Abstract
The onset of thermal convection in an electrically conducting fluid saturating a porous medium, uniformly heated from below, salted by one chemical and embedded in an external transverse magnetic field is analyzed. The critical Rayleigh thermal numbers at which steady and Hopf convection can occur, are determined. Sufficient conditions guaranteeing the effective onset of convection via steady or oscillatory state are provided.
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Bhadauria, B.S., Sherani, A.: Onset of Darcy-convection in a magnetic-fluid-saturated porous medium subject to temperature modulation of the boundaries. Transp. Porous Media 73, 349–368 (2008)
Capone, F., De Luca, R.: Porous MHD convection: effect of Vadasz inertia term. Transp. Porous Media 118(3), 519–536 (2017)
Capone, F., Rionero, S.: Porous MHD convection: stabilizing effect of magnetic field and bifurcation analysis. Ric. Mat. 65, 163–186 (2016)
Capone, F., Rionero, S.: Brinkmann viscosity action in porous MHD convection. Int. J. Non Linear Mech. 85, 109–117 (2016). (2013) 192–200
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Dover, New York (1981)
Joseph, D.D.: Stability of fluid motions I, II. In: Springer Tracts in Natural Philosophy, Vol. 27–28. Springer, Berlin, Heidelberg (1976)
Merkin, D.R.: Introduction to the Theory of Stability, Texts in Applied Mathematics, vol. 24, p. xx+319. Springer, New York (1997)
Mulone, G., Rionero, S.: A non-linear stability analysis of the magnetic Bénard problem through the Lyapunov direct method. Arch. Ration. Mech. Anal. 103, 347–368 (1988)
Mulone, G., Rionero, S.: Necessary and sufficient conditions for nonlinear stability in the magnetic Bénard problem. Arch. Ration. Mech. Anal. 166, 197–218 (2003)
Nield, D.A., Bejan, A.: Convection in Porous Media, IV edn. Springer, Berlin (2012)
Rionero, S.: Heat and mass transfer by convection in multicomponent Navier–Stokes mixture: absence of subcritical instabilities and global nonlinear stability via the Auxiliary System Method. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei 25(4), 369 (2014)
Rionero, S.: Dynamic of thermo-MHD flows via a new approach. Rend. Lincei Mat. Appl. 28, 21–47 (2017)
Srivastava, A.K., Bhadauria, B.S., Gupta, V.K.: Magneto-convection in an anisotropic porous layer with Soret effect. Int. J. Non Linear Mech. 47, 426–438 (2012)
Straughan, B.: The Energy Method, Stability, and Nonlinear Convection, Appl. Math. Sci., vol. 91, 2nd edn. Springer, Berlin (2004)
Straughan, B.: Stability and Wave Motion in Porous Media, Appl. Math. Sci., vol. 165. Springer, Berlin (2008)
Straughan, B.: Convection with Local thermal Non-equilibrium and Microfluidic Effects. Advances in Mechanics and Mathematics. Springer, Berlin (2015)
Thompson, W.B.: Thermal convection in a magnetic field. Philos. Mag. Sc. Ser. 7(42), 1417–1432 (1951)
Vimala, S., Damodaran, S., Sivakumar, R., Sekhar, T.V.S.: The role of magnetic Reynolds number in MHD forced convection heat transfer. Appl. Math. Model. 40, 6737–6753 (2016)
Acknowledgements
This paper has been performed under the auspices of G.N.F.M. of INdAM. One of the authors (R. De Luca) acknowledges Progetto Giovani GNFM 2017 “Analisi dei sistemi biologici complessi”. The Authors should like to thank an anonymous referee for suggestions which have led to improvements in the manuscript.
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This paper is dedicated to Prof. Tommaso Ruggeri in the occasion of his 70th birthday.
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Capone, F., De Luca, R. Double diffusive convection in porous media under the action of a magnetic field. Ricerche mat 68, 469–483 (2019). https://doi.org/10.1007/s11587-018-0417-5
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DOI: https://doi.org/10.1007/s11587-018-0417-5