Thermo-convective instability in a rotating ferromagnetic fluid layer with temperature modulation

Abstract

We study the thermoconvective instability in a rotating ferromagnetic fluid confined between two parallel infinite plates with temperature modulation at the boundaries. We use weakly nonlinear stability theory to analyze the stationary convection in terms of critical Rayleigh numbers. The influence of parameters such as the Taylor number, the ratio of the magnetic force to the buoyancy force and the magnetization on the flow behaviour and structure are investigated. The heat transfer coefficient is analyzed for both the in-phase and the out-of-phase modulations. A truncated Fourier series is used to obtain a set of ordinary differential equations for the time evolution of the amplitude of convection for the ferromagnetic fluid flow. The system of differential equations is solved using a recent multi-domain spectral collocation method that has not been fully tested on such systems before. The solutions sets are presented as sets of trajectories in the phase plane. For some supercritical values of the Rayleigh number, spiralling trajectories that transition to chaotic solutions are obtained. Additional results are presented in terms of streamlines and isotherms for various Rayleigh numbers.

Effect of synchronized and unsynchronized boundary temperature modulation on the regulation of heat transfer in a ferrofluid with Fe3O4 nanoparticles

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“…et al, 11 Suslov, 12 Singh and Bajaj, 13 Laroze et al, 14 Sibanda and Noreldin, 15 and more recently Neha Aanam et al, 16 Melson et al, 17 and references therein shed light on various aspects of convective instability in ferromagnetic liquids, like, thermogravitational convection, convection in a vertical slot with effects of rotation, temperature modulation of the boundaries, variable or magnetic-field-dependent viscosity, binary ferroliquids, and so on.…”