Magnetic Bénard convection

Schwab, Lauren E.; Hildebrandt, U.; Stierstadt, Klaus

doi:10.1016/0304-8853(83)90412-2

Cited by 119 publications

(58 citation statements)

References 2 publications

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“…A similar analysis but with the fluid confined between ferromagnetic plates has been carried out by Gotoh and Yamada [9] using linear stability analysis. Schwab et al [10] have experimentally investigated the problem of Finlayson in the case of a strong magnetic field and detected the onset of convection by plotting the Nusselt number versus the Rayleigh number. Stiles and Kagan [11] have extended the problem to allow for the dependence of effective shear viscosity on temperature and colloid concentration.…”

Section: Introductionmentioning

confidence: 99%

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

Nanjundappa¹,

Shivakumara

Prakash

2012

Journal of Magnetism and Magnetic Materials

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a b s t r a c tA model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength N s , magnetic number M 1 Darcy number Da and the non-linearity of magnetization parameter M 3 is to hasten, while increase in the ratio of viscosities L, Biot number Bi and magnetic susceptibility w is to delay the onset of ferroconvection.Further, increase in Bi, Da À 1 and N s and decrease in L, M 1 and M 3 is to diminish the dimension of convection cells.

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Section: Introductionmentioning

confidence: 99%

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

Nanjundappa¹,

Shivakumara

Prakash

2012

Journal of Magnetism and Magnetic Materials

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“…The Navier-Stokes equations of motion of a magnetized ferrofluid contain a magnetic body force term n 0 M • VJT, where /x 0 is the permeability of free space, M the magnetization of the ferrofluid and VH the gradient of the magnetic field H. Experiments [20] and theoretical investigations [2,8,24,26] have shown that an horizontal layer of ferrofluid in an externally uniform, vertical magnetostatic field and a vertical temperature gradient is unstable to periodic roll cells. Vortex motion can be induced in the ferrofluid layer when the magnetic Rayleigh number, which measures the ratio of the magnetic body force to the dissipative forces and is an analogue of the more familiar gravitational Rayleigh number, exceeds its critical value.…”

Section: Introductionmentioning

confidence: 99%

Strongly nonlinear vortices in magnetized ferrofluids

Russell

Blennerhassett

Stiles

1998

J. Aust. Math. Soc. Series B, Appl. Math

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Nonlinear convective roll cells that develop in thin layers of magnetized ferrofluids heated from above are examined in the limit as the wavenumber of the cells becomes large. Weakly nonlinear solutions of the governing equations are extended to solutions that are valid at larger distances above the curves of marginal stability. In this region, a vortex flow develops where the fundamental vortex terms and the correction to the mean are determined simultaneously rather than sequentially. The solution is further extended into the nonlinear region of parameter space where the flow has a core-boundary layer structure characterized by a simple solution in the core and a boundary layer containing all the harmonics of the vortex motion. Numerical solutions of the boundary layer equations are presented and it is shown that the heat transfer across the layer is significantly greater than in the conduction state.

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“…Convective instability of ferromagnetic fluids has been predicted by Finlayson (1970). Schwab et al (1983) investigated experimentally the Finlayson's problem in the case of a strong magnetic field and detected the onset of convection by plotting the Nusselt number versus the Rayleigh number. Then, the critical Rayleigh number corresponds to a discontinuity in the slope.…”

Section: Introductionmentioning

confidence: 99%

“…Then, the critical Rayleigh number corresponds to a discontinuity in the slope. Later, Stiles and Kagan (1990) examined the experimental problem reported by Schwab et al (1983) and generalized Finlayson's model assuming that under a strong magnetic field, the rotational viscosity augments the shear viscosity. Furthermore, Vaidyanathan et al, (1991) investigated the theoretically the convective instability of a ferromagnetic fluid in a porous medium of large permeability by use of the Brinkman model.…”

Section: Introductionmentioning

confidence: 99%

Effect of Soret and Temperature Dependent Viscosity on Thermohaline Convection in a Ferrofluid Saturating a Porous Medium

Sekar¹,

Raju²

2014

International Journal of Applied Mechanics and Engineering

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Soret driven ferrothermoconvective instability in multi-component fluids has a wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation of the effect of temperature dependent viscosity on a Soret driven ferrothermohaline convection heated from below and salted from above subjected to a transverse uniform magnetic field in the presence of a porous medium. The Brinkman model is used in the study. It is found that the stationary mode of instability is preferred. For a horizontal fluid layer contained between two free boundaries an exact solution is examined using the normal mode technique for a linear stability analysis. The effect of salinity has been included in magnetization and density of the fluid. The critical thermal magnetic Rayleigh number for the onset of instability is obtained numerically for sufficiently large values of the buoyancy magnetization parameter M 1 using the method of numerical Galerkin technique. It is found that magnetization and permeability of the porous medium destabilize the system. The effect of temperature dependent viscosity stabilizes the system on the onset of convection.

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Magnetic Bénard convection

Cited by 119 publications

References 2 publications

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

Strongly nonlinear vortices in magnetized ferrofluids

Effect of Soret and Temperature Dependent Viscosity on Thermohaline Convection in a Ferrofluid Saturating a Porous Medium

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