Chaotic convection in a ferrofluid

Laroze, David; Siddheshwar, P. G.; Pleiner, Harald

doi:10.1016/j.cnsns.2013.01.016

Cited by 59 publications

(45 citation statements)

References 67 publications

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“…A weakly nonlinear analysis is now embarked upon by means of truncated representations of Fourier series for velocity and temperature fields to find the effect of various parameters on finite amplitude convection and to know the amount of heat transfer.^ [27]. This aspect was also demonstrated in generalized Lorenz models of viscoelastic fluid convection, electroconvection, and ferroconvection [20,28,29] The third order generalized Lorenz system described by Eqs. (18)- (20) is uniformly bounded in time and possesses many properties of the full problem.…”

Section: Linear Stability Analysismentioning

confidence: 99%

Nonlinear Rayleigh–Bénard Convection With Variable Heat Source

Siddheshwar

Titus²

2013

Journal of Heat Transfer

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Linear and nonlinear Rayleigh-Bénard convections with variable heat source (sink) are studied analytically using the Fourier series. The strength of the heat source is characterized by an internal Rayleigh number, R¡, whose ejfect is to decrease the critical external Rayleigh number. Linear theory involving an autonomous system (linearized Lorenz model) further reveals that the critical point at pre-onset can only be a saddle point. In the postonset nonlinear study, analysis of the generalized Lorenz model leads us to two other critical points that take over from the critical point of the pre-onset regime. Classical analysis of the Lorenz model points to the possibility of chaos. The effect of R¡ is shown to delay or advance the appearance of chaos depending on whether R, is negative or positive. This aspect is also reflected in its ejfect on the Nusselt number. The Lyapunov exponents provide useful information on the closing in and opening out of the trajectories of the solution of the Lorenz model in the cases of heat sink and heat source, respectively. The Ginzburg-Landau models for the problem are obtained via the 3-mode and 5-mode Lorenz models of the paper.

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Section: Linear Stability Analysismentioning

confidence: 99%

Nonlinear Rayleigh–Bénard Convection With Variable Heat Source

Siddheshwar

Titus²

2013

Journal of Heat Transfer

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“…Our experiments show that such a simplified treatment does not always produce accurate results. For example, computational results reported for a monocomponent model in [8,9] show that irregular regimes of convection arise only far beyond the convection threshold (i.e., for very large values of the governing flow parameters, such as thermal and magnetic Rayleigh numbers). The current experimental investigation of an actual ferromagnetic nanofluid demonstrates that this is not always so even in well-studied flow situations such as convection in a spherical cavity heated from below.…”

Section: Introductionmentioning

confidence: 97%

Intermittent flow regimes near the convection threshold in ferromagnetic nanofluids

et al. 2015

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The onset and decay of convection in a spherical cavity filled with ferromagnetic nanofluid and heated from below are investigated experimentally. It is found that, unlike in a single-component Newtonian fluid where stationary convection sets in as a result of supercritical bifurcation and where convection intensity increases continuously with the degree of supercriticality, convection in a multicomponent ferromagnetic nanofluid starts abruptly and has an oscillatory nature. The hysteresis is observed in the transition between conduction and convection states. In moderately supercritical regimes, the arising fluid motion observed at a fixed temperature difference intermittently transitions from quasiharmonic to essentially irregular oscillations that are followed by periods of a quasistationary convection. The observed oscillations are shown to result from the precession of the axis of a convection vortex in the equatorial plane. When the vertical temperature difference exceeds the convection onset value by a factor of 2.5, the initially oscillatory convection settles to a steady-state regime with no intermittent behavior detected afterward. The performed wavelet and Fourier analyses of thermocouple readings indicate the presence of various oscillatory modes with characteristic periods ranging from one hour to several days.

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“…The Lyapunov exponents are presented in the form of 2-D maps as a function of the relevant parameters of the system [37,38]. Also, a zooming technique to explore in more detail the different regimes will be used [39,40,41].…”

Section: Dynamical Indicatorsmentioning

confidence: 99%

“…Apart from the Lyapunov spectrum analysis, there are other methods of quantifying the dynamical behaviour of a system, such as the Fourier spectrum, Poincaré sections, or correlation functions, just to mention few [10,12,17,41]. The classical technique to understand the time series of each component of m i is to take the Fast Fourier Transform (FFT) which gives a complex discrete signal, S (ϖ), in the frequency space ϖ = (ϖ 1 , ..., ϖ n ), producing a set of pairs {ϖ k , S (ϖ k )}.…”

Section: Dynamical Indicatorsmentioning

confidence: 99%

Hyper-chaotic Magnetisation Dynamics of Two Interacting Dipoles

et al. 2015

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The present work is a numerical study of the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of a time-dependent external magnetic field using the Landau-Lifshitz equation. Particles are coupled through the dipole-dipole interaction. The applied magnetic field is made of a constant longitudinal amplitude component and a time dependent transversal amplitude component. Dynamical states obtained are represented by their Lyapunov exponents and bifurcation diagrams. The dependence on the largest and the second largest Lyapunov exponents, as a function of the magnitude and frequency of the applied magnetic field, and the relative distance between particles, is studied. The system presents multiple transitions between regular and chaotic behaviour depending on the control parameters. In particular, the system presents consistent hyper-chaotic states.

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Chaotic convection in a ferrofluid

Cited by 59 publications

References 67 publications

Nonlinear Rayleigh–Bénard Convection With Variable Heat Source

Nonlinear Rayleigh–Bénard Convection With Variable Heat Source

Intermittent flow regimes near the convection threshold in ferromagnetic nanofluids

Hyper-chaotic Magnetisation Dynamics of Two Interacting Dipoles

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