heat Transport by Longitudinal Rolls in Dilute Nanoliquids
,” J. Nanofluids
3
(4).25.
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 Transfer
, 68
, pp. 211
–214
.10.1016/j.ijheatmasstransfer.2013.09.026
26.
Agarwal
, S.
, 2014
, “Natural Convection in a Nanofluid Saturated Rotating Porous Layer: A More Realistic Approach
,” Transp. Porous Media
, 104
(3
), pp. 581
–592
.10.1007/s11242-014-0351-2
27.
Kuznetso
, A. V.
, and
Nield
, D. A.
, 2010
, “Effect of Local Thermal Non-Equilibrium on the Onset of Convection in Porous Medium Layer Saturated by a Nanofluid
,” Transp. Porous Media
, 83
(1
), pp. 425
–436
.10.1007/s11242-009-9452-8
28.
Nield
, D. A.
, and
Kuznetsov
, A. V.
, 2010
, “The Effect of Local Thermal Non Equilibrium on the Onset of Convection in a Nanofluid
,” ASME J. Heat Transfer
, 132
(5
), p. 052405
.10.1115/1.4000474
29.
Agarwal
, S.
, and
Bhadauria
, B. S.
, 2011
, “Natural Convection in a Nanofluid Saturated Rotating Porous Layer With Thermal Non Equilibrium Model
,” Transp. Porous Media
, 90
(2
), pp. 627
–654
.10.1007/s11242-011-9807-9
30.
Bhadauria
, B. S.
, and
Agarwal
, S.
, 2011
, “Convective Transport in a Nanofluid Saturated Porous Layer With Thermal Non Equilibrium Model
,” Transp. Porous Media
, 88
(1
), pp. 107
–131
.10.1007/s11242-011-9727-8
31.
Keblinski
, P.
, and
Cahil
, D. G.
, 2005
, “Comments on Model for Heat Conduction in Nanofluids
,” Phys. Rev. Lett.
, 95
, p. 209401
.10.1103/PhysRevLett.95.209401
32.
Chandrashekhar
, S.
, 1961
, Hydrodynamic and Hydromagnetic Stability
, Oxford University
, Oxford
, UK.33.
Drazin
, P. G.
, and
Reid
, D. H.
, 1981
, Hydrodynamic Stability
, Cambridge University
, Cambridge
, UK.
You do not currently have access to this content.
