Abstract
Instability of natural convection in nanofluids is investigated in this work. As a result of Brownian motion and thermophoresis of nanoparticles, the critical Rayleigh number is shown to be much lower, by one to two orders of magnitude, as compared to that for regular fluids. The highly promoted turbulence, in the presence of nanoparticles for as little as 1% in volume fraction, significantly enhances heat transfer in nanofluids, which may be much more pronounced than the enhancement of the effective thermal conductivity alone. Seven dominating groups are extracted from the nondimensional analysis. By extending the method of eigenfunction expansions in conjunction with the method of weighted residuals, closed-form solutions are derived for the Rayleigh number to justify such remarkable change by the nanoparticles at the onset of instability.
1.
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.
0003-6951, 78
, pp. 718
–720
.2.
Lee
, S.
, Choi
, S. U. S.
, Li
, S.
, and Eastman
, J. A.
, 1999, “Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles
,” ASME J. Heat Transfer
0022-1481, 121
, pp. 280
–289
.3.
Xuan
, Y.
, and Li
, Q.
, 2000, “Heat Transfer Enhancement of Nanofluids
,” Int. J. Heat Mass Transfer
0017-9310, 21
, pp. 58
–64
.4.
Choi
, S. U. S.
, Zhang
, Z. G.
, Yu
, W.
, Lockwood
, F. E.
, and Grulke
, E. A.
, 2001, “Anomalous Thermal Conductivity Enhancement in Nanotube Suspensions
,” Appl. Phys. Lett.
0003-6951, 79
, pp. 2252
–2254
.5.
Das
, S. K.
, Putra
, N.
, Thiesen
, P.
, and Roetzel
, W.
, 2003, “Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids
,” ASME J. Heat Transfer
0022-1481, 125
, pp. 567
–574
.6.
Pak
, B. C.
, and Cho
, Y.
, 1998, “Hydrodynamics and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particles
,” Exp. Heat Transfer
0891-6152, 11
, pp. 151
–170
.7.
Xuan
, Y.
, and Li
, Q.
, 2003, “Investigation of Convective Heat Transfer and Flow Features of Nanofluids
,” ASME J. Heat Transfer
0022-1481, 125
, pp. 151
–155
.8.
Xuan
, Y.
, and Roetzel
, W.
, 2000, “Conceptions for Heat Transfer Correlation of Nanofluids
,” Int. J. Heat Mass Transfer
0017-9310, 43
, pp. 3701
–3707
.9.
Maïga
, S.
, Nguyen
, C. T.
, Galanis
, N.
, and Roy
, G.
, 2004, “Heat Transfer Behaviors of Nanofluids Under in a Uniformly Heated Tube
,” Superlattices Microstruct.
0749-6036, 35
, pp. 543
–557
.10.
Buongiorno
, J.
, 2006, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
0022-1481, 128
, pp. 240
–250
.11.
Yu
, W.
, and Choi
, S. U. S.
, 2003, “The Role of Interfacial Layers in the Enhanced Thermal Conductivity: A Renovated Maxwell Model
,” J. Nanopart. Res.
1388-0764, 5
, pp. 167
–171
.12.
Jang
, S. P.
, and Choi
, S. U. S.
, 2004, “Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids
,” Appl. Phys. Lett.
0003-6951, 84
(21
), pp. 4316
–4318
.13.
Kumar
, D. H.
, Patel
, H. E.
, Rajeev Kumar
, V. R.
, Sundararajan
, J.
, Pradeep
, T.
, and Das
, S. K.
, 2004, “Model for Heat Conduction in Nanofluids
,” Phys. Rev. Lett.
0031-9007, 93
, p. 144301
.14.
Keblinski
, P.
, Phillpot
, S. R.
, Choi
, S. U. S.
, and Eastman
, J. A.
, 2002, “Mechanisms of Heat Flow in Suspensions of Nano-Sized Particles (Nanofluids)
,” Int. J. Heat Mass Transfer
0017-9310, 45
, pp. 855
–863
.15.
Chen
, G.
, 2001, “Ballistic-Diffusive Heat-Conduction Equation
,” Phys. Rev. Lett.
0031-9007, 86
(11
), pp. 2297
–2300
.16.
Vadasz
, P.
, 2006, “Heat Conduction in Nanofluid Suspensions
,” ASME J. Heat Transfer
0022-1481, 128
, pp. 465
–477
.17.
Ma
, H. B.
, Wilson
, C.
, Yu
, Q.
, Choi
, U. S.
, and Tirumala
, M.
, 2006, “An Experimental Investigation of Heat Transport Capability in a Nanofluid Oscillating Heat Pipe
,” ASME J. Heat Transfer
0022-1481, 128
, pp. 1213
–1216
.18.
McNab
, G. S.
, and Meisen
, A.
, 1973, “Thermophoresis in Liquids
,” J. Colloid Interface Sci.
0021-9797, 44
(2
), p. 339
.19.
Jang
, S. P.
, and Choi
, U. S. U.
, 2004, “Free Convection in a Rectangular Cavity (Bénard Convection) With Nanofluids
,” Proceedings of the 2004 IMECE
, Anaheim, CA, Nov. 13–20.20.
Incropera
, F. P.
, Dewitt
, D. P.
, Bergman
, T. L.
, and Lavine
, A. S.
, 2007, Introduction to Heat Transfer
, 5th ed., Wiley
, Hoboken, NJ
.21.
Yih
, C. S.
, 1977, Fluid Mechanics: A Concise Introduction to the Theory
, West River Press
, Ann Arbor, MI
, Chap. 9.22.
Chandrasekhar
, S.
, 1961, Hydrodynamic and Hydromagnetic Stability
, Oxford University Press
, Oxford
.23.
Finlayson
, B. A.
, 1972, The Method of Weighted Residuals and Variational Principles
, Academic
, New York
.Copyright © 2008
by American
Society of Mechanical Engineers
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