Linear Stability of Convection in a Viscoelastic Nanofluid Layer
This paper presents a linear stability analysis of
natural convection in a horizontal layer of a viscoelastic
nanofluid. The Oldroyd B model was utilized to describe the
rheological behavior of a viscoelastic nanofluid. The model
used for the nanofluid incorporated the effects of Brownian
motion and thermophoresis. The onset criterion for stationary
and oscillatory convection was derived analytically. The effects
of the Deborah number, retardation parameters, concentration
Rayleigh number, Prandtl number, and Lewis number on the
stability of the system were investigated. Results indicated that
there was competition among the processes of thermophoresis,
Brownian diffusion, and viscoelasticity which caused
oscillatory rather than stationary convection to occur.
Oscillatory instability is possible with both bottom- and
top-heavy nanoparticle distributions. Regimes of stationary and
oscillatory convection for various parameters were derived and
are discussed in detail.
[1] Choi, S.: Enhancing thermal conductivity of fluids with nanoparticles. In:
Siginer D.A., Wang, H.P. (eds.) Developments and Applications of
Non-Newtonian Flows, ASME FED- Vol. 231/ MD-Vol. 66, New York,
1995, pp. 99-105.
[2] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal
conductivity and viscosity of liquid by dispersing ultra-fine particles
(dispersion of ╬│-Al2O3, SiO2, and TiO2 ultra-fine particles), Netsu
Bussei (Japan) 7 (1993) 227-233.
[3] J.A. Eastman, S. Choi, S. Li, L.J. Thompson, Anomalously increased
effective thermal conductivity of ethylene glycol-based nanofluids
containing copper nanoparticles, Appl. Phys. Lett. 78 (2001) 718-720.
[4] J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf.
128 (2006) 240-250.
[5] D.Y. Tzou, Instability of nanofluids in natural convection, ASME J. Heat
Transf. 130 (2008) 072401.
[6] D.Y. Tzou, Thermal instability of nanofluids in natural convection, Int. J.
Heat Mass Transf. 51 (2008) 2967-2979.
[7] D.A. Nield, A.V. Kuznetsov, The onset of convection in a horizontal
nanofluid layer of finite depth, European J. Mech. B/Fluids 29 (2010)
217-223.
[8] C.M. Vest, V.S. Arpaci, Overstability of a viscoelastic fluid layer heated
from below, J. Fluid Mech. 36 (1969) 613-623.
[9] M. Sokolov, R.I. Tanner, Convective stability of a general viscoelastic
fluid heated from below, Phys. Fluids 15 (1972) 534-539.
[10] S. Rosenblat, Thermal convection in a viscoelastic liquid, J.
Non-Newtonian Fluid Mech. 21 (1986) 201-223.
[11] J. Martinez-Mardones, C. Perez-Garcia, Linear instability in viscoelastic
fluid convection J. Phys. Condens. Matter 2 (1990) 1281-1290.
[12] J. Martinez-Mardones, C. Perez-Garcia, Bifurcation analysis and
amplitude equations for viscoelastic convective fluids, II Nuovo Cimento
14 (1992) 961-975.
[13] R.G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31 (1992)
213-221.
[14] R.E. Khayat, Non-linear overstability in the thermal convection of
viscoelastic fluid, J. Non-Newtonian Fluid Mech. 58 (1995) 331-356.
[15] P. Kolodner, Oscillatory convection in viscoelastic DNA suspensions, J.
Non-Newtonian Fluid Mech. 75 (1998) 167-192.
[16] J. Martinez-Mardones, R. Tiemann, D. Walgraef, Rayleigh-Benard
convection in binary viscoelastic fluid, Physica A 283 (2000) 233-236.
[17] J. Martinez-Mardones, R. Tiemann, D. Walgraef, Thermal convection
thresholds in viscoelastic binary fluids, J. Non-Newtonian Fluid Mech. 93
(2000) 1-15.
[18] J. Martinez-Mardones, R. Tiemann, D. Walgraef, Amplitude equation for
stationary convection in a binary viscoelastic fluid, Physica A 327 (2003)
29-33.
[19] D. Laroze, J. Martinez-Mardones, J. Bragard, Thermal convection in a
rotating binary viscoelastic liquid mixture, Eur. Phys. J. Spec. Top. 146
(2007) 291-300.
[20] D. Laroze, J. Martinez-Mardones, J. Bragardc, C. Peirez-Garcia, Realistic
rotating convection in a DNA suspension, Physica A 385 (2007)
433-438.
[21] M.S. Malashetty, M. Swamy, The onset of double diffusive convection in
a viscoelastic fluid layer, J. Non-Newtonian Fluid Mech. 165 (2010)
1129-1138.
[22] D.A. Nield, A Note on the Onset of Convection in a Layer of a Porous
Medium Saturated by a Non-Newtonian Nanofluid of Power-Law Type,
Transp. Porous Med. (2010) DOI 10.1007/s11242-010-9671-z.
[23] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability,
Clarendon Press, Oxford, UK, 1961.
[24] M.S. Malashetty, M. Swamy, R. Heera, The onset of convection in a
binary viscoelastic fluid saturated porous layer, Z. Angew. Math. Mech.
89 (2009) 356-369.
[25] M.S. Malashetty, W. Tan, M. Swamy, The onset of double diffusive
convection in a binary viscoelastic fluid saturated anisotropic porous
layer Phys. Fluids 21 (2009) 084101.
[1] Choi, S.: Enhancing thermal conductivity of fluids with nanoparticles. In:
Siginer D.A., Wang, H.P. (eds.) Developments and Applications of
Non-Newtonian Flows, ASME FED- Vol. 231/ MD-Vol. 66, New York,
1995, pp. 99-105.
[2] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal
conductivity and viscosity of liquid by dispersing ultra-fine particles
(dispersion of ╬│-Al2O3, SiO2, and TiO2 ultra-fine particles), Netsu
Bussei (Japan) 7 (1993) 227-233.
[3] J.A. Eastman, S. Choi, S. Li, L.J. Thompson, Anomalously increased
effective thermal conductivity of ethylene glycol-based nanofluids
containing copper nanoparticles, Appl. Phys. Lett. 78 (2001) 718-720.
[4] J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf.
128 (2006) 240-250.
[5] D.Y. Tzou, Instability of nanofluids in natural convection, ASME J. Heat
Transf. 130 (2008) 072401.
[6] D.Y. Tzou, Thermal instability of nanofluids in natural convection, Int. J.
Heat Mass Transf. 51 (2008) 2967-2979.
[7] D.A. Nield, A.V. Kuznetsov, The onset of convection in a horizontal
nanofluid layer of finite depth, European J. Mech. B/Fluids 29 (2010)
217-223.
[8] C.M. Vest, V.S. Arpaci, Overstability of a viscoelastic fluid layer heated
from below, J. Fluid Mech. 36 (1969) 613-623.
[9] M. Sokolov, R.I. Tanner, Convective stability of a general viscoelastic
fluid heated from below, Phys. Fluids 15 (1972) 534-539.
[10] S. Rosenblat, Thermal convection in a viscoelastic liquid, J.
Non-Newtonian Fluid Mech. 21 (1986) 201-223.
[11] J. Martinez-Mardones, C. Perez-Garcia, Linear instability in viscoelastic
fluid convection J. Phys. Condens. Matter 2 (1990) 1281-1290.
[12] J. Martinez-Mardones, C. Perez-Garcia, Bifurcation analysis and
amplitude equations for viscoelastic convective fluids, II Nuovo Cimento
14 (1992) 961-975.
[13] R.G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31 (1992)
213-221.
[14] R.E. Khayat, Non-linear overstability in the thermal convection of
viscoelastic fluid, J. Non-Newtonian Fluid Mech. 58 (1995) 331-356.
[15] P. Kolodner, Oscillatory convection in viscoelastic DNA suspensions, J.
Non-Newtonian Fluid Mech. 75 (1998) 167-192.
[16] J. Martinez-Mardones, R. Tiemann, D. Walgraef, Rayleigh-Benard
convection in binary viscoelastic fluid, Physica A 283 (2000) 233-236.
[17] J. Martinez-Mardones, R. Tiemann, D. Walgraef, Thermal convection
thresholds in viscoelastic binary fluids, J. Non-Newtonian Fluid Mech. 93
(2000) 1-15.
[18] J. Martinez-Mardones, R. Tiemann, D. Walgraef, Amplitude equation for
stationary convection in a binary viscoelastic fluid, Physica A 327 (2003)
29-33.
[19] D. Laroze, J. Martinez-Mardones, J. Bragard, Thermal convection in a
rotating binary viscoelastic liquid mixture, Eur. Phys. J. Spec. Top. 146
(2007) 291-300.
[20] D. Laroze, J. Martinez-Mardones, J. Bragardc, C. Peirez-Garcia, Realistic
rotating convection in a DNA suspension, Physica A 385 (2007)
433-438.
[21] M.S. Malashetty, M. Swamy, The onset of double diffusive convection in
a viscoelastic fluid layer, J. Non-Newtonian Fluid Mech. 165 (2010)
1129-1138.
[22] D.A. Nield, A Note on the Onset of Convection in a Layer of a Porous
Medium Saturated by a Non-Newtonian Nanofluid of Power-Law Type,
Transp. Porous Med. (2010) DOI 10.1007/s11242-010-9671-z.
[23] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability,
Clarendon Press, Oxford, UK, 1961.
[24] M.S. Malashetty, M. Swamy, R. Heera, The onset of convection in a
binary viscoelastic fluid saturated porous layer, Z. Angew. Math. Mech.
89 (2009) 356-369.
[25] M.S. Malashetty, W. Tan, M. Swamy, The onset of double diffusive
convection in a binary viscoelastic fluid saturated anisotropic porous
layer Phys. Fluids 21 (2009) 084101.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:58364", author = "Long Jye Sheu", title = "Linear Stability of Convection in a Viscoelastic Nanofluid Layer", abstract = "This paper presents a linear stability analysis of
natural convection in a horizontal layer of a viscoelastic
nanofluid. The Oldroyd B model was utilized to describe the
rheological behavior of a viscoelastic nanofluid. The model
used for the nanofluid incorporated the effects of Brownian
motion and thermophoresis. The onset criterion for stationary
and oscillatory convection was derived analytically. The effects
of the Deborah number, retardation parameters, concentration
Rayleigh number, Prandtl number, and Lewis number on the
stability of the system were investigated. Results indicated that
there was competition among the processes of thermophoresis,
Brownian diffusion, and viscoelasticity which caused
oscillatory rather than stationary convection to occur.
Oscillatory instability is possible with both bottom- and
top-heavy nanoparticle distributions. Regimes of stationary and
oscillatory convection for various parameters were derived and
are discussed in detail.", keywords = "instability, viscoelastic, nanofluids, oscillatory,
Brownian, thermophoresis", volume = "5", number = "10", pages = "2009-7", }
