Research PapersNo Access

ON THE ONSET OF RAYLEIGH–BÉNARD CONVECTION IN A LAYER OF NANOFLUID IN HYDROMAGNETICS

RAMESH CHAND

Department of Mathematics, Government College, Dhaliara (Kangra), Himachal Pradesh, India

https://doi.org/10.1142/S0219581X13500385Cited by:10 (Source: Crossref)

Abstract

Rayleigh–Bénard convection in a horizontal layer of nanofluid in the presence of uniform vertical magnetic field is investigated by using Galerkin weighted residuals method. The model used for the nanofluid describes the effects of Brownian motion and thermophoresis. Linear stability theory based upon normal mode analysis is employed to find expressions for Rayleigh number and critical Rayleigh number. The boundaries are considered to be free–free, rigid–rigid and rigid–free. The influence of magnetic field on the stability is investigated and it is found that magnetic field stabilizes the fluid layer. It is also observed that the system is more stable in the case of rigid–rigid boundaries and least stable in case of free–free boundaries. The expression for Rayleigh number for oscillatory convection has also been derived for free–free boundaries.

Keywords:

References

H. Bénard, Revue Generale des Sciences Pures et. Appliqués 11, 1261 (1900). Google Scholar
L. Rayleigh, Philos. Mag. 32, 529 (1916) . Google Scholar
S. Chandrasekhar , Hydrodynamic and Hydromagnetic Stability ( Oxford University Press, Dover Publication , New York , 1961 ) . Google Scholar
S. Choi, Developments and Applications of Non-Newtonian Flows 231, eds. D. A. Siginer and H. P. Wang (ASME FED, 1995) pp. 99–105. Google Scholar
Y. Xuan and Q. Li, ASME J. Heat Transfer 125, 151 (2003), DOI: 10.1115/1.1532008. Web of Science, Google Scholar
S. C. Tzeng, C. W. Lin and K. D. Huang, Acta Mech. 179, 11 (2005), DOI: 10.1007/s00707-005-0248-9. Web of Science, Google Scholar
J. Buongiorno, ASME J. Heat Transfer 128, 240 (2006), DOI: 10.1115/1.2150834. Web of Science, Google Scholar
P. Vadasz, ASME J. Heat Transfer 128, 465 (2006), DOI: 10.1115/1.2175149. Web of Science, Google Scholar
Z. Alloui, P. Vasseur and M. Reggio, Int. J. Therm. Sci. 50, 385 (2010), DOI: 10.1016/j.ijthermalsci.2010.04.006. Web of Science, Google Scholar
A. V. Kuznetsov and D. A. Nield, Transport Porous Media 83, 425 (2010), DOI: 10.1007/s11242-009-9452-8. Web of Science, Google Scholar
A. V. Kuznetsov and D. A. Nield, Transp. Porous Medium 81, 409 (2010), DOI: 10.1007/s11242-009-9413-2. Web of Science, Google Scholar
A. V. Kuznetsov and D. A. Nield, Transport Porous Media 85, 941 (2010), DOI: 10.1007/s11242-010-9600-1. Web of Science, Google Scholar
D. A. Nield and A. V. Kuznetsov, Int. J. Heat Mass Transf. 52, 5796 (2009), DOI: 10.1016/j.ijheatmasstransfer.2009.07.023. Web of Science, Google Scholar
D. A. Nield and A. V. Kuznetsov, Eur. J. Mech. B/Fluids 29, 217 (2010), DOI: 10.1016/j.euromechflu.2010.02.003. Web of Science, Google Scholar
D. A. Nield and A. V. Kuznetsov, J. Heat Transfer 132, 052405 (2010), DOI: 10.1115/1.4000474. Web of Science, Google Scholar
D. A. Nield and A. V. Kuznetsov, J. Heat Transfer 132, 074503 (2010), DOI: 10.1115/1.4001125. Web of Science, Google Scholar
D. A. Nield and A. V. Kuznetsov, Int. J. Heat Fluid Flow 32, 771 (2011), DOI: 10.1016/j.ijheatfluidflow.2011.03.010. Web of Science, Google Scholar
D. A. Nield and A. V. Kuznetsov, Transport Porous Media 87, 765 (2011), DOI: 10.1007/s11242-011-9717-x. Web of Science, Google Scholar
J. Kim, Y. T. Kang and C. K. Choi, Phys. Fluids 16, 2395 (2011), DOI: 10.1063/1.1739247. Web of Science, Google Scholar
L. J. Sheu, Transp. Porous Med. 88, 461 (2011), DOI: 10.1007/s11242-011-9749-2. Web of Science, Google Scholar
L. J. Sheu, World Sci. Eng. Technol. 58, 289 (2011). Web of Science, Google Scholar
D. Yadav, G. S. Agrawal and R. Bhargava, Int. J. Eng. Sci. 49, 1171 (2011), DOI: 10.1016/j.ijengsci.2011.07.002. Web of Science, Google Scholar
D. Yadav, G. S. Agrawal and R. Bhargava, Int. J. Theor. Appl. Multiscale Mech. 2, 198 (2012), DOI: 10.1504/IJTAMM.2012.049931. Web of Science, Google Scholar
R. Chand and G. C. Rana, Transp Porous Med. 95, 269 (2012), DOI: 10.1007/s11242-012-0042-9. Web of Science, Google Scholar
R. Chand and G. C. Rana, Int. J. Heat Mass Transfer 55, 5417 (2012), DOI: 10.1016/j.ijheatmasstransfer.2012.04.043. Web of Science, Google Scholar
R. Chand and G. C. Rana, J. Fluids Eng. 134, 121203 (2012), DOI: 10.1115/1.4007901. Web of Science, Google Scholar
D. Y. Tzou, Int. J. Heat Mass Transfer 51, 2967 (2008), DOI: 10.1016/j.ijheatmasstransfer.2007.09.014. Web of Science, Google Scholar
D. Y. Tzou, ASME J. Heat Transfer 30, 372 (2008). Google Scholar