Linear Stability Analysis on Rotationally Modulated Reactive DDC in Anisotropic Porous Media

In this paper the rotational influence on double diffusive reactive convection in anisotropic porous layer saturated with a binary mixture is analyzed using linear stability theory. The Darcy model with the Coriolis term is employed to study the influence of rotation, chemical reaction, and anisotropy on system stability. The effects of Taylor number, reaction rate, solute Rayleigh number, Lewis number, anisotropy parameters, and normalized porosity are examined. Rotation is found to be stabilizing, while chemical reactions can either stabilize or destabilize the system. Anisotropy significantly affects the stability criterion. Stationary and oscillatory convection are illustrated graphically.

Rotation, Chemical reaction, Porous layer, Anisotropy & Double Diffusive Convection

1. Chakrabarti, A., Gupta, A.S.: Nonlinear thermohaline convection in a rotating porous medium, Mech. Res. Commun. 8(9) (1981) [Google Scholar] [Crossref]

2. Gaikwad, S. N., Malashetty, M. S. and Prasad, K. R.: An analytical study of linear and nonlinear double diffusive convection in a fluid saturated anisotropic porous layer with Soret effect, Appl. Math. Model, 33, pp. 3617 (2009) [Google Scholar] [Crossref]

3. Gaikwad, S. N., Malashetty, M. S. and Prasad, K. R.: Linear and nonlinear double diffusive convection in a fluid saturated anisotropic porous layer with cross diffusion effects, Transp. Porous Media, 80, pp. 537 (2009) [Google Scholar] [Crossref]

4. Gatica, J. E., Viljoen, H. J. and Hlavacek, V.: Interaction between chemical reaction and natural convection in porous media, Chem. Eng. Sci. 44(9), pp. 1853 (1989) [Google Scholar] [Crossref]

5. Guo, J., Kaloni, P.N.: Nonlinear stability problem of a rotating doubly diffusive porous layer, J. Math. Anal. Appl. 190, pp. 37-390 (1995) [Google Scholar] [Crossref]

6. Horton, C.W. and Rogers, F.T.: Convection currents in a porous medium, J. Appl. Phys., 16, pp. 367-370 (1945) [Google Scholar] [Crossref]

7. Ingham, I. Pop.: Transport Phenomena in Porous Media, Oxford: Pergamon Press (1998) [Google Scholar] [Crossref]

8. Ingham, I. Pop.: Transport Phenomena in Porous Media, vol. (III), Oxford: Elsevier (2005) [Google Scholar] [Crossref]

9. Jupp, T. E. and Woods, A. W.: Thermally-driven reaction fronts in porous media, J. Fluid Mech, pp. 484-329 (2003) [Google Scholar] [Crossref]

10. Lapwood, E.R.: Convection of a fluid in a porous medium, Proc. Camb. Phil. Soc., 44, pp. 508-521 (1948) [Google Scholar] [Crossref]

11. Lombardo, S., Mulone, G.: Necessary and sufficient conditions of global nonlinear stability for rotating double diffusive convection in a porous medium, Continuum Mech. Thermodyn. 14(16), pp. 527-540 (2002) [Google Scholar] [Crossref]

12. Malashetty, M. S. and Bharati Biradar, S.: The onset of double diffusive reaction-convection in an anisotropic porous layer, Phys. Fluids, 23, 064102, doi: 10.1063/1.3598469 (2011) [Google Scholar] [Crossref]

13. Malashetty, M. S. and Gaikwad, S. N.: Onset of convective instabilities in binary liquid mixtures with fast chemical reactions in a porous medium, Heat Mass Transfer, 39, pp. 415 (2003) [Google Scholar] [Crossref]

14. Malashetty, M. S. and Heera, R.: The effect of rotation on the onset of double diffusive convection in a horizontal anisotropic porous layer, Transp. Porous Media, 74, pp. 105 (2008) [Google Scholar] [Crossref]

15. Malashetty, M. S. and Swamy, M.: The onset of convection in a binary fluid saturated anisotropic porous layer, Int. J. Therm. Sci, 49, pp. 867 (2010) [Google Scholar] [Crossref]

16. McKibbin, R.: Thermal convection in layered and anisotropic porous media, a review. In: Wooding: R.A., White, I., Convective Flows in Porous Media, Wellington: Department of Scientific and Industrial Research, pp. 113-127 (1985) [Google Scholar] [Crossref]

17. Nield, D.A. and Bejan, A.: Convection in Porous Media, (3rd edn), New York: Springer-Verlag (2006) [Google Scholar] [Crossref]

18. Phillips, O. M.: Geological Fluid Dynamics, New York: Cambridge University Press (2009) [Google Scholar] [Crossref]

19. Pritchard, D. and Richardson, C. N.: The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer, J. Fluid Mech., 9, pp. 571 (2007) [Google Scholar] [Crossref]

20. Rudraiah, N., Shivakumara, I.S., Friedrich, R.: The effect of rotation on linear and nonlinear double diffusive convection in a sparsely packed porous medium, Int. J. Heat Mass Transfer 29, pp. 1301-1317 (1986) [Google Scholar] [Crossref]

21. Steinberg, V. and Brand, H.: Amplitude equations for the onset of convection in a reactive mixture in a porous medium, J. Chem. Phys., 80(1), pp. 431 (1984) [Google Scholar] [Crossref]

22. Steinberg, V. and Brand, H.: Convective instabilities of binary mixtures with fast chemical reaction in a porous medium, J. Chem. Phys., 78(5), pp. 2655 (1983) [Google Scholar] [Crossref]

23. Storesletten L.: Effects of anisotropy on convection in horizontal and inclined porous layers, In: Ingham, D.B. et al., Emerging Technologies and Techniques in Porous Media, Netherlands : Kluwer Academic Publishers, pp. 285-306 (2004) [Google Scholar] [Crossref]

24. Storesletten, L.: Effects of anisotropy on convective flow through porous media, In: Ingham, D.B., Pop, I., Transport Phenomena in Porous Media, Oxford: Pergamon Press, pp. 261-283 (1998) [Google Scholar] [Crossref]

25. Tyvand, P. A.: Thermohaline instability in anisotropic porous media, Water Resour. Res., 16, pp. 325 (1980) [Google Scholar] [Crossref]

26. Vadas: Emerging Topics in Heat and Mass Transfer in Porous Media, New York: Springer (2008) [Google Scholar] [Crossref]

27. Vafai: Handbook of Porous Media, New York : Marcel Dekker (2000) [Google Scholar] [Crossref]

28. Vafai: Handbook of Porous Media, London/Boca Raton: Taylor & Francis/CRC Press, FL (2005) [Google Scholar] [Crossref]

29. Viljoen, H. J., Gatica, J. E. and Hlavacek, V.: Bifurcation analysis of chemically driven convection, Chem. Eng. Sci., 45(2), pp. 503 (1990) [Google Scholar] [Crossref]

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