An analytical study of linear and nonlinear double diffusive convection in a fluid saturated anisotropic porous layer with Soret effect

Applied Mathematical Modelling

Volumn 33, Issue 9, 2009, Pages 3617-3635

  Gaikwad, S N ^a   Malashetty, M S ^a   Rama Prasad, K ^a  

^a GULBARGA UNIVERSITY   (India)

Author keywords

Anisotropic porous layer; Critical Rayleigh number; Double diffusive convection; Double Fourier series; Lewis number; Soret parameter

Indexed keywords

ANISOTROPIC POROUS LAYER; CRITICAL RAYLEIGH NUMBER; DOUBLE DIFFUSIVE CONVECTION; DOUBLE FOURIER SERIES; LEWIS NUMBER; SORET PARAMETER;

ANISOTROPY; ELECTRIC CURRENTS; FOURIER ANALYSIS; FOURIER SERIES; HARMONIC ANALYSIS; LINEAR STABILITY ANALYSIS; MASS TRANSFER;

NONLINEAR ANALYSIS;

EID: 67349153341     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2008.12.013     Document Type: Article

References (34)

1. Turner J.S. Buoyancy Effects in Fluids (1973), Cambridge University Press, London
2. Turner J.S. Double diffusive phenomena. Ann. Rev. Fluid Mech. 6 (1974) 37-56
3. Turner J.S. Multicomponent convection. Ann. Rev. Fluid Mech. 17 (1985) 11-44
4. Huppert H.E., and Turner J.S. Double diffusive convection. J. Fluid Mech. 106 (1981) 299-329
5. Platten J.K., and Legros J.C. Convection in Liquids (1984), Springer-Verlag, Berlin
6. Nield D.A., and Bejan A. Convection in Porous Media (2006), Springer-Verlag, Berlin
7. Trevisan O.V., and Bejan A. Combined heat and mass transfer by natural convection in a porous medium. Adv. Heat Transfer 20 (1990) 315-352
8. Mojtabi A., and Charrier-Mojtabi M.C. Double diffusive convection in porous media. In: Vafai K. (Ed). Hand Book of Porous Media (2000), Marcel Dekkes, New York 559-603
9. Mojtabi A., and Charrier-Mojtabi M.C. Double diffusive convection in porous media. In: Vafai K. (Ed). Hand Book of Porous Media. second ed. (2005), Taylor and Francis, New York 269-320
10. Mamou M. Stability analysis of double - diffusive convection in porous enclosures. In: Ingham D.B., and Pop I. (Eds). Transport Phenomena in Porous Media, II (2002), Elsevier, Oxford 113-154
11. Hurle D.T.J., and Jakeman E. Soret-driven thermosolutal convection. J. Fluid Mech. 47 (1971) 667-687
12. Straughan B., and Hutter K. A priori bounds and structural stability for double diffusive convection incorporating the Soret effect. Proc. Royal Soc. London A 455 (1999) 767-777
13. Knobloch E. Convection in binary fluids. Phys. Fluids 23 9 (1980) 1918-1920
14. Rudraiah N., and Malashetty M.S. The influence of coupled molecular diffusion on double diffusive convection in a porous medium. ASME J. Heat Transfer 108 (1986) 872-876
15. Rudraiah N., and Siddheshwar P.G. A weak nonlinear stability analysis of double diffusive convection with cross-diffusion in a fluid saturated porous medium. Heat Mass Transfer 33 (1998) 287
16. Patil P.R., and Subramanian L. Soret instability in anisotropic porous medium with temperature dependent viscosity. Fluid Dyn. Res. 10 (1992) 159-168
17. Barten W., Lucke M., Kamps M., and Schnitz R. Convection in binary fluid mixtures. I. Extended traveling-wave and stationary states. Phys. Rev. E 51 (1995) 5636-5661
18. La Porta A., and Surko C.M. Convective instability in a fluid mixture heated from above. Phys. Rev. Lett. 80 17 (1998) 3759-3762
19. Bahloul A., Boutana N., and Vasseur P. Double-diffusive and Soret-induced convection in a shallow horizontal porous layer. J. Fluid Mech. 491 (2003) 325-352
20. Mansour A., Amahmid A., Hasnaoui M., and Bourie M. Multiplicity of solutions induced by thermosolute convection in a square porous cavity heated from below and subjected to horizontal concentration gradient in the presence of Soret effect. Numer. Heat-Transfer Part A 49 (2006) 69-94
21. Castinel G., and Combarnous M. Critere d' apparition de la convection naturelle dans une couche poreuse anisotrope horizontale. C.R. Acad. Sci. B 278 (1974) 701-704
22. Epherre J.F. Critere d' apparition de la convection naturelle dans une couche poreuse anisotrope. Rev. Gen Therm. 168 (1975) 949-950
23. Kvernvold O., and Tyvand P.A. Nonlinear thermal convection in anisotropic porous media. J. Fluid Mech. 90 (1979) 609-624
24. Tyvand P.A. Thermohaline instability in anisotropic porous media. Water Resur. Res. 16 2 (1980) 325-330
25. Nilsen T., and Storesletten L. An analytical study on natural convection in isotropic and anisotropic porous channels. Trans. ASME J. Heat Transfer 112 (1990) 396-401
26. Tyvand P.A., and Storesletten L. Onset of convection in an anisotropic porous medium with oblique principal axes. J. Fluid Mech. 226 (1991) 371-382
27. Govender S. On the effect of anisotropy on the stability of convection in a rotating porous media. Transp. Porous Media 64 (2006) 413-422
28. Govender S. Coriolise effect on the stability of centrifugally driven convection in a rotating anisotropic porous layer subject to gravity. Transp. Porous Media 69 (2007) 55-66
29. Malashetty M.S., and Swamy M. The effect of rotation on the onset of convection in a horizontal anisotropic porous layer. Int. J. Thermal Sci. 46 (2007) 1023-1032
30. M.S. Malashetty, Rajasekhar Heera, The effect of rotation on the onset of double diffusive convection in a horizontal anisotropic porous layer, Transp. Porous Media 2007, doi: 10.1007/s11242-007-91837.
31. Malashetty M.S., and Swamy M. Linear and non-linear double convection in a fluid saturated anisotropic porous layer. Proc. Int. Conf. Adv. Appl. Math. (2005) 253-264
32. Storesletten L. Effects of anisotropy on convective flow through porous media. In: Ingham D.B., and Pop I. (Eds). Transport Phenomena in Porous Media (1998), Pergamon Press, Oxford 261-283
33. Horton C.W., and Rogers F.T. Convection currents in a porous medium. J. Appl. Phys. 16 (1945) 367-370
34. Lapwood E.R. Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 44 (1948) 508-521