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9929
Effect of Gravity Modulation on Weakly Non-Linear Stability of Stationary Convection in a Dielectric Liquid
Abstract:
The effect of time-periodic oscillations of the Rayleigh- Benard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg- Landau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection and this helps in quantifying the heat transfer in dielectric liquids in terms of the Nusselt number. The effect of electrical Rayleigh number and the amplitude of modulation on heat transport is studied.
Digital Object Identifier (DOI):

References:

[1] P. M. Gresho, R. L. Sani, "The effects of gravity modulation on the stability of a heated Fluid layer," J. Fluid Mech., 1970, vol. 40, pp.783- 806.
[2] G. Z.Gershuni, E. M. Zhukhovitskii, I. S. Iurkov, "On convective stability in the presence of periodically varying parameter," J. Appl. Math. Mech., 1970, vol. 34, pp.470-480.
[3] S.Biringen, L. J. Peltier, "Numerical simulation of 3D B'enard convection with gravitational modulation," Phys. Fluids., 1990, vol.(A)2, pp.754- 764.
[4] A. A. Wheeler, G. B. McFadden, B. T. Murray, S. R. Coriell, "Convective stability in the Rayleigh-Bnard and directional solidification problems: High-frequency gravity modulation," Phys. Fluids., 1991, vol.(A)3, pp.2847-2858.
[5] R.Clever, G. Schubert, F. H. Busse, "Two-dimensional oscillatory convection in a gravitationally modulated fluid layer," J. Fluid Mech., 1993a, vol. 253, pp. 663-680.
[6] R. Clever, G. Schubert, F.H. Busse, "Three-dimensional oscillatory convection in a gravitationally modulated fluid layer," Phys.Fluids., 1993b, vol.(A)5, pp. 2430-2437.
[7] J.L. Rogers, W. Pesch, O. Brausch, M.F. Schatz, "Complex-ordered patterns in shaken convection," Phys. Rev., 2005, vol. (E) 71, pp. 066214(1-18).
[8] S. Aniss, J. P. Brancher, M. Souhar, "Asymptotic study and weakly nonlinear analysis at the onset of Rayleigh-Bnard convection in Hele-Shaw cell," Phys.Fluids, 1995, vol. 7(5), pp.926-934.
[9] S. Aniss, M. Souhar, M. Belhaq, "Asymptotic study of the convective parametric instability in Hele-Shaw cell," Phys. Fluids, 2000, vol. 12(2), pp.262-268.
[10] B. S. Bhadauria and Lokenath Debnath, "Effects of modulation on Rayleigh-Benard convection part I.," IJMMS, 2004, pp.991-1001.
[11] B. S. Bhadauria, "Time-periodic heating of Rayleigh-Bnard convection in a vertical magnetic field," Phys. Scripta., 2006,vol. 73, pp. 296-302.
[12] B. Q. Li,"G-jitter induced free convection in a transverse magnetic field," Int. J. Heat Mass Transfer., 1996, vol 39, No.14, pp.2853-2860.
[13] B . Pan and B. Q. Li, "Effect of magnetic field on oscillatory mixed convection," Int. J. Heat Mass Transfer., 1998, vol 41, pp.2705-2710.
[14] M. S. Malashetty, V. Padmavathy, "Effect of gravity modulation on the onset of convection In a fluid porous layer," Int. J. Eng. Sci., 1997, vol.35, pp.829-839.
[15] R. L. J. Skarda, "Instability of a gravity-modulated fluid layer with surface tension variation," J. Fluid Mech., 2001,vol.434, pp. 243-271.
[16] S. Govender, "Stability of Convection in a Gravity Modulated Porous Layer Heated from Below," Transport in Porous Media., 2004, vol. 57, pp.113-123.
[17] S. Govender, "Stability of Gravity Driven Convection in a Cylindrical Porous Layer Subjected to Vibration," Transport in Porous Media., 2006, vol. 63, pp.489-502.
[18] Y. Shu, B. Q. Li, B. R. Ramaprian, "Convection in modulated thermal gradients and gravity: Experimental measurements and numerical simulations," Int. J. Heat Mass Transfer., (2005), vol. 48, pp.145-160.
[19] S. Govender, "Linear Stability and Convection in a Gravity Modulated Porous Layer Heated from Below: Transition from Synchronous to Subharmonic Solutions," Transport in Porous Media., 2005, vol. 63, pp.227-238.
[20] V.K. Siddavaram and G. M. Homsy, "The effects of gravity modulation on fluid mixing. Part1. Harmonic modulation," J. Fluid Mech., 2006, vol. 562, pp.445-475.
[21] V.K. Siddavaram and G. M. Homsy, "The effects of gravity modulation on fluid mixing. Part 2. Stochastic modulation," J. Fluid Mech., 2007, vol.579, pp.445-466.
[22] Saneshan Govender, "An analogy between a gravity modulated porous layer heated from below and the inverted pendulum with an oscillating pivot point," Transp. in Porous Med. 2007, vol. 67, pp.323-328.
[23] T. Boulal, S. Aniss, M. Belhaq,"Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer," Phy. Review., 2007, vol. E 76, pp. 056320(1-5).
[24] P. G. Siddheshwar and A. Annamma, "Rayleigh-Benard convection in a dielectric liquid: time-periodic body force," Procc. Appl. Math.Mech., 2007, vol. 7, pp. 2100083-21300084.
[25] P. G. Siddheshwar, B. S. Bhaduria, Pankaj Mishra and Atul K. Srivastava, "Weak non-linear stability analysis of stationary magnetoconvection in a Newtonian liquid under temperature or gravity modulation," International Journal of Non-Linear Mechanics, 2012, vol.47(5), pp.418-425.
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