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Thermomagnetic convection in a layer of ferrofluid placed in a uniform oblique external magnetic field

Published online by Cambridge University Press:  05 January 2015

Habibur Rahman  and
Sergey A. Suslov
Habibur Rahman
Affiliation:
Department of Mathematics, H38, Swinburne University of Technology, John Street, Hawthorn, VIC 3122, Australia
Sergey A. Suslov*
Affiliation:
Department of Mathematics, H38, Swinburne University of Technology, John Street, Hawthorn, VIC 3122, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Linear stability of magnetoconvection of a ferromagnetic fluid contained between two infinite differentially heated non-magnetic plates in the presence of an oblique uniform external magnetic field is studied in zero gravity conditions. The thermomagnetic convection that arises is caused by the spatial variation of magnetisation occurring due to its dependence on the temperature. The critical values of the governing parameters at which the transition between motionless and convective states is observed are determined for various field inclination angles and for fluid magnetic parameters that are consistently chosen from a realistic experimental range. It is shown that, similar to natural paramagnetic fluids, the most prominent convection patterns align with the in-layer component of the applied magnetic field but in contrast to such paramagnetic fluids the instability patterns detected in ferrofluids can be oscillatory. It is also found that, contrary to paramagnetic fluids, the stability characteristics of magnetoconvection in ferrofluids depend on the magnitude of the applied field which becomes an additional parameter of the problem. This is shown to be due to the nonlinearity of the magnetic field distribution within the ferrofluid.

JFM classification

MHD and Electrohydrodynamics: Magnetic fluids MHD and Electrohydrodynamics: Magneto convection MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 316 - 348
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Copyright
© 2015 Cambridge University Press 

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References

Ageikin, D. I. 1950 Determination of heat emission by means of thermomagnetic convection. Proc. USSR Acad. Sci. 74, 229–232 (in Russian).Google Scholar
Albrecht, T., Bührer, C., Fähnle, M., Maier, K., Platzek, D. & Reske, J. 1997 First observation of ferromagnetism and ferromagnetic domains in a liquid metal. Appl. Phys. A 65, 215–220.Google Scholar
Altmeyer, S., Hoffmann, Ch., Leschhorn, A. & Lücke, M. 2010 Influence of homogeneous magnetic fields on the flow of a ferrofluid in the Taylor–Couette system. Phys. Rev. E 82, 016321.CrossRefGoogle ScholarPubMed
Bashtovoy, V. G., Berkovsky, B. M. & Vislovich, A. N. 1988 Introduction to Thermomechanics of Magnetic Fluids. Hemisphere.Google Scholar
Blums, E., Cebers, A. O. & Maiorov, M. M. 1997 Magnetic Fluids. Walter de Gruyter.Google Scholar
Bogatyrev, G. P. & Gilev, V. G. 1984 Concentration dependence of the viscosity of a magnetic liquid in an external field. Magnetohydrodynamics 20, 249–252.Google Scholar
Bogatyrev, G. P. & Shaidurov, G. F. 1976 Convective stability of a horizontal layer of ferromagnetic fluid in a uniform magnetic field. Magnetohydrodynamics 3, 137–146.Google Scholar
Bozhko, A. A., Pilugina, T. V., Putin, G. F., Shupenik, D. V. & Suhanovsky, A. N. 1998 On instability of thermogravitational flow in a ferrofluid vertical layer in the transversal magnetic field. In Proceedings of the 8th International Conference on Magnetic Fluids, Plyos, Russia (ed. Schelykalov, Yu. Ya.), pp. 75–78. Ivanovo State Power University, Ivanovo, Russia.Google Scholar
Bozhko, A. A. & Putin, G. F. 1991 Experimental investigation of thermo-magnetic convection in uniform external field. Bull. Acad. Sci. USSR Phys. Series 55, 1149–1156.Google Scholar
Bozhko, A. A. & Putin, G. F. 2003 Heat transfer and flow patterns in ferrofluid convection. Magnetohydrodynamics 39, 147–169.Google Scholar
Bozhko, A. A. & Putin, G. F. 2009 Thermomagnetic convection as a tool for heat and mass transfer control in nanosize materials under microgravity conditions. Microgravity Sci. Technol. 21, 89–93.Google Scholar
Bozhko, A. A., Putin, G. F., Sidorov, A. S. & Suslov, S. A. 2013 Convection in a vertical layer of stratified magnetic fluid. Magnetohydrodynamics 49, 143–152.Google Scholar
Bozhko, A. A. & Tynjala, T. 2005 Influence of gravitational sedimentation of magnetic particles on ferrofluid convection in experiments and numerical simulations. J. Magn. Magn. Mater. 289, 281–285.CrossRefGoogle Scholar
Elmore, W. C. 1938 The magnetisation of ferromagnetic colloids. Phys. Rev. 54, 1092–1095.CrossRefGoogle Scholar
Engler, H., Borin, D. & Odenbach, S. 2009 Thermomagnetic convection influenced by the magnetoviscous effect. J. Phys. Conf. Ser. 149, 012105.Google Scholar
Finlayson, B. A. 1970 Convective instability of ferromagnetic fluids. J. Fluid Mech. 40, 753–767.CrossRefGoogle Scholar
Hart, J. E. 1971 Stability of the flow in a differentially heated inclined box. J. Fluid Mech. 47, 547–576.Google Scholar
Hatziavramidis, D. & Ku, H.-C. 1985 An integral Chebyshev expansion method for boundary-value problems of O.D.E. type. Comput. Maths Applics. 11 (6), 581–586.Google Scholar
Hennenberg, M., Wessow, B., Slavtchev, S., Desaive, Th. & Scheild, B. 2006 Steady flows of laterally heated ferrofluid layer: influence of inclined strong magnetic field and gravity level. Phys. Fluids 18, 093602.Google Scholar
Huang, J., Edwards, B. F. & Gray, D. D 1997 Thermoconvective instability of paramagnetic fluids in a uniform magnetic field. Phys. Fluids 9, 1819–1825.Google Scholar
Ivanov, A. O., Kantorovich, S. S., Reznikov, E. N., Holm, C., Pshenichnikov, A. F., Lebedev, A., Chremos, A. & Camp, P. J. 2007 Magnetic properties of polydisperse ferrofluids: a critical comparison between experiment, theory, and computer simulation. Phys. Rev. E 75, 061405.Google Scholar
Koji, F., Hideaki, Y. & Masahiro, I. 2007 A mini heat transport device based on thermosensitive magnetic fluid. Nanoscale Microscale Thermophys. Engng 11, 201–210.Google Scholar
Ku, H.-C. & Hatziavramidis, D. 1984 Chebyshev expansion methods for the solution of the extended Graetz problem. J. Comput. Phys. 56, 495–512.Google Scholar
Lange, A. 2004 Magnetic Soret effect: application of the ferrofluid dynamics theory. Phys. Rev. E 70, 046308.Google Scholar
Lebedev, A. V. & Lysenko, S. N. 2011 Magnetic fluids stabilized by polypropylene glycol. J. Magn. Magn. Mater. 323, 1198–1202.Google Scholar
Lian, W., Xuan, Y. & Li, Q. 2009 Design method of automatic energy transport devices based on the thermomagnetic effect of magnetic fluids. Intl J. Heat Mass Transfer 52, 5451–5458.Google Scholar
MATLAB 2013 Matlab R2013a. The MathWorks, Inc., 3 Apple Drive, Natick, MA, USA.Google Scholar
Matsuki, H. & Murakami, K. 1987 Performance of an automatic cooling device using a temperature-sensitive magnetic fluid. J. Magn. Magn. Mater. 6, 363–365.CrossRefGoogle Scholar
Mukhopadhyay, A., Ganguly, R., Sen, S. & Puri, I. K. 2005 A scaling analysis to characterize thermomagnetic convection. Intl J. Heat Mass Transfer 48, 3485–3492.Google Scholar
Odenbach, S. 1995 Microgravity experiments on thermomagnetic convection in magnetic fluids. J. Magn. Magn. Mater. 149, 155–157.Google Scholar
Odenbach, S. 2002a Ferrofluids: Magnetically Controllable Fluids and Their Applications. Springer.Google Scholar
Odenbach, S. 2002b Magnetoviscous Effects in Ferrofluids. Springer.Google Scholar
Odenbach, S. 2004 Recent progress in magnetic fluid research. J. Phys.: Condens. Matter 16, R1135–R1150.Google Scholar
Odenbach, S. 2009 Colloidal Magnetic Fluids: Basics, Development and Applications of Ferrofluids, Lecture Notes in Physics. Springer.Google Scholar
Odenbach, S. & Müller, H. W. 2005 On the microscopic interpretation of the coupling of the symmetric velocity gradient to the magnetization relaxation. J. Magn. Magn. Mater. 289, 242–245.Google Scholar
Odenbach, S. & Raj, K. 2000 The influence of large particles and agglomerates on the magnetoviscous effect in ferrofluids. Magnetohydrodynamics 36 (4), 312–319.Google Scholar
Pop, L. M. & Odenbach, S. 2006 Investigation of microscopic reason for the magnetoviscous effect in ferrofluid studied by small angle neutron scattering. J. Phys.: Condens. Matter 18, S2785–S2802.Google Scholar
Pshenichnikov, A. F. 2007 A mutual-inductance bridge for analysis of magnetic fluids. Instrum. Exp. Tech. 50, 509–514.Google Scholar
Rosensweig, R. E. 1979 Fluid dynamics and science of magnetic fluids. Adv. Electron. Electron Phys. 48, 103–199.CrossRefGoogle Scholar
Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.Google Scholar
Ryskin, A. & Pleiner, H. 2004 Influence of a magnetic field on the Soret-effect-dominated thermal convection in ferrofluids. Phys. Rev. E 69, 046301.Google Scholar
Ryskin, A. & Pleiner, H. 2007 Magnetic-field-driven instability in stratified ferrofluids. Phys. Rev. E 75, 056303.Google Scholar
Schwab, L., Hildebrandt, U. & Stierstadt, K. 1983 Magnetic Bénard convection. J. Magn. Magn. Mater. 39, 113–114.Google Scholar
Suslov, S. A. 2008 Thermo-magnetic convection in a vertical layer of ferromagnetic fluid. Phys. Fluids 20 (8), 084101.Google Scholar
Suslov, S. A., Bozhko, A. A. & Putin, G. F. 2008 Thermo-magneto-convective instabilities in a vertical layer of ferro-magnetic fluid. In Proceedings of the XXXVI International Summer School–Conference ‘Advanced Problems in Mechanics’, Repino, Russia (ed. Indeitsev, D. A. & Krivtsov, A. M.), pp. 644–651. Institute of Problems of Mechanics of the Russian Academy of Sciences, St. Petersburg, Russia.Google Scholar
Suslov, S. A., Bozhko, A. A., Putin, G. F. & Sidorov, A. S. 2010 Interaction of gravitational and magnetic mechanisms of convection in a vertical layer of a magnetic fluid. Phys. Proc. 9, 167–170.Google Scholar
Suslov, S. A., Bozhko, A. A., Sidorov, A. S. & Putin, G. F. 2012 Thermomagnetic convective flows in a vertical layer of ferrocolloid: perturbation energy analysis and experimental study. Phys. Rev. E 86, 016301.Google Scholar
Suslov, S. A. & Paolucci, S. 1995 a Stability of mixed-convection flow in a tall vertical channel under non-Boussinesq conditions. J. Fluid Mech. 302, 91–115.Google Scholar
Suslov, S. A. & Paolucci, S. 1995 b Stability of natural convection flow in a tall vertical enclosure under non-Boussinesq conditions. Intl J. Heat Mass Transfer 38, 2143–2157.Google Scholar
Tagg, R. & Weidman, P. D. 2007 Linear stability of radially-heated circular Couette flow with simulated radial gravity. Z. Angew. Math. Phys. 58, 431–456.Google Scholar
Tangthieng, C., Finlayson, B. A., Maulbetsch, J. & Cader, T. 1999 Heat transfer enhancement in ferrofluids subjected to steady magnetic fields. J. Magn. Magn. Mater. 201, 252–255.Google Scholar
Tsebers, A. O. 1982 Thermodynamic stability of magnetofluids. Magnetohydrodynamics 18, 137–142.Google Scholar
Völker, T. & Odenbach, S. 2003 The influence of a uniform magnetic field on the Soret coefficient of magnetic nanoparticles. Phys. Fluids 15, 2198–2207.Google Scholar
Weiss, P. 1907 L’hypothèse du champ moléculaire et la propriété ferromagnétique. J. Phys. Theor. Appl. 6, 661–690.Google Scholar
Zablotsky, D., Mezulis, A. & Blums, E. 2009 Surface cooling based on thermomagnetic convection: numerical simulation and experiment. Intl J. Heat Mass Transfer 52, 5302–5308.Google Scholar
Zebib, A. 1996 Thermal convection in a magnetic fluid. J. Fluid Mech. 321, 121–136.Google Scholar