Amplitude equation for stationary convection in a rotating viscoelastic magnetic fluid

Laroze, David; Pérez, Laura M.; Bragard, J.; Cordaro, E. G.; Martínez-Mardones, J.

doi:10.22364/mhd.47.2.7

Cited by 9 publications

(4 citation statements)

References 5 publications

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“…The dependence of

\overset{N u (τ)}{true}

on different parameters is represented graphically. The range of values for the parameters can be found in Laroze et al 26 …”

Section: Resultsmentioning

confidence: 99%

“…Pérez et al 25 studied the effect of viscoelasticity on convection in Oldroyd magnetic liquid and found that viscoelasticity had no influence on stationary convection. Laroze et al 26 investigated the combined effects of viscoelasticity and rotation on the Ginzburg–Landau equation for stationary convection in a ferroliquid for ideal velocity boundary conditions. Laroze et al 27 studied the effects of viscoelasticity on surface tension‐driven instability in a thin layer of ferroliquid.…”

Section: Introductionmentioning

confidence: 99%

“…The dependence of Nu τ ( ) on different parameters is represented graphically. The range of values for the parameters can be found in Laroze et al 26 We first discuss the results of linear stability analysis. Oscillatory mode of convection is possible if ω 2 given by Equation ( 30) is positive.…”

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confidence: 99%

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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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“…The dependence of

\overset{N u (τ)}{true}

on different parameters is represented graphically. The range of values for the parameters can be found in Laroze et al 26 …”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear analysis of the effect of viscoelasticity on ferroconvection

2021

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“…For their study, the explicit expressions of stationary convection thresholds have been demonstrated according to the parameters of the system. Interesting studies on convection in ferrofluids and for various situations have been theoretically conducted in [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Stationary convection in a binary mixture of ferrofluids in a porous medium

Hounsou¹,

Monwanou²,

Miwadinou³

et al. 2020

Fluid Dyn. Res.

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The Brinkman model is used to study the criterion of appearance of stationary convection in a porous horizontal layer saturated by a binary mixture of ferrofluids and heated from below. The analytical expression of the Rayleigh number is determined by dimensionless numbers for the combined effects of buoyancy and magnetic force on the one hand and magnetic force alone on the other. The effect of Darcy's number, ratio of viscosities, each of the magnetic parameters and the binary parameter is illustrated on the appearance and size of the convection cells. The increasing of the number of Darcy D a , each of the magnetic parameters M 1 , M 3 , ψ m and the separation ratio ψ accelerates the appearance of stationary convection. On the other hand, when the ratio of the viscosity ∧ or the magnetic parameter M 2 is increased, the beginning of the convection is delayed and the system is stable. We have also noticed that the size of the convection structures is contracted with each of the parameters M 1 , M 2 , ψ, ψ m and for low values of the parameter M 3 . But by increasing the number of Darcy, the ratio of viscosities or for very high values of M 3 the size of the convection cells is enlarged. Finally, it should be noted that convection sets in with great delay when the magnetic mechanisms alone are highlighted.

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