Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

doi:10.1088/1674-1056/22/5/054702

中国物理B ›› 2013, Vol. 22 ›› Issue (5): 54702-054702.doi: 10.1088/1674-1056/22/5/054702

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Rajib Basu^a, G. C. Layek^b

a Department of Mathematics, Nistarini College, Purulia-723101, West Bengal, India;
b Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India

收稿日期:2012-07-09 修回日期:2012-11-23 出版日期:2013-04-01 发布日期:2013-04-01

Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Rajib Basu^a, G. C. Layek^b

a Department of Mathematics, Nistarini College, Purulia-723101, West Bengal, India;
b Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India

Received:2012-07-09 Revised:2012-11-23 Online:2013-04-01 Published:2013-04-01
Contact: G. C. Layek E-mail:goralayek@yahoo.com

摘要/Abstract

摘要： Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the framework of Darcy for porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.

关键词: double-diffusive convection, porous media, Soret and Dufour effects, linear stability analysis

Abstract: Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the framework of Darcy for porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.

Key words: double-diffusive convection, porous media, Soret and Dufour effects, linear stability analysis

中图分类号: (Multidiffusive convection)

47.55.pd

47.56.+r (Flows through porous media)

Rajib Basu, G. C. Layek. Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above[J]. 中国物理B, 2013, 22(5): 54702-054702.

Rajib Basu, G. C. Layek. Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above[J]. Chin. Phys. B, 2013, 22(5): 54702-054702.

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Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

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