Thermomagnetic Convection in a Ferrofluid Layer with Throughflow

Authors

  • Savitha B Department of Mathematics, Raja Rajeswari College of Engineering, Bangalore, Karnataka, India
  • C. E. Nanjundappa Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore, Karnataka, India

DOI:

https://doi.org/10.37591/joeam.v11i3.5334

Keywords:

Thermomagnetic convection, ferrofluids, vertical throughflow, Galerkin technique, Prandtl number

Abstract

The effect of vertical throughflow on the onset of thermomagnetic convection in a ferrofluid layer in the presence uniform vertical magnetic field is investigated theoretically. Both the boundaries are considered to be rigid-ferromagnetic and 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 as a perturbation parameter. Results show that the effect of magnetic number

References

Rosensweig RE. Ferrohydrodynamics Cambridge University Press Cambridge. New York, Melbourne. 1985.

Raj K, Moskowitz R. Commercial applications of ferrofluids. Journal of Magnetism and Magnetic Materials. 1990 Apr 1;85(1–3):233–45.

Rudraiah N., Kamiyama S. Electromagnetic Forces and Applications. 1992.

Blums E, Cebers A, Maiorov MM. Magnetic fluids. Walter de Gruyter; 2010 Oct 13.

Finlayson BA. Convective instability of ferromagnetic fluids. Journal of Fluid Mechanics. 1970 Mar;40(4):753–67.

Gotoh K, Yamada M. Thermal convection in a horizontal layer of magnetic fluids. Journal of the Physical Society of Japan. 1982 Sep 15;51(9):3042–8. https://doi.org/10.1143/JPSJ.51.3042

Rudraiah N, Sekhar GN. Convection in magnetic fluids with internal heat generation. ASME Journal of Heat Transfer. 1991;113:122–27p.

Ganguly R, Sen S, Puri IK. Heat transfer augmentation using a magnetic fluid under the influence of a line dipole. Journal of Magnetism and Magnetic Materials. 2004 Apr 1;271(1):63–73.

Odenbach S. Recent progress in magnetic fluid research. Journal of physics: condensed matter. 2004 Jul 30;16(32): R1135.

Kaloni PN, Lou JX. Convective instability of magnetic fluids. Physical Review E. 2004 Aug 31;70(2):026313.

Nanjundappa CE, Shivakumara IS. Effect of velocity and temperature boundary conditions on convective instability in a ferrofluid layer. Journal of heat transfer. 2008 Oct 1;130(10). https://doi.org/10.1115/1.2952742.

Singh J, Bajaj R. Temperature modulation in ferrofluid convection. Physics of Fluids. 2009 Jun 22;21(6):064105. https://doi.org/10.1063/1.3153912

Nanjundappa C, Shivakumara I, Srikumar K. Effect of MFD viscosity on the onset of ferromagnetic fluid layer heated from below and cooled from above with constant heat flux. Measurement Science Review. 2009 Jan 1;9(3):75–80.

Shivakumara IS, Lee J, Nanjundappa CE. Onset of thermogravitational convection in a ferrofluid layer with temperature dependent viscosity. Journal of heat transfer. 2012 Jan 1;134(1). https://doi.org/10.1115/1.4004758

Shvartsblat DD. The spectrum of perturbations and convective instability of a plane, horizontal fluid layer with permeable boundaries: PMM vol. 32, no. 2, 1968, pp. 276–281. Journal of Applied Mathematics and Mechanics. 1968 Jan 1;32(2):266–71. https://doi.org/10.1115/1.4004758

Shvartsblat DL. Steady convective motions in a plane horizontal fluid layer with permeable boundaries. Fluid Dynamics. 1969 Sep 1;4(5):54–9.

Gershuni GZ, Zhukhovitskii EM, Kelly RE. Convective stability of incompressible fluids. Jerusalem Keter. 1976.

Nield DA. Throughflow effects in the Rayleigh-Bénard convective instability problem. Journal of Fluid Mechanics. 1987 Dec;185:353–60. https://doi.org/10.1017/ S0022112087003203

Shivakumara IS, Suma SP. Effects of throughflow and internal heat generation on the onset of convection in a fluid layer. Acta Mechanica. 2000 Sep 1;140(3– 4):207–17.

Weilepp J, Brand HR. Coupling between Marangoni and Rosensweig instabilities. Part I: the transfer wave. Eur. Phys. J., Appl. Phys. 2001;16:217–29.

Finlayson B. The Method of Weighted Residuals and Variational Principles Academic Press. New York. 1972.

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Published

2021-02-15

Issue

Vol. 11 No. 3 (2020)

Section

Review Article

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