Viscous potential flow analysis of magnetohydrodynamic Rayleigh–Taylor instability with heat and mass transfer

Awasthi, Mukesh Kumar

doi:10.1007/s40435-013-0050-9

Cited by 15 publications

(3 citation statements)

References 24 publications

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“…The general theory of the motions of viscous and viscoelastic fluids was explained [10]. The effect of the magnetic field on the Rayleigh-Taylor instability (RTI) of two viscous fluids was investigated [11]. Characteristically, the viscosity originated only in a normal stress tensor.…”

Section: Greek Symbols English Symbolsmentioning

confidence: 99%

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Effects of Uniform/Periodic Magnetic Fields on the Nonlinear Stability of Double Interfaces Between Three Magnetic Fluids Saturated in Porous Media

Moatimid

Sayed

Zekry

2022

Preprint

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The current manuscript tackles the interaction between three viscous magnetic fluids placed on three layers and saturated in porous media. Two of them fill half the spaces above and below a thin layer that lies in the middle region. All layers are laterally extended to infinity in both horizontal directions. All fluids move in the same horizontal direction with different uniform velocities and are driven by pressure gradients. The system is stressed by tangential stationary/periodic magnetic fields. The viscous potential theory (VPT) is used to simplify the mathematical procedure. The motion of the fluids is described by the Brinkman-Darcy equations, and Maxwell equations are used for the magnetic field. The nonlinear technique is typically relying on solving linear equations of motion and presenting the nonlinear boundary conditions. The novelty of the problem concerns the nonlinear stability of the double interface under the impact of periodic magnetic fields. Therefore, the approach has resulted in two nonlinear characteristic differential equations governing the surface displacements. Accordingly, the development amplitudes of surface waves are designated by two nonlinear Schrödinger equations. Stability is theoretically analyzed; the nonlinear stability criterion is derived, and the corresponding nonlinear stability conditions are explored in detail. Approximate bounded solutions of the perturbed interfaces are estimated. Additionally, the thickness of the intermediate layer as a function of time is plotted. The impact of different parameters on the stability profile is investigated. For the middle layer, it is found that magnetic permeability, as well as viscosity, have a stabilizing effect. By contrast, the basic streaming, as well as permeability, have a destabilizing influence. The analysis of the periodic case shows that the lower interface is much more stable than the upper one. Engineering applications like petroleum products manufacturing and the electromagnetic field effect can be used to control the growth of the perturbation and then the recovery of crude oil from the pores of reservoir rocks.

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Section: Greek Symbols English Symbolsmentioning

confidence: 99%

“…In employing the VPT, the Navier Stokes equation behaves analogously with Euler's equation in the case of an incompressible fluid [7][8][9][10][11][12], where…”

Section: Fig1a: Sketch Of the Physical Modelmentioning

confidence: 99%

Effects of Uniform/Periodic Magnetic Fields on the Nonlinear Stability of Double Interfaces Between Three Magnetic Fluids Saturated in Porous Media

Moatimid

Sayed

Zekry

2022

Preprint

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“…To our knowledge, the case concerning finite-thickness media has only been studied when the involved media are ideal fluids or plasmas (Harris 1962, Lau et al 2011. In some research, a viscous fluid has also been considered, but it was assumed to be limited by rigid walls (Awasthi 2014). On the other hand, for the MRT instability involving an elastic medium, it seems to have been studied only for the simplest configuration of two semi-infinite media (Sun & Piriz 2014).…”

Section: Introductionmentioning

confidence: 99%

Magneto-Rayleigh–Taylor instability in an elastic finite-width medium overlying an ideal fluid

Piriz

Tahir

2019

J. Fluid Mech.

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We present the linear theory of two-dimensional incompressible magneto-Rayleigh-Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and below the layer. As expected, magnetic field effects and elasticity effects together enhance the stability of thick layers. However, the situation becomes more complicated for relatively thin slabs, and a number of new and unexpected phenomena are observed. In particular, when the magnetic field beneath the layer dominates, its effects compete with effects due to elasticity, and counteract the elasticity stabilising effects. As a consequence, the layer can become more unstable than when only one of these stabilising mechanism is acting. This somewhat unexpected result is explained by the different physical mechanisms for which elasticity and magnetic fields stabilise the system. Implications for experiments on magnetically driven accelerated plates and implosions are discussed. Moreover, the relevance for triggering of crust-quakes in strongly magnetised neutron stars is also pointed out.

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Structural stability of a porous channel of electrical flow affected by periodic velocities

Alkharashi,

Alotaibi

2023

J Eng Math

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Viscous potential flow analysis of magnetohydrodynamic Rayleigh–Taylor instability with heat and mass transfer

Cited by 15 publications

References 24 publications

Effects of Uniform/Periodic Magnetic Fields on the Nonlinear Stability of Double Interfaces Between Three Magnetic Fluids Saturated in Porous Media

Effects of Uniform/Periodic Magnetic Fields on the Nonlinear Stability of Double Interfaces Between Three Magnetic Fluids Saturated in Porous Media

Magneto-Rayleigh–Taylor instability in an elastic finite-width medium overlying an ideal fluid

Structural stability of a porous channel of electrical flow affected by periodic velocities

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