Stationary thermal convection in a viscoelastic ferrofluid

“…Since the linear instability threshold of the conducting state in the stationary case is independent of the viscoelastic properties [9,10], we will only recall here the main results of the linear analysis [1,2]. The Rayleigh number obtained as the eigenvalue of the linear part of system (7) is given by [2]:…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

“…(9) is the GL equation and describes the variation on the slow time and spatial scales of the convective pattern. The coefficients τ 0 and ξ 2 0 are the growth rate of the amplitude and the curvature of the marginal stability curve, respectively, and they can be calculated straightforwardly from the linear theory analysis [10]. In Eq.…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

“…Another limiting case is given when we set Ta = 0 in Eq. 12, where the viscoelastic limit described in [10] is retrieved. The main results are displayed in Fig.…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

“…Convection in viscoelastic fluids has been studied by Parmentier et al [8]. Recently, studies on stationary and oscillatory convection in viscoelastic magnetic fluid have been done [9][10][11]. Other important features of magnetic fluids, in both experimental and theoretical situations, are discussed at length in Refs.…”

mentioning

confidence: 99%

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Meniscus of a magnetic fluid in the field of a current-carrying wire: two-dimensional numerical simulations

Eißmann¹,

Lange²,

Odenbach³

2011

MHD

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We report both theoretical and numerical results on convection for a magnetic fluid under rotation in a viscoelastic carrier liquid. The viscoelastic properties are given by the Oldroyd model. We focus on the stationary convection for idealized boundary conditions. Close to the first bifurcation, the coefficients of the corresponding amplitude equation are determined. The effect of the Kelvin force and of the rotation on instability thresholds for a diluted suspension are also emphasized.

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Nonlinear analysis of the effect of viscoelasticity on ferroconvection

2021

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This paper concerns a nonlinear analysis of the effects of viscoelasticity on convection in ferroliquids. We consider the Oldroyd model for the constitutive equation of the liquid. The linear stability analysis yields the critical value of the Rayleigh number for the onset of oscillatory convection in Maxwell and Jeffrey ferroliquids. The use of a minimal mode double Fourier series in the nonlinear perturbation equations yields a Khayat–Lorenz model for the ferromagnetic liquid, and that is scaled further to get the classical Lorenz model as a limiting case. The scaled Khayat–Lorenz model thus obtained is solved numerically and the solution is used to compute the time‐dependent Nusselt number, which quantifies the heat transport. The results are analyzed for the dependence of the time‐averaged Nusselt number on different parameters.

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Stationary thermal convection in a viscoelastic ferrofluid

Cited by 16 publications

References 67 publications

Thermal convection thresholds in a Oldroyd magnetic fluid

Thermal convection thresholds in a Oldroyd magnetic fluid

Meniscus of a magnetic fluid in the field of a current-carrying wire: two-dimensional numerical simulations

Nonlinear analysis of the effect of viscoelasticity on ferroconvection

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