Skip to main content
SpringerLink
Log in

Onset of Marangoni-Bénard Ferroconvection with Temperature Dependent Viscosity

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

The effect of temperature dependent viscosity on the onset of Marangoni-Bénard ferroconvection under microgravity conditions in a horizontal ferrofluid layer in the presence of a uniform vertical magnetic field has been studied. The viscosity is considered to be varying exponentially with temperature. The lower rigid and the upper horizontal free boundaries are considered to be perfectly insulated to temperature perturbations. The resulting eigenvalue problem is solved numerically using the Galerkin technique as well as analytically by regular perturbation technique with wave number a as a perturbation parameter. It is observed that the analytical results agree well with those obtained numerically. The characteristics of stability of the system are strongly dependent on the viscosity parameter B. It is found that increase in the viscosity parameter B has a stabilizing effect on the onset of Marangoni-Bénard ferroconvection. Moreover, the nonlinearity of fluid magnetization M 3 is observed to have no consequence on the onset of convection in the case of fixed heat flux boundary conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bashtovoy, V.G., Berkovsky, B.M., Vislovich, A.N.: Introduction to Thermomechanics of Magneticfluids. Hemisphere, Washington (1988)

    Google Scholar 

  • Berkovsky, B.M., Medvedev, V.F., Krakov, M.S.: Magnetic Fluids Engineering Applications. Oxford University Press, Oxford (1993)

    Google Scholar 

  • Blums, E., Cebers, A., Maiorov, M.M.: Magnetic Fluids. deGruyter, New York (1997)

    Google Scholar 

  • Bozhko, A., Putin, G.: Thermomagnetic convection as a tool for heat and mass transfer control in nanosize materials under microgravity conditions. Microgravity Sci. Technol. 21, 89–93 (2009)

    Article  Google Scholar 

  • Capone, F., Gentile, M.: Nonlinear stability analysis of convection for fluids with exponentially temperature-dependent viscosity. Acta Mech. 107, 53–64 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Char, M.I., Chen, C.C.: Influence of viscosity variation on the stationary Benard-Marangoni instability with a boundary slab of finite conductivity. Acta Mech. 135, 181–198 (1999)

    Article  MATH  Google Scholar 

  • Engler, H., Odenbach, S.: Parametric modulation of thermomagnetic convection in magnetic fluids. J. Phys. Condens. Matter 20, 204135-1–204135-5 (2008)

    Article  Google Scholar 

  • Finlayson, B.A.: Convective instability of ferromagnetic fluids. J. Fluid Mech. 40, 753–767 (1970)

    Article  MATH  Google Scholar 

  • Finlayson, B.A.: Method of Weighted Residuals and Variational Principles. Academic Press, London (1972)

    MATH  Google Scholar 

  • Gotoh, K., Yamada, M.: Thermal convection in a horizontal layer of magnetic fluids. J. Phys. Soc. Jpn. 51, 3042–3048 (1982)

    Article  Google Scholar 

  • Hashim, I., Awang Kechil, S.: Active control of Marangoni instability in a fluid layer with temperature-dependent viscosity in a microgravity environment. Fluid Dyn. Res. 41, 045504–045512 (2009)

    Article  Google Scholar 

  • Hennenberg, M., Weyssow, B., Slavtchev, S., Alexandrov, V., Desaive, T.: Rayleigh-Marangoni-Bénard instability of a ferrofluid layer in a vertical magnetic field. J. Magn. Magn. Mater. 289, 268–271 (2005)

    Article  Google Scholar 

  • Hennenberg, M., Weyssow, B., Slavtchev, S., Scheld, B.: Coupling between stationary Marangoni and Cowley-Rosensweig instabilities in a deformable ferrofluid layer. Fluid Dyn. Mater. Proc. 1, 101–107 (2007)

    Google Scholar 

  • Kaloni, P.N., Lou, J.X.: Convective instability of magnetic fluids under alternating magnetic fields. Phys. Rev. E 70, 0663113–026324 (2004)

    Article  Google Scholar 

  • Lalas, D.P., Carmi, S.: Thermoconvective stability of ferrofluids. Phys. Fluids 4, 436–437 (1971)

    Article  Google Scholar 

  • Nanjundappa, C.E., Shivakumara, I.S.: Effect of velocity and temperature boundary conditions on convective instability in a ferrofluid layer. ASME J. Heat Transf. 130, 1045021–1045025 (2008)

    Article  Google Scholar 

  • Nanjundappa, C.E., Shivakumara, I.S., Srikumar, K.: Effect of MFD viscosity on the onset of ferromagnetic fluids layer heated from below and cooled from above with constant heat flux. Meas. Sci. Rev. 9(3), 77–78 (2009)

    Article  Google Scholar 

  • Nanjundappa, C.E., Shivakumara, I.S., Arunkumar, R.: Bénard–Marangoni ferroconvection with magnetic field dependent viscosity. J. Magn. Magn. Mater. 322, 2256–2263 (2010)

    Article  Google Scholar 

  • Nanjundappa, C.E., Shivakumara, I.S., Arunkumar, R.: Onset of Bénard-Marangoni ferroconvection with internal heat generation. Microgravity Sci. Technol. 23, 29–39 (2011)

    Article  Google Scholar 

  • Odenbach, S.: Microgravity experiments on thermomagnetic convection in magneticfluids. J. Magn. Magn. Mater. 149, 155–157 (1995)

    Article  Google Scholar 

  • Odenbach, S.: On the stability of a free surface of a magnetic fluid under microgravity. J. Magn. Magn. Mater. 170, 309–316 (1997)

    Article  Google Scholar 

  • Odenbach, S.: Microgravity research as a tool for the investigation of effects in magnetic. Fluids J. Magn. Magn. Mater. 201, 149–154 (1999)

    Article  Google Scholar 

  • Odenbach, S.: Recent progress in magnetic fluid research. J. Phys. Condens. Matter 16, 1135–1150 (2004)

    Article  Google Scholar 

  • Qin, Y., Kaloni, P.N.: Nonlinear stability problem of a ferromagnetic fluid with surface tension effect. Eur. J. Mech. B/Fluids 13, 305–321 (1994)

    MathSciNet  MATH  Google Scholar 

  • Rosensweig, R.E.: Ferrohydrodynamics. Cambridge University Press, New York (1985)

    Google Scholar 

  • Shliomis, M.I.: Magnetic fluids. Soviet Phys. Uspekhi (Engl. Trans.) 17, 153–169 (1974)

    Article  Google Scholar 

  • Shivakumara, I.S., Lee, J., Nanjundappa, C.E.: Onset of thermogravitational convection in a ferrofluid layer with temperature dependent viscosity. ASME J. Heat Trans. 134, 0125011–0125017 (2012)

    Article  Google Scholar 

  • Shivakumara, I.S., Nanjundappa, C.E.: Marangoni ferroconvection with different initial temperature gradients. J. Energy Heat Mass Transf. 28, 45–61 (2006)

    Google Scholar 

  • Shivakumara, I.S., Rudraiah, N., Nanjundappa, C.E.: Effect of non-uniform basic temperature gradient on Rayleigh–Bénard–Marangoni convection in ferrofluids. J. Magn. Magn. Mater. 248, 379–395 (2002)

    Article  Google Scholar 

  • Singh, J., Bajaj, R.: Temperature modulation in ferrofluid convection. Phys. Fluids 21, 0641051–06410512 (2009)

    Google Scholar 

  • Singh, J., Bajaj, R.: Convective instability in a ferrofluid layer with temperature-modulated rigid boundaries. Fluid Dyn. Res. 43, 025502-1–025502-26 (2011)

    Article  MathSciNet  Google Scholar 

  • Stengel, K.C., Oliver, D.S., Booker, J.R.: Onset of convection in a variable-viscosity fluid. J. Fluid Mech. 120, 411–431 (1982)

    Article  MATH  Google Scholar 

  • Stiles, P.J., Kagan, M.J.: Thermoconvective instability of a ferrofluid in a strong magnetic field. J. Colloid Interface Sci. 134, 435–449 (1990)

    Article  Google Scholar 

  • Sunil, Mahajan, A.: A nonlinear stability analysis for magnetized ferrofluid heated from below. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 464, 83–98 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Weilepp, J., Brand, H.R.: Competition between the Bénard-Marangoni and the Rosensweig instability inmagnetic fluids. J. Phys. II France 6, 419–441 (1996)

    Article  Google Scholar 

  • Weilepp, J., Brand, H.R.: Coupling between Marangoni and Rosensweig instabilities. Part I: the transfer wave. Eur. Phys. J. Appl. Phys. 16, 217–229 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore, 560 056, India

    C. E. Nanjundappa

  2. UGC-Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore, 560 001, India

    I. S. Shivakumara

  3. Department of Mathematics, Sai Vidya Institute of Technology, Bangalore, 560 064, India

    R. Arunkumar

Authors
  1. C. E. Nanjundappa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. S. Shivakumara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Arunkumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. E. Nanjundappa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nanjundappa, C.E., Shivakumara, I.S. & Arunkumar, R. Onset of Marangoni-Bénard Ferroconvection with Temperature Dependent Viscosity. Microgravity Sci. Technol. 25, 103–112 (2013). https://doi.org/10.1007/s12217-012-9330-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12217-012-9330-9

Keywords

Search

Navigation