Current issue
Archive
About the Journal
About
Editorial Board
Abstract & Indexing
Contact
Editorial Policies
Authorship & COI
Ethical principles
Principles of Transparent Checklist
Open access
For Authors
Instructions to Authors
Detailing Guidelines for Authors
Review process
Review sheet
How to submit
Open Access license
ORIGINAL PAPER
Energy Stability of Benard-Darcy Two-Component Convection of Maxwell Fluid
1
Department of Mathematics, Art and Science Faculty Ondokuz Mayis University 55139 Atakum/Samsun-TURKEY
2
Bangalore University, Central College Campus Bangalore 560 001, INDIA
Online publication date: 2013-04-19
Publication date: 2013-03-01
International Journal of Applied Mechanics and Engineering 2013;18(1):125-135
KEYWORDS
energy stability analysisLyapunov direct methodB´enard-Darcy convectionviscoelastictwocomponent Maxwell fluidstress relaxation
ABSTRACT
Energy stability of a horizontal layer of a two-component Maxwell fluid in a porous medium heated and salted from below is studied under the Oberbeck-Boussinesq-Darcy approximation using the Lyapunov direct method. The effect of stress relaxation on the linear and non-linear critical stability parameters is clearly brought out with coincidence between the two when the solute concentration is dilute. Qualitatively, the result of porous and clear fluid cases is shown to be similar. In spite of lack of symmetry in the problem it is shown that non linear exponential stability can be handled.
REFERENCES (24)
1.
Alloui Z., Vasseur P., Robillard L. and Bahloul A. (2010): Onset of double-diffusive convection in a horizontal Brinkman cavity. - Chemical Engineering Communications, vol.197, pp.387-399.
2.
Awad F.G., Sibanda P. and Motsa S.S. (2010): On the linear stability analysis of a Maxwell fluid with double-diffusive convection. - Applied Mathematical Modelling, vol.34, pp.3509-3517.
4.
Fu C., Zhang Z. and Tan W. (2007): Numerical simulation of thermal convection of a viscoelastic fluid in a porous square box heated from below. - Physics of Fluids, vol.19, 104-107.
5.
Haro M.L., Rio J.A.P. and Whitaker S. (1996): Flow of Maxwell fluid in porous media. - Transport in Porous Media 25, pp.167-192.
6.
Kim M.S., Lee S.B., Kim S. and Chung B.J. (2003): Thermal instability of viscoelastic fluids in porous media. - Int. J. Heat and Mass Transfer, vol.46, pp.5065-5072.
7.
Kumar P. and Singh M. (2006): On a viscoelastic fluid heated from below in a porous medium. - Journal of Non- Equilibrium Thermodynamics, vol.31, No.2, pp.189-203.
8.
Lombardo S., Mulone G. and Straughan B. (2001): Non-linear stability in the Benard problem for double-diffusive mixture in a porous medium. - Mathematical Methods in the Applied Sciences, Math. Meth. Appl. Sci., vol.24, pp.1229-1246.
9.
Long J.S., Chen J.H., Chen H.K., Tam L.M. and Chao Y.C. (2009): A unified system describing dynamics of chaotic convection. - Chaos, Solitons and Fractals, vol.41, pp.123-130.
10.
Long J.S., Tam L.M., Chen J.H., Chen H.K., Lin K.T. and Yuan Kang (2008): Chaotic convection of viscoelastic fluids in porous media. - Chaos, Solitons and Fractals, vol.37, pp.113-124.
11.
Malashetty M.S. and Kulkarni S. (2009): The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model. - J. Non-Newtonian Fluid Mech., vol.162, pp.29-37.
12.
Malashetty M.S., Swamy M. and Heera R. (2009): The onset of convection in a binary viscoelastic fluid saturated porous layer. - ZAMM. Z. Angew. Math. Mech., vol.89, No.5, pp.356-369.
13.
Malashetty M.S., Tan W. and Swamy M. (2009): The onset of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer. - Physics of Fluids, vol.21, pp.084101.
14.
Mulone G. and Rionero S. (1998): Unconditional nonlinear exponential stability in the Benard problem for a mixture: necessary and sufficient conditions. - Rendiconti Mat. Acc. Lincei, series 9, 9, pp.221-236.
15.
Nield D.A. and Bejan A. (2006): Convection in Porous Media. - New York: Springer-Verlag.
16.
Sharma R.C. and Sunil (1994): Thaermal instability of Oldroydian viscoelastic fluid with suspended particles in hydromagnetics in porous medium. - Polymer-Plastics Technology and Engineering, vol.33, No.3.
17.
Shivakumara I.S. and Sureshkumar S. (2008): Effect of throughflow and quadratic drag on the stability of a doubly diffusive Oldroyd-B fluid-saturated porous layer. - J. Geophys. Eng., vol.5, pp.268-280.
18.
Siddheshwar P.G. and Sri Krishna C.V. (2001): Rayleigh -Benard convection in a viscoelastic fluid-filled high-porosity medium with non uniform basic temperature gradient. - IJMMS, vol.25, No.9, pp.609-619.
19.
Siddheshwar P.G. and Sri Krishna C.V. (2003): Linear and non - linear analyses of convection in a micropolar fluid occupying a porous medium. - Int. J. Nonlinear Mech., vol.38, pp.1561-1579.
20.
Sri Krishna C.V. (2001): Effects of non-inertial acceleration on the onset of convection in a second-order fluidsaturated porous medium. - International Journal of Engineering Science, vol.39, pp.599-609.
21.
Tan W.C. and Masouka T. (2007): Stability analysis of Maxwell fluid in a porous medium heated from below. - Phys. Lett. A 360, pp.454-460.
23.
Wang S. and Tan W.C. (2008): Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below. - Phys Lett. A 372, pp.3046-3050.
24.
Wang S. and Tan W. (2011): Stability analysis of Soret-driven double-diffusive convection of Maxwell fluid in a porous medium. - International Journal of Heat and Fluid Flow, vol.32, pp.88-94.
Share
RELATED ARTICLE
| eISSN: | 2353-9003 |
| ISSN: | 1734-4492 |
Task: edition of a scientific journal, its internationalization and ensuring open access to the journal via the Internet
© 2006-2024 Journal hosting platform by Bentus
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.
