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Rayleigh-Bénard-Taylor Convection of Newtonian Nanoliquid

Authors: P. G. Siddheshwar, T. N. Sakshath


In the paper we make linear and non-linear stability analyses of Rayleigh-Bénard convection of a Newtonian nanoliquid in a rotating medium (called as Rayleigh-Bénard-Taylor convection). Rigid-rigid isothermal boundaries are considered for investigation. Khanafer-Vafai-Lightstone single phase model is used for studying instabilities in nanoliquids. Various thermophysical properties of nanoliquid are obtained using phenomenological laws and mixture theory. The eigen boundary value problem is solved for the Rayleigh number using an analytical method by considering trigonometric eigen functions. We observe that the critical nanoliquid Rayleigh number is less than that of the base liquid. Thus the onset of convection is advanced due to the addition of nanoparticles. So, increase in volume fraction leads to advanced onset and thereby increase in heat transport. The amplitudes of convective modes required for estimating the heat transport are determined analytically. The tri-modal standard Lorenz model is derived for the steady state assuming small scale convective motions. The effect of rotation on the onset of convection and on heat transport is investigated and depicted graphically. It is observed that the onset of convection is delayed due to rotation and hence leads to decrease in heat transport. Hence, rotation has a stabilizing effect on the system. This is due to the fact that the energy of the system is used to create the component V. We observe that the amount of heat transport is less in the case of rigid-rigid isothermal boundaries compared to free-free isothermal boundaries.

Keywords: Nanoliquid, rigid-rigid, rotation, single-phase.

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[1] S. Agarwal, B. S. Bhadauria and P. G. Siddheshwar, Thermal instability of a nanofluid saturating a rotating anisotropic porous medium, Special Topics and Reviews in Porous Media: An International Journal, 2(1), 53-64, 2011.
[2] C. Beaume, A. Bergeon, H. C. Kao and E. Knobloch, Convectons in a rotating fluid layer, Journal of Fluid Mechanics, 717, 417-448, 2013.
[3] B. S. Bhadauria and S. Agarwal, Natural convection in a nanofluid saturated rotating porous layer: A nonlinear study, Transport in Porous Media, 87, 585-602, 2011.
[4] J. K. Bhattacharjee, Rotating Rayleigh-Bénard convection with modulation, Journal of Physics A: Mathematical and General, 22(24), L1135, 1989.
[5] H. C. Brinkman, The viscosity of concentrated suspensions and solutions, The Journal of Chemical Physics, 20, 571, 1952.
[6] F. H. Busse, Thermal Convection in Rotating Systems, Proceedings of US National Congress of Applied Mechanics, American Society of Mechanical Engineers, 299-305, 1982.
[7] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, London, 1961.
[8] S. Chandrasekhar, The instability of a layer of fluid heated below and subject to Coriolis forces, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 217, 306-327, 1953.
[9] S. M. Cox and P. C. Matthews, New instabilities in two-dimensional rotating convection and magnetoconvection, Physica D: Nonlinear Phenomena, 149(3), 210-229, 2001.
[10] G. P. Galdi and B. Straughan, A nonlinear analysis of the stabilizing effect of rotation in the B´enard problem, In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 402(1823), 257-283, 1985.
[11] R. L. Hamilton and O. K. Crosser, Thermal conductivity of heterogeneous two-component systems, Industrial and Engineering Chemistry Fundamentals, 1, 187-191, 1962.
[12] E. S. Knobloch, Rotating Convection: Recent Developments, International Journal of Engineering Science, 36, 1421-1450, 1998.
[13] Y. Liu and R. E. Ecke, Heat transport measurements in turbulent rotating Rayleigh-B´enard convection, Physical Review E, 80(3), 036314, 2009.
[14] J. M. Lopez and F. Marques, Centrifugal effects in rotating convection: nonlinear dynamics, Journal of Fluid Mechanics, 628, 269-297, 2009.
[15] A. J. Pearlstein, Effect of rotation on the stability of a doubly diffusive fluid layer, Journal of Fluid Mechanics, 103, 389-412, 1981.
[16] D. H. Riahi, The effect of Coriolis force on nonlinear convection in a porous medium, International Journal of Mathematics and Mathematical Sciences, 17(3), 515-536, 1994 .
[17] H. T. Rossby, A Study of B´enard Convection with and without Rotation, Journal of Fluid Mechanics, 36, 309-335, 1969.
[18] P. G. Siddheshwar and N. Meenakshi, Amplitude equation and heat transport for Rayleigh Bénard convection in Newtonian liquids with nanoparticles, International Journal of Applied and Computational Mathematics, 2, 1-22, 2016.
[19] S. G. Tagare, A. B. Babu and Y. Rameshwar, Rayleigh-Bénard convection in rotating fluids, International Journal of Heat and Mass Transfer, 51, 1168-1178, 2008.
[20] P. Vadasz, Coriolis effect on gravity-driven convection in a rotating porous layer heated from below, Journal of Fluid Mechanics, 376, 351-375, 1998.
[21] R. K. Vanishree and P. G. Siddheshwar, Effect of rotation on thermal convection in an anisotropic porous medium with temperature-dependent viscosity, Transport in porous media, 81(1), 73, 2010.
[22] G. Veronis, Cellular convection with finite amplitude in a rotating fluid, Journal of Fluid Mechanics, 5(03), 401-435, 1959.
[23] D. Yadav, G. S. Agrawal and R. Bhargava, Thermal instability of rotating nanofluid layer, International Journal of Engineering Science, 49(11), 1171-1184, 2011.