A linear and nonlinear stability analysis of a viscoelastic fluid in a porous medium layer saturated by a nanofluid with thermal conductivity and viscosity dependent on the nanoparticle volume fraction is studied. To simulate the momentum equation in porous media, a modified Darcy model has been used. To describe the rheological behavior of viscoelastic nanofluids, an Oldroyd-B type constitutive equation has been used. The onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the truncated representation of Fourier series method is used to find the transient heat and mass transfer.
Issue Section:
Micro/Nanoscale Heat Transfer
References
1.
Hussein
, A. M.
, Sharma
, K. V.
, Bakar
, R. A.
, and Kadirgama
, K.
, 2014
, “A Review of Forced Convection Heat Transfer Enhancement and Hydrodynamic Characteristics of a Nanofluid
,” Renewable Sustainable Energy Rev.
, 29
, pp. 734
–743
.2.
Dalkilica
, A. S.
, Kayacıa
, N.
, Celena
, A.
, Tabatabaeia
, M.
, Yıldıza
, O.
, Daungthongsukb
, W.
, and Wongwisesc
, S.
, 2012
, “Forced Convective Heat Transfer of Nanofluids—A Review of the Recent Literature
,” Curr. Nanosci.
, 8
(6
), pp. 949
–969
.3.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2009
, “Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid
,” Int. J. Heat Mass Transfer
, 52
(1), pp. 5796
–5801
.4.
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
.5.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2010
, “Effect of Local Thermal Non-Equilibrium on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid
,” Transp. Porous Media
, 83
(2
), pp. 425
–436
.6.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2010
, “The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium
,” Transp. Porous Media
, 85
(3
), pp. 941
–951
.7.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2012
, “The Onset of Convection in a Layer of a Porous Medium Saturated by a Nanofluid: Effects of Conductivity and Viscosity Variation and Cross-Diffusion
,” Transp. Porous Media
, 92
(3
), pp. 837
–846
.8.
Umavathi
, J. C.
, and Mohite
, M. B.
, 2014
, “Double-Diffusive Convective Transport in a Nanofluid-Saturated Porous Layer With Cross Diffusion and Variation of Viscosity and Conductivity
,” Heat Transfer Asian Res.
, 43
(7
), pp. 628
–652
.9.
Buongiorno
, J.
, 2006
, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
, 128
(3
), pp. 240
–250
.10.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2011
, “The Onset of Double-Diffusive Convection in a Nanofluid Layer
,” Int. J. Heat Fluid Flow
, 32
(4
), pp. 771
–776
.11.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2010
, “The Onset of Convection in a Horizontal Nanofluid Layer of Finite Depth
,” Eur. J. Mech., B: Fluids
, 29
(3
), pp. 217
–223
.12.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2014
, “The Onset of Convection in a Horizontal Nanofluid Layer of Finite Depth: A Revised Model
,” Int. J. Heat Mass Transfer
, 77
, pp. 915
–918
.13.
Vest
, C. M.
, and Arpaci
, V. S.
, 1969
, “Over Stability of a Viscoelastic Fluid Layer Heated From Below
,” J. Fluid Mech.
, 36
(03
), pp. 613
–623
.14.
Sokolov
, M.
, and Tanner
, R. I.
, 1972
, “Convective Stability of a General Viscoelastic Fluid Heated From Below
,” Phys. Fluids
, 15
(4
), pp. 534
–539
.15.
Rosenblat
, S.
, 1986
, “Thermal Convection of a Viscoelastic Fluid
,” J. Non-Newtonian Fluid Mech.
, 21
(2
), pp. 201
–223
.16.
Martinez-Mardones
, J.
, and Perez-Garcia
, C.
, 1990
, “Linear Instability in Viscoelastic Fluid Convection
,” J. Phys.: Condens. Matter
, 2
(5
), pp. 1281
–1290
.17.
Martinez-Mardones
, J.
, and Perez-Garcia
, C.
, 1992
, “Bifurcation Analysis and Amplitude Equations for Viscoelastic Convective Fluids
,” II Nuovo Cimento
, 14
(9
), pp. 961
–975
.18.
Larson
, R. G.
, 1992
, “Instabilities in Viscoelastic Flows
,” Rheol. Acta
, 31
(3
), pp. 213
–221
.19.
Li
, Z.
, and Khayat
, R. E.
, 2005
, “Three-Dimensional Thermal Convection of Viscoelastic Fluids
,” Phys. Rev. E
, 71
(6
), p. 066305
.20.
Phillips
, T. N.
, and Williams
, A. J.
, 2002
, “Comparison of Creeping and Inertial Flow of an Oldroyd-B Fluid Through Planar and Axisymmetric Contractions
,” J. Non-Newtonian Fluid Mech.
, 108
(1–3), pp. 25
–47
.21.
Alves
, M. A.
, Oliveira
, P. J.
, and Pinho
, F. T.
, 2003
, “Benchmark Solutions for the Flow of Oldroyd-B and PTT Fluids in Planar Contractions
,” J. Non-Newtonian Fluid Mech.
, 110
(1
), pp. 45
–75
.22.
Lozinski
, A.
, and Owens
, R. G.
, 2003
, “An Energy Estimate for the Oldroyd-B Model: Theory
,” J. Non-Newtonian Fluid Mech.
, 112
(2–3), pp. 161
–176
.23.
Tiwari
, R. K.
, and Das
, M. K.
, 2007
, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids
,” Int. J. Heat Mass Transfer
, 50
(9–10), pp. 2002
–2018
.24.
Brinkman
, H. C.
, 1952
, “The Viscosity of Concentrated Suspensions and Solutions
,” J. Chem. Phys.
, 20
(4
), pp. 571
–581
.25.
Maxwell
, J. C.
, 1904
, A Treatise on Electricity and Magnetism
, 2nd ed., Oxford University Press
, Oxford, UK
.26.
Nield
, D. A.
, 2008
, “General Heterogeneity Effects on the Onset of Convection in a Porous Medium
,” Emerging Topics in Heat and Mass Transfer in Porous Media
, P.
Vadász
, ed., Springer
, New York
, pp. 63
–84
.27.
Horton
, C. W.
, and Rogers
, F. T.
, 1945
, “Convection Currents in a Porous Medium
,” J. Appl. Phys.
, 6
(16
), pp. 367
–370
.28.
Lapwood
, E. R.
, 1948
, “Convection of a Fluid in a Porous Medium
,” Proc. Cambridge Philos. Soc.
, 44
(04
), pp. 508
–521
.29.
Sheu
, L. J.
, 2011
, “Thermal Instability in a Porous Medium Layer Saturated With a Viscoelastic Nanofluid
,” Transp. Porous Media
, 88
(3
), pp. 461
–477
.30.
Umavathi
, J. C.
, and Mohite
, M. B.
, 2016
, “Convective Transport in a Porous Medium Layer Saturated With a Maxwell Nanofluid
,” J. King Saud Univ., Eng. Sci.
, 28
(1
), pp. 56
–68
.31.
Malashetty
, M. S.
, Swamy
, M. S.
, and Sidram
, W.
, 2011
, “Double Diffusive Convection in a Rotating Anisotropic Porous Layer Saturated With Viscoelastic Fluid
,” IJTS
, 50
(9
), pp. 1757
–1769
.32.
Bhadauria
, B. S.
, and Agarwal
, S.
, 2011
, “Natural Convection in a Nanofluid Saturated Rotating Porous Layer: A Nonlinear Study
,” Transp. Porous Media
, 87
(2
), pp. 585
–602
.33.
Agarwal
, S.
, Bhadauria
, B. S.
, Sacheti
, N. C.
, Chandran
, P.
, and Singh
, A. K.
, 2012
, “Non-Linear Convective Transport in a Binary Nanofluid Saturated Porous Layer
,” Transp. Porous Media
, 93
(1
), pp. 29
–49
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