Abstract
Penetrative convection in a horizontal ferrofluid-saturated porous layer in the presence of a uniform applied vertical magnetic field has been investigated via the internal heating model using the Brinkman-extended Darcy equation. The rigid-isothermal boundaries of the porous layer are considered to be either paramagnetic or ferromagnetic. The eigenvalue problem is solved numerically using the Galerkin method with either thermal or magnetic Rayleigh number as the eigenvalue. The stability of the system is significantly affected by the internal heating in the porous layer. It is noted that the paramagnetic boundaries with large magnetic susceptibility delay the onset of penetrative ferroconvection the most when compared to very low magnetic susceptibility as well as ferromagnetic boundaries. An increase in the value of magnetic Rayleigh number (R m ), heat source strength (N S ) and non-linearity of magnetization (M 3) is to hasten the onset of ferroconvection. In addition, the stability of the system when heated from above and also in the absence of thermal buoyancy has been discussed in detail.
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References
Rosensweig, R.E.: Ferrohydrodynamics. Cambridge University Press, London; reprinted with corrections (Dover, New York, 1997) (1985)
Bashtovoy V.G., Berkovsky B.N., Vislovich A.N.: Introduction to Thermomechanics of Magnetic Fluids. Hemisphere Co., Washington, DC (1988)
Berkovsky B.M., Medvedev V.F., Krakov M.S.: Magnetic Fluids, Engineering Applications. Oxford University Press, New York (1993)
Finlayson B.A.: Convective instability of ferromagnetic fluids. J. Fluid Mech. 40, 753–767 (1970)
Odenbach S.: Recent progress in magnetic fluid research. J. Phys. Condens. Matter. 16, R1135–R1150 (2004)
Kaloni P.N., Lou J.X.: Convective instability of magnetic fluids. Phys. Rev. E. 70, 026313–026324 (2004)
Shivakumara I.S., Nanjundappa C.E.: Effects of Coriolis force and different basic temperature gradients on Marangoni ferroconvection. Acta Mech. 182, 113–124 (2006)
Sunil A.M.: A nonlinear stability analysis for magnetized ferrofluid heated from below. Proc. R. Soc. Lond. A. 464, 83–98 (2008)
Nanjundappa C.E., Shivakumara I.S.: Effect of velocity and temperature boundary conditions on convective instability in a ferrofluid layer. ASME J. Heat Trans. 130, 104502–11045025 (2008)
Singh J., Bajaj R.: Temperature modulation in ferrofluid convection. Phys. Fluids. 21, 064105–106410512 (2009)
Rosensweig R.E., Zahn, M., Volger, T.: Stabilization of fluid penetration through a porous medium using magnetizable fluid. In: Berkovsky, B (ed.), Thermomechanics of Magnetic Fluids. Hemisphere, pp. 195–211. Washington, D.C. (1978)
Zahn, M., Rosensweig, R.E.: Stability of magnetic fluid penetration through a porous medium with uniform magnetic field oblique to the interface. IEEE Trans. Magn. 16, (1980)
Vaidaynathan G., Sekar R., Balasubramanian R.: Ferroconvective instability of fluids saturating a porous medium. Int. J. Engg. Sci. 29, 1259–1267 (1991)
Qin Y., Chadam J.: A non-linear stability problem of ferromagnetic fluids saturating a porous medium with inertial effects. Appl. Math. lett. 8, 25–29 (1995)
Borglin S.E., Mordis J., Oldenburg C.M.: Experimental studies of the flow of ferrofluid in porous media. Trans. Porous Med. 41, 61–80 (2000)
Shivakumara I.S., Nanjundappa C.E., Ravisha M.: Thermomagnetic convection in a magnetic nanofluid saturated porous medium. Int. J. Appl. Math Eng. Sci. 2, 157–170 (2008)
Shivakumara I.S., Nanjundappa C.E., Ravisha M.: Effect of boundary conditions on the onset of thermomagnetic convection in a ferrofluid saturated porous medium. ASME J. Heat Transf. 131, 101003-1–101003-9 (2009)
Straughan, B.: Mathematical Aspects of Penetrative Convection. Longman (1993)
Capone F., Gentile M., Hill A.A.: Penetrative convection in a fluid layer with through flow. Ricerche mat. 57, 251–260 (2008)
Carr M., de Putter S.: Penetrative convection in a horizontally isotropic porous layer. Cont. Mech. Therm. 15, 33–43 (2003)
Straughan B.: Resonant porous penetrative convection. Proc. R. Soc. Lond. A 460, 2913–2927 (2004)
Hill A.A., Rionero S., Straughan B.: Global stability for penetrative convection in a fluid layer with throughflow in porous materials. IMA J. Appl. Math. 72, 635–643 (2007)
Rudraiah N., Sekhar G.N.: Convection in magnetic fluids with internal heat generation. ASME J. Heat Trans. 113, 122–127 (1991)
Gotoh K., Yamada M.: Thermal convection in a horizontal layer of magnetic fluids. J. Phys. Soc. Jpn. 51, 3042–3048 (1982)
Sparrow E.M., Goldstein R.J., Jonsson U.K.: Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profiles. J. Fluid Mech. 18, 513–528 (1964)
Guo J., Kaloni P.N.: Double diffusive convection in a porous medium, nonlinear stability and the Brinkman effect. Stud. Appl. Math. 94, 341–358 (1995)
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Nanjundappa, C.E., Ravisha, M., Lee, J. et al. Penetrative ferroconvection in a porous layer. Acta Mech 216, 243–257 (2011). https://doi.org/10.1007/s00707-010-0367-9
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DOI: https://doi.org/10.1007/s00707-010-0367-9