Abstract
The influence of local thermal nonequilibrium with Cattaneo effects in the solid on the onset of thermal-convective instability in a horizontal layer of Darcy porous medium saturated by a ferrofluid in the presence of a uniform vertical magnetic field is investigated. The presence of the Cattaneo effect is to instill instability via oscillatory motion as well which is not reminiscent of the observed instability phenomenon in its absence. Increase in the value of the solid thermal relaxation time parameter τ is found to advance the onset of oscillatory ferroconvection. The onset of stationary ferroconvection is delayed, while the onset of oscillatory convection is accelerated with an increase in the value of the interphase heat transfer coefficientH t. The threshold value of H t, at which the transition from stationary to oscillatory convection takes place, decreases with increasing τ noticeably and marginally with increasing magnetic parameter M 3, while it increases with increasing ratio of conductivities α and magnetic number M 1. The critical wave number for stationary convection is found to be higher than for oscillatory convection.
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References
Rosensweig R.E.: Ferrohydrodynamics. Cambridge University Press, Cambridge (1985)
Berkovsky B.M., Medvedev V.F., Krakov M.S.: Magnetic Fluids: Engineering Applications. Oxford University Press, New York (1993)
Blums E.S., Cebers A.O., Maiorov M.M.: Magnetic Fluids. de Gruyter, New York (1997)
Hergt R., Andrä W., Ambly C.G., Hilger I., Kaiser W.A., Richter U., Schmidt H.G.: Physical limitations of hypothermia using magnetite fine particles. IEEE Trans. Magn. 34, 3745–3754 (1998)
Alexiou C., Arnold W., Hulin P., Klein R., Schmidt A., Bergemann C., Parak F.G.: Therapeutic efficacy of ferrofluid bound anticancer agent. Magnetohydrodynamics 37, 318–322 (2001)
Odenbach S.: Recent progress in magnetic fluid research. J. Phys. Condens. Matter 16, R1135–R1150 (2004)
Ganguly R., Sen S., Puri I.K.: Heat transfer augmentation using a magnetic fluid under the influence of a line dipole. J. Magn. Magn. Mater. 271, 63–73 (2004)
Kaloni P.N., Lou J.X.: Convective instability of magnetic fluids. Phys. Rev. E 70, 026313–026324 (2004)
Nkurikiyimfura I., Wang Y., Pan Z.: Heat transfer enhancement by magnetic nanofluids—a review. Renew. Sustain. Energy Rev. 21, 548–561 (2013)
Rosensweig R.E., Zahn M., Vogler T: Stabilization of fluid penetration through a porous medium using magnetizable fluids. In: Berkovsky, B (ed.) Thermomechanics of Magnetic Fluids, pp. 195–211. Hemisphere, Washington (1978)
Zhan 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, 275–282 (1980)
Vaidyanathan G., Sekar R., Balasubramanian R.: Ferroconvective instability of fluids saturating a porous medium. Int. J. Eng. Sci. 29, 259–1267 (1991)
Qin Y., Chadam J.: A non-linear stability problem for ferromagnetic fluids in a porous medium. Appl. Math. Lett. 8(2), 25–29 (1995)
Borglin S.E., Mordis J., Oldenburg C.M.: Experimental studies of the flow of ferrofluid in porous media. Transp. Porous Med. 41, 61–80 (2000)
Sunil, , Maharajan A.: A nonlinear stability analysis for thermoconvective magnetized ferrofluid saturating a porous medium. Transp. Porous Med. 76, 327–343 (2009)
Shivakumara I.S., Nanjundappa C.E., Ravisha M.: Thermomagnetic convection in a magnetic nanofluid saturated porous medium. Int. J. Appl. Math. Eng. Sci. 2(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)
Nanjundappa C.E., Shivakumara I.S., Ravisha M.: The onset of ferroconvection in a horizontal saturated porous layer heated from below and cooled from above with constant heat flux subject to MFD viscosity. Int. Commun. Heat Mass Transf. 37, 1246–1250 (2010)
Virto L., Carbonell M., Castilla R., Gamez-Montero P.J.: Heating of saturated porous media in practice: several causes of local thermal non-equilibrium. Int. J. Heat Mass Transf. 52, 5412–5422 (2009)
Sunil, , Sharma Poonam, Mahajan Amit: Nonlinear ferroconvection in a porous layer using a thermal nonequilibrium model. Spec. Top. Rev. Porous Med. 1, 105–121 (2010)
Lee J., Shivakumara I.S., Ravisha M.: Effect of thermal non-equilibrium on convective instability in a ferromagnetic fluid saturated porous medium. Transp. Porous Med. 86, 103–124 (2011)
Shivakumara I.S., Lee J., Ravisha M., Gangadhara Reddy R.: The onset of Brinkman ferroconvection using a thermal non-equilibrium model. Int. J. Heat Mass Transf. 54, 2116–2125 (2011)
Shivakumara I.S., Lee J., Ravisha M., Gangadhara Reddy R.: The effects of local thermal nonequilibrium and MFD viscosity on the onset of Brinkman ferroconvection. Meccanica 47, 1359–1378 (2012)
Cattaneo C.: Sulla conduzione del calore. Atti Sem. Mat. Fis. Univ. Modena 3, 83–101 (1948)
Straughan B., Franchi F.: Bénard convection and the Cattaneo law of heat conduction. Proc. R. Soc. A 96, 175–178 (1984)
Lebon G., Cloot A.: Bénard–Marangoni, instability in a Maxwell–Cattaneo fluid. Phys. Lett. A 105, 361–364 (1984)
Straughan B.: Thermal convection with the Cattaneo–Christov model. Int. J. Heat Mass Transf. 53, 95–98 (2010)
Straughan, B.: Heat Waves. Series in Applied Math Science, vol. 177. Springer, New York (2011)
Straughan B.: Porous convection with local thermal non-equilibrium temperatures and with Cattaneo effects in the solid. Proc. R. Soc. A 469, 20130187 (2013)
Stranges D.F., Khayat R.E., Albaalbaki B.: Thermal convection of non-Fourier fluids. Linear stab. Int. J. Therm. Sci. 74, 14–23 (2014)
Haddad S.A.M.: Thermal instability in Brinkman porous media with Cattaneo–Christov heat flux. Int. J. Heat Mass Transf. 68, 659–668 (2014)
Shivakumara I.S., Ravisha M., Ng C.O., Varun V.L.: A thermal non-equilibrium model with Cattaneo effect for convection in a Brinkman porous layer. Int. J. Non Linear Mech. 71, 39–47 (2015)
Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (2013)
Finlayson B.A.: Convective instability of ferromagnetic fluids. J. Fluid Mech. 40, 753–767 (1970)
Banu N., Rees D.A.S.: Onset of Darcy–Benard convection using a thermal non-equilibrium Model. Int. J. Heat Mass Transf. 45, 2221–2228 (2002)
Auernhammer G.K., Brand H.R.: Thermal convection in a rotating layer of a magnetic fluid. Eur. Phys. J. B 16, 157–168 (2000)
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Shivakumara, I.S., Ravisha, M., Ng, CO. et al. Porous ferroconvection with local thermal nonequilibrium temperatures and with Cattaneo effects in the solid. Acta Mech 226, 3763–3779 (2015). https://doi.org/10.1007/s00707-015-1402-7
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DOI: https://doi.org/10.1007/s00707-015-1402-7