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Linear Stability of Convection in a Viscoelastic Nanofluid Layer

Authors: Long Jye Sheu


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, thermophoresis, oscillatory, Brownian

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[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.