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Nonlinear stability of laminar flows in an inclined heated layer with an imposed magnetic field
Author(s) -
Xu Lanxi
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6284
Subject(s) - laminar flow , prandtl number , mathematics , nonlinear system , mechanics , stability (learning theory) , magnetic field , flow (mathematics) , mathematical analysis , classical mechanics , physics , heat transfer , geometry , quantum mechanics , machine learning , computer science
Nonlinear stability of stationary laminar flow solutions of two inclined parallel planes filled with a hydromagnetic fluid heated from below is studied via Lyapunov direct method. In order to determine the energy stability bound for the critical Rayleigh number ( R a E ) explicitly, for R a < R a E , the laminar flow solutions of the problem are nonlinearly unconditionally and exponentially stable, and we consider just transverse perturbations. Compared with the results in the literature, conditions for the nonlinear stability obtained in this article have no restriction on the magnetic Prandtl number Pm.