рус eng
«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 51

Ferrohydrodynamic Instability of a Viscoelastic Magnetic Fluid Layer under the Influence of Time-varying Magnetic Field

Author(s)
Chandrashekar Balaji1, Sokalingam Maruthamanikandan2, Chandrappa Rudresha3, V. Vidya Shree4

1CMR Institute of Technology, Bengaluru, India

2Presidency University, Bengaluru, India

3Sir MVIT, Bengaluru, India

4SJB Institute of Technology, Bengaluru, India

Abstract
The current work concerns the impact of a time-varying magnetic field on the threshold of Oldroyd-B viscoelastic magnetic fluid convection in the presence of both modulated and unmodulated magnetic fields. A time-varying magnetic field plays a crucial role in creating circulation in small passages where the effect of gravity is absent or ineffective. The resulting eigenvalue problem is obtained by a regular perturbation expansion under the assumption of a small modulation amplitude. The impact of the magnetic parameter, Prandtl number, stress relaxation parameter, strain retardation parameter and magnetic field modulation frequency, were discussed. The study shows that, the magnetic field modulation has a destabilizing impact on the system with convection occurs faster.
About the Authors

Chandrashekar Balaji, Asst. Prof., CMR Institute of Technology, Bengaluru 560037, India, balaji.c@cmrit.ac.in

Sokalingam Maruthamanikandan, Prof., Presidency University, Bengaluru, 560064, India, maruthamanikandan@presidencyuniversity.in

Chandrappa Rudresha, Asst. Prof., Sir MVIT, Bengaluru, 562157, India, rudresha maths@sirmvit.edu

V. Vidya Shree, Asst. Prof., SJB Institute of Technology, Bengaluru, 560060, India, vidyashreev@sjbit.edu.in

For citation

Balaji C., Maruthamanikandan S., Rudresha C., V. Vidya Shree Ferrohydrodynamic Instability of a Viscoelastic Magnetic Fluid Layer under the Influence of Time-varying Magnetic Field. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 51, pp. 34–49.

https://doi.org/10.26516/1997-7670.2025.51.34

Keywords
magnetic fluid, time-varying (modulation) magnetic field, viscoelasticity
UDC
519.6:532
MSC
76E06, 35B20, 76A10
DOI
https://doi.org/10.26516/1997-7670.2025.51.34
References
  1. Ahmed N., Maruthamanikandan S., Nagasmitha B. Oscillatory porous medium ferroconvection in a viscoelastic magnetic fluid with non-classical heat conduction. East European Journal of Physics, 2023, no. 2, pp. 296–309. https://doi.org/10.26565/2312-4334-2023-2-34
  2. Balaji C., Rudresha C., Vidya Shree V., Maruthamanikandan S. Effect of magnetic field modulation on Benard–Taylor ferroconvection. Journal of Physical Studies, 2023, vol. 27, no. 4, pp. 4401–4408. https://doi.org/10.30970/jps.27.4401
  3. Belyaev A.V., Smorodin B.L. Convection of a ferrofluid in an alternating magnetic field. Journal of Applied Mechanics and Technical Physics, 2009, vol. 50, no. 4, pp. 558–565. https://doi.org/10.1007/s10808-009-0075-1
  4. Chandrasekhar S. Hydrodynamic and hydromagnetic Stability. International Series of Monographs on Physics, 1961. https://doi.org/10.1063/1.3058072
  5. Chandrashekar B., Chandrappa R., Venkatesh V.S., Sokalingam M. Ferrohydrodynamic instability of a couple stress magnetic fluid layer under the influence of time-dependent sinusoidal magnetic field. Iraqi Journal of Applied Physics, 2022, vol. 18, no. 4, pp. 15–19.
  6. Engler H., Odenbach S. Thermomagnetic convection in magnetic fluids influenced by a time-modulated magnetic field. Proceedings in Applied Mathematics and Mechanics, 2008, vol. 8, no. 1, pp. 10951–10952. https://doi.org/10.1002/pamm.200810951
  7. Finlayson B.A. Convective instability of ferromagnetic fluids. Journal of Fluid Mechanics, 1970, vol. 40, no. 4, pp. 753–767. https://doi.org/10.1017/S0022112070000423
  8. Hakeem A.K.A., Govindaraju M., Ganga B. Influence of inclined Lorentz forces on entropy generation analysis for viscoelastic fluid over a stretching sheet with nonlinear thermal radiation and heat source/sink. Journal of Heat and Mass Transfer Research, 2019, vol. 6, no. 1, pp. 1–10. https://doi.org/10.22075/JHMTR.2018.13611.1198
  9. Hounsou P., Miwadinou C.H., Monwanou A.V. Thermal convection thresholds in an Oldroyd magnetic fluid in porous media. Pramana – Journal of Physics, 2023, vol. 97, no. 4, p. 152. https://doi.org/10.1007/s12043-023-02631-z
  10. Kaloni P.N., Lou J.X. Convective instability of magnetic fluids under alternating magnetic fields. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2005, vol. 71, no. 6, pp. 1–12. https://doi.org/10.1103/PhysRevE.71.066311
  11. Kole M., Khandekar S. Engineering applications of ferrofluids: A review. Journal of Magnetism and Magnetic Materials, 2021, vol. 537, p. 168222. https://doi.org/10.1016/j.jmmm.2021.168222
  12. Kolkka R.W., Ierley G.R. On the convected linear stability of a viscoelastic Oldroyd B fluid heated form below. Journal of Non-Newtonian Fluid Mechanics, 1987, vol. 25, no. 2, pp. 209–237. https://doi.org/10.1016/0377-0257(87)85044-9
  13. Maruthamanikandan S., Thomas N. M., Mathew S. Thermorheological and magnetorheological effects on Marangoni-ferroconvection with internal heat generation. Journal of Physics: Conference Series, 2018, vol. 1139, no. 1. https://doi.org/10.1088/1742-6596/1139/1/012024
  14. Mathew S., Maruthamanikandan S. Darcy-Brinkman ferroconvection with temperature dependent viscosity. Journal of Physics: Conference Series, 2018, vol. 1139, no. 1. https://doi.org/10.1088/1742-6596/1139/1/012023
  15. Matura P., Lucke M. Thermomagnetic convection in a ferrofluid layer exposed to a time-periodic magnetic field. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2009, vol. 80, no. 2, p. 026314. https://doi.org/10.1103/PhysRevE.80.026314
  16. Nayak M.K., Saranya S., Ganga B., Hakeem A.K.A., Sharma R.P., Makinde O.D. Influence of relaxation-retardation viscous dissipation on chemically reactive flow of Oldroyd-B nanofluid with hyperbolic boundary conditions. Heat Transfer, 2020, vol. 49, no. 8, pp. 4945–4967. https://doi.org/10.1002/htj.21861
  17. Perez L.M., Bragard J., Diaz P., Mancini H.L., Laroze D., Pleiner H. Magnetoviscous effect on thermal convection thresholds in an Oldroyd magnetic fluid. Journal of Magnetism and Magnetic Materials, 2017, vol. 444, pp. 432–438. https://doi.org/10.1016/j.jmmm.2017.07.052
  18. Rudresha C., Balaji C., Vidya Shree V., Maruthamanikandan S. Effect of electric field modulation on the onset of electroconvection in a dielectric fluid anisotropic porous layer. Journal of Computational Applied Mechanics, 2022, vol. 53, no. 4, pp. 510–523. https://doi.org/10.22059/JCAMECH.2022.348183.753
  19. Scherer C., Figueiredo Neto A.M. Ferrofluids: properties and applications. Brazilian Journal of Physics, 2005, vol. 35, pp. 718–727. https://doi.org/10.1590/S0103-97332005000400018
  20. Shliomis M.I., Smorodin B.L. Convective instability of magnetized ferrofluids. Journal of Magnetism and Magnetic Materials, 2002, vol. 252, pp. 197–202. https://doi.org/10.1016/S0304-8853(02)00712-6
  21. Takashima M., Ghosh A.K. Electrohydrodynamic instability in a viscoelastic liquid layer. Journal of the Physical Society of Japan, 1979, vol. 47, no. 5. pp. 1717–1722. https://doi.org/10.1143/JPSJ.47.1717
  22. Thomas N.M., Maruthamanikandan S. Chemical reaction-driven ferroconvection in a porous medium. Advances in Fluid Dynamics, Springer, 2021, pp. 363–371. https://doi.org/10.1007/978-981-15-4308-1_28
  23. Torres-Diaz I., Rinaldi C. Recent progress in ferrofluids research: novel applications of magnetically controllable and tunable fluids. Soft Matter, 2014, vol. 10, pp. 8584–8602. https://doi.org/10.1039/C4SM01308E
  24. Vidya Shree V., Rudresha C., Balaji C., Maruthamanikandan S. Effect of magnetic field dependent viscosity on Darcy-Brinkman ferroconvection with second sound. East European Journal of Physics, 2022, no. 4, pp. 112–117. https://doi.org/10.26565/2312-4334-2022-4-10
  25. Zakaria K., Sirwah M.A. Nonlinear behavior of the surface waves between two magnetic fluid layers. Physica Scripta, 2012, vol. 86, no. 6, p. 65704. https://doi.org/10.1088/0031-8949/86/06/065704
  26. Zhang Z., Fu C., Tan W. Linear and nonlinear stability analyses of thermal convection for Oldroyd-B fluids in porous media heated from below. Physics of Fluids, 2008, vol. 20, no. 8, p. 84103. https://doi.org/10.1063/1.2972154

Full text (english)