Effect of Vertical Vibrations on the Onset of Binary Convection
More details
Hide details
Department of Mathematics, Government College Gulbarga 585 105, Karnataka, INDIA
Online publication date: 2013-09-06
Publication date: 2013-08-01
International Journal of Applied Mechanics and Engineering 2013;18(3):899–910
In the present work the linear stability analysis of double diffusive convection in a binary fluid layer is performed. The major intention of this study is to investigate the influence of time-periodic vertical vibrations on the onset threshold. A regular perturbation method is used to compute the critical Rayleigh number and wave number. A closed form expression for the shift in the critical Rayleigh number is calculated as a function of frequency of modulation, the solute Rayleigh number, Lewis number, and Prandtl number. These parameters are found to have a significant influence on the onset criterion; therefore the effective control of convection is achieved by proper tuning of these parameters. Vertical vibrations are found to enhance the stability of a binary fluid layer heated and salted from below. The results of this study are useful in the areas of crystal growth in micro-gravity conditions and also in material processing industries where vertical vibrations are involved
Bejan A. (1993): Heat Transfer. - John Wiley and Sons, Inc.
Chandrasekhar S. (1981): Hydrodynamic and Hydromagnetic Stability. - New York: Dover.
Clever R., Schubert G. and Busse F. (1993): Two dimensional oscillatory convection in gravitationally modulated fluid layer. - J. Fluid Mech., vol. 253, pp.663-680.
Dyko M.P. and Vafai K. (2007): Effect of gravity modulation on convection in a horizontal annulus. - Int. J. Heat Mass Transf., vol.50, pp.348-360.
Farooq A. and Homsy G.M. (1996): Linear and nonlinear dynamics of a differentially heated slot under gravity modulation. - J. Fluid Mech., vol.313, pp.1-38.
Gershuni G.Z., Zhukhovitskii E.M. and Iurkov I.S. (1970): On convective stability in the presence of periodically varying parameter. - J. Appl. Math. Mech., vol.34, pp.442-452.
Gresho P.M. and Sani R.L. (1970): The effect of gravity modulation on the stability of a heated fluid layer. - J. Fluid Mech., vol.40, pp.783-806.
Huppert H.E. and Turner J.S. (1981): Double diffusive convection. - J. Fluid Mech., vol.106, pp.299-329.
Li B.Q. (2001): Stability of modulated-gravity-induced thermal convection in magnetic fields. - Phys. Rev . E., vol.63, pp.041508-1-9.
Malashetty M.S. and Padmavathi V. (1997): Effect of gravity modulation on the onset of convection in fluid and porous layer. - Int. J. Engng. Sci., vol.35, pp.829-840.
Malashetty M.S. and Swamy M.S. (2011): Effect of gravity modulation on the onset of thermal convection in rotating fluid and porous layer. - Phys. Fluids, vol.23, pp.064108-1-11.
Murray B.T., Coriell S.R. and McFadden G.B. (1991): The effect of gravity modulation on solutal convection during directional solidification. - J. Crystal Growth, vol.110, pp.713-723.
Platten J.K. and Legros J.C. (1984): Convection in Liquids. -Berlin: Springer-Verlag.
Rogers J.R., Pesch W., Brausch O. and Schatz M.F. (2005): Complex-ordered patterns in shaken convection. - Phys. Rev. E., vol.71, pp.066214-1-18.
Saunders B.V., Murray B.T., McFadden G.B., Coriell S.R. and Wheeler A.A. (1992): The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid. - Phys. Fluids A., vol.4, pp.1176-1189.
Shu Y., Li B.Q. and Ramaprian B.R. (2005): Convection in modulated thermal gradients and gravity: Experimental measurements and numerical simulations. - Int. J. Heat Mass Transf., vol.48, pp.145-160.
Turner J.S. (1973): Buoyancy Effects in Fluids. - London: Cambridge University Press.
Turner J.S. (1974): Double diffusive phenomena. - Ann. Rev. Fluid Mech., vol.6, pp.37-56.
Turner J.S. (1985): Double diffusive phenomena. - Ann. Rev. Fluid. Mech., vol.17, pp.11-44.
Venezian G. (1969): Effect of modulation on the onset of thermal convection. - J. Fluid Mech., vol.35, pp.243-254.
Wadih M. and Roux B. (1988): Natural convection in a long vertical cylinder under gravity modulation. - J. Fluid Mech., vol.193, pp.391-415.
Yakubovich V.A. and Starzhinskii V.M. (1975): Linear Differential Equations with Periodic Coefficients. - New York: John Wiley.
Yu Y., Chan C.L. and Chen C.F. (2007): Effect of gravity modulation on the stability of a horizontal double-diffusive layer. - J. Fluid Mech., vol.589, pp.183-213.
Zen’kovskaya S.M. and Rogovenko T.N. (1999): Filtration convection in a high-frequency vibration field. - J. Appl. Mech. Tech. Phys., vol.40, pp.379-385.