The Onset of Rayleigh-Bénard-Marangoni Convection in a Ferromagnetic Fluid Layer

Year : 2025 | Volume : 16 | Issue : 01 | Page : 1-9
    By

    R. Mahesh Kumar,

  • Savitha B,

  1. Associate Professor, Department of Mathematics, MES Pre-University College of Arts, Commerce and Science, Karnataka, India
  2. Associate Professor, Department of Mathematics, Raja Rajeswari College of Engineering, Karnataka, India

Abstract

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This study examined the implications of magnetic boundary conditions, which are vertical in nature, on buoyancy and surface tension–driven ferrothermal convection (FTC) in a ferrofluid layer. While the upper surface is stress-free and susceptible to general thermal boundary issues, the bottom surface is stiff and insulating against temperature changes. The eigenvalue issue is solved analytically using the regular perturbation method and numerically using the Galerkin technique. According to analysis, raising the Biot number slows down the magnetic field, yet raising the Marangoni number delays the onset. Furthermore, in the absence of the Biot number, the magnetization nonlinearity parameter has zero impact on FTC. The beginning of Rayleigh-Bénard-Marangoni (RBM) convection in a four-dimensional ferromagnetic fluid confined between two horizontal limits is examined in this paper, with particular attention to the effects of temperature gradients and temperature- and magnetic field–driven fluctuations in surface tension. We investigated the interplay between the field of magnetic attraction and thermocapillary forces by determining the circumstances under which RBM convection is initiated using numerical simulations and linear stability analysis. The findings demonstrate how the stability and pattern creation of convective structures are impacted by ferromagnetic features, ranging critical Rayleigh and Marangoni numbers, and magnetic interactions. With possible uses in engineering systems, including cooling devices, magnetic targeting, and enhanced material processing, these discoveries advance our knowledge of the intricate behavior of fluids with magnets in thermally and magnetically regulated conditions.

Keywords: Marangoni number, ferrothermal convection, insulating, regular perturbation technique, Galerkin technique

[This article belongs to Journal of Experimental & Applied Mechanics ]

How to cite this article:
R. Mahesh Kumar, Savitha B. The Onset of Rayleigh-Bénard-Marangoni Convection in a Ferromagnetic Fluid Layer. Journal of Experimental & Applied Mechanics. 2025; 16(01):1-9.
How to cite this URL:
R. Mahesh Kumar, Savitha B. The Onset of Rayleigh-Bénard-Marangoni Convection in a Ferromagnetic Fluid Layer. Journal of Experimental & Applied Mechanics. 2025; 16(01):1-9. Available from: https://journals.stmjournals.com/joeam/article=2025/view=0



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References

  1. Rosensweig RE. Ferrohydrodynamics. Cambridge, UK: Cambridge University Press; 1985.
  2. Bashtovoy VG Berkovsky BN, Vislovich AN. Introduction to Thermo Mechanics of Magnetic Fluids. Washington, DC, USA: Hemisphere Co.; 1988.
  3. Berkovsky BM Medvedev VF, Krakov MS. Magnetic Fluids: Engineering Applications. Oxford, UK: Oxford University Press; 1993.
  4. Odenbach S. Magnetic fluids – suspensions of magnetic dipoles and their magnetic controls. J Phys Condens Matter. 2003; 15 (15):, S1497.
  5. Finlayson BA. Method of Weighted Residuals and Variational Principles. San Diego, CA, USA: Academic Press; 1972.
  6. Qin Y, Kaloni PN. Nonlinear stability problem of a ferromagnetic fluid with surface tension effect. Eur J Mech B Fluids. 1994; 13: 305–321.
  7. Hennenberg M, Weyssow B, Slavtchev S, Legros JC. Coupling between Marangoni and Rosensweig instabilities. Part I: the transfer wave. Eur Phys J Appl Phys. 2001; 16: 217–229.
  8. Shivakumara IS, Rudraiah N, Nanjundappa CE. The effect of different forms of basic temperature gradients on the onset of ferroconvection driven by combined surface tension and buoyancy forces. Indian J Pure Appl Phys. 2002; 40: 95–106.
  9. Shivakumara IS, Nanjundappa CE. Marngoni ferroconvection with different initial temperature gradients. J Energy Heat Mass Transfer. 2006; 28: 1–45.
  10. Nanjundappa CE, Shivakumara IS. Effect of velocity and temperature boundary conditions on convective instability in a ferrofluid layer. ASME J Heat Transfer. 2008; 130: 104502-1–1045021-5.
  11. Nanjundappa CE, Shivakumara IS, Srikumar K. On the penetrative Bénard–Marangoni convection in a ferromagnetic fluid layer. Aerospace Sci Technol. 2013; 27 (1): 57–66.
  12. Nanjundappa CE, Shivakumara IS, Arunkumar R. Bénard–Marangoni ferroconvection with magnetic field dependent viscosity. J Magn Magn Mater. 2010; 322 (15): 2256–2263.
  13. Nanjundappa CE, Shivakumara IS, Savitha B. Onset of Bénard–Marangoni rroconvection with a convective surface boundary condition: the effects of cubic temperature profile and MFD viscosity. Int Commun Heat Mass Transfer. 2014; 51: 39–44.
  14. Nanjundappa CE, Shivakumara IS, Arunkumar R. Onset of Marangoni-Bénard ferroconvection with temperature dependent viscosity. Microgravity Sci Technol. 2013; 25: 103–112.
  15. Nanjundappa, Prakash HN, Shivakumara IS, Lee J. Effect of temperature dependent viscosity on the onset of Bénard–Marangoni ferroconvection. Int Commun Heat Mass Transfer. 2014; 51: 25–30.
  16. Nanjundappa CE, Shivakumara IS, Arunkumar R. Onset of Bénard-Marangoni ferroconvection with internal heat generation. Microgravity Sci Technol. 2011; 23: 29–39.
  17. Shivakumara IS, Nanjundappa CE. Effects of Coriolis force and different basic temperature gradients on Marangoni ferroconvection. Acta Mech. 2006; 182: 113–124.
  18. Nanjundappa CE, Shivakumara IS, Lee J. Effect of Coriolis force on Bénard–Marangoni convection in a rotating ferrofluid layer with MFD viscosity. Microgravity Sci Technol. 2015; 27: 27–37.
  19. Sparrow EM, Goldstein RJ, Jonsson UK. Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profiles. J Fluid Mech. 1964; 18 (4): 513–528.
Regular Issue Subscription Original Research
Volume 16
Issue 01
Received 29/10/2024
Accepted 05/01/2025
Published 25/01/2025
Publication Time 88 Days
85

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