Current issue
Special issue
Archive
About the Journal
About
Editorial Board
Abstract & Indexing
Contact
Funding/Grants
Editorial Policies
Authorship & COI
Ethical principles
Special Issues Editorial and Peer Review Policy
Principles of Transparent Checklist
Open access
For Authors
Instructions to Authors
Review process
Review sheet
How to submit
ORIGINAL PAPER
Effect of Vertical Vibrations on the Onset of Binary Convection
1
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
KEYWORDS
ABSTRACT
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
FUNDING
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest.
DATA AVAILABILITY
All data generated or analysed during this study are included in this published article.
REFERENCES (24)
2.
Chandrasekhar S. (1981): Hydrodynamic and Hydromagnetic Stability. - New York: Dover.
3.
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.
4.
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.
5.
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.
6.
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.
7.
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.
8.
Huppert H.E. and Turner J.S. (1981): Double diffusive convection. - J. Fluid Mech., vol.106, pp.299-329.
9.
Li B.Q. (2001): Stability of modulated-gravity-induced thermal convection in magnetic fields. - Phys. Rev . E., vol.63, pp.041508-1-9.
10.
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.
11.
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.
12.
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.
13.
Platten J.K. and Legros J.C. (1984): Convection in Liquids. -Berlin: Springer-Verlag.
14.
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.
15.
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.
16.
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.
17.
Turner J.S. (1973): Buoyancy Effects in Fluids. - London: Cambridge University Press.
18.
Turner J.S. (1974): Double diffusive phenomena. - Ann. Rev. Fluid Mech., vol.6, pp.37-56.
19.
Turner J.S. (1985): Double diffusive phenomena. - Ann. Rev. Fluid. Mech., vol.17, pp.11-44.
20.
Venezian G. (1969): Effect of modulation on the onset of thermal convection. - J. Fluid Mech., vol.35, pp.243-254.
21.
Wadih M. and Roux B. (1988): Natural convection in a long vertical cylinder under gravity modulation. - J. Fluid Mech., vol.193, pp.391-415.
22.
Yakubovich V.A. and Starzhinskii V.M. (1975): Linear Differential Equations with Periodic Coefficients. - New York: John Wiley.
23.
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.
24.
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.
Share
RELATED ARTICLE
| eISSN: | 2353-9003 |
| ISSN: | 1734-4492 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
