https://doi.org/10.1140/epjp/s13360-026-07514-x
Regular Article
Nonlinear stability and dynamics of Rayleigh–Bénard convection in variable viscosity ferromagnetic liquids
1
Department of Mathematics, RV College of Engineering, 560059, Bengaluru, Karnataka, India
2
Centre for Mathematical Needs, Christ University, 560029, Bengaluru, Karnataka, India
3
Department of Mathematics, BMS College of Engineering, 560019, Bengaluru, Karnataka, India
a
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Received:
24
October
2025
Accepted:
1
March
2026
Published online:
16
March
2026
Abstract
Rayleigh–Bénard convection in ferromagnetic liquids provides a fundamental framework for understanding magneto-thermal transport in systems where buoyancy, magnetic forces and material properties interact. Most nonlinear studies of ferroconvection, however, assume constant viscosity, even though in practical ferrofluids viscosity may vary with temperature and be influenced by an applied magnetic field. In this work, we examine the stability and nonlinear dynamics of a Newtonian ferromagnetic liquid confined between rigid isothermal boundaries and subjected to a uniform vertical magnetic field, while explicitly accounting for viscosity variations arising from thermal and magnetic effects. Linear stability analysis is carried out using a truncated Galerkin approach, leading to an analytical expression for the stationary critical Rayleigh number that incorporates the viscosity-dependence parameter and magnetic numbers. To investigate post-onset behavior, a generalized Lorenz-type system is derived through a minimal Fourier–Galerkin truncation, allowing steady, oscillatory and irregular convection states to be explored within a low-dimensional nonlinear framework. Heat transport is interpreted through a Nusselt number formulation expressed in terms of the reduced system variables, with time-averaged values used in non-steady regimes. The model recovers established constant-viscosity ferroconvection results in the appropriate limiting case and demonstrates how viscosity variation modifies stability thresholds, amplitude saturation and convective transport trends. The present formulation provides a compact theoretical basis for assessing the combined influence of thermorheological and magnetorheological effects on convection dynamics in ferrofluid layers relevant to magnetic thermal control applications.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
