**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30998

##### Linear Stability of Convection in a Viscoelastic Nanofluid Layer

**Authors:**
Long Jye Sheu

**Abstract:**

**Keywords:**
Instability,
Viscoelastic,
Nanofluids,
thermophoresis,
oscillatory,
Brownian

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1072493

**References:**

[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.