Abstract
The onset of double-diffusive convection in a horizontal fluid-saturated porous layer is examined by taking the Soret effect into consideration. The linear and nonlinear stability analyses are derived, and the corresponding eigenvalue problems are solved. The nonlinear stability analysis is achieved by using the energy method. In both the cases of linear and nonlinear stability theories, the onset criterion for all possible modes is derived analytically. For numerical computations of the eigenvalue problem, the Chebyshev tau method is employed. It is observed that the effect of stabilization or destabilization caused by the Soret parameter is significant for the Soret parameters which are less than \(Sr = 2\). In the absence of the Soret effect, the linear and nonlinear stability thresholds coincide.
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Acknowledgements
This work is a part of my Ph.D. thesis at Indian Institute of Technology, Hyderabad. I thank my supervisor, Dr. P. A. L. Narayana, for his valuable suggestions. The insightful comments made by the reviewers are very helpful for the improvement of this manuscript.
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Deepika, N. Linear and Nonlinear Stability of Double-Diffusive Convection with the Soret Effect. Transp Porous Med 121, 93–108 (2018). https://doi.org/10.1007/s11242-017-0949-2
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DOI: https://doi.org/10.1007/s11242-017-0949-2