Kelvin-Helmholtz instability for flow in porous media under the influence of oblique magnetic fields: A viscous potential flow analysis

Moatimid, Galal M.; Allah, M. H. Obied; Hassan, Mohamed A.

doi:10.1063/1.4825146

Cited by 18 publications

(5 citation statements)

References 29 publications

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“…To minimize the mathematical manipulations, he considered the symmetric and antisymmetric disturbances. Furthermore, Moatimid et al investigated the influences of suction and injection at the boundaries of two‐phase fluids. Moreover, they studied the influence of the normal streaming velocity on the interface instability.…”

Section: Introductionmentioning

confidence: 99%

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

Moatimid

Eldabe

Sayed

2019

Heat Trans. Asian Res.

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The current article aims at investigating the effect of a periodic tangential magnetic field on the stability of a horizontal flat sheet. The media were considered porous, the three viscous-fluid layers were initially streaming with uniform velocities, and the magnetic field admitted the presence of free-surface currents. Furthermore, the transfer of mass and heat phenomenon was taken into account. The analysis, in this paper, was followed by the viscous potential theory. Moreover, the stability of the boundary-value problem resulted in coupled secondorder linear differential equations with damping and complex coefficients. In regard to the uniform and periodic magnetic field, the standard normal mode approach was applied to deduce a general dispersion relation and judge the stability criteria. In addition, several unfamiliar cases were reported, according to appropriate data choices. The stability conditions were theoretically analyzed, and the influences of the various parameters in the stability profile were identified through a set of diagrams. In accordance wth the oscillating field, the coupled dispersion equations were combined to give the established Mathieu equation. Therefore, the governed transition curves were, theoretically, obtained. Finally, the results were numerically confirmed. K E Y W O R D S magnetic field, mass and heat transfer, porous media, stability analysis, viscous potential flow

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Section: Introductionmentioning

confidence: 99%

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

Moatimid

Eldabe

Sayed

2019

Heat Trans. Asian Res.

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“…9,29 At the boundary between the two the Oldroydian viscoelastic nanofluids, the stresses must be balanced. Two types of boundary conditions suffice the properly constrain the field equations: conditions at an infinite (perpendicular) distance from the system and conditions at the dividing interface.…”

Section: Problem Definition and Mathematical Formulationmentioning

confidence: 99%

“…8 He used the multiple time scales method in order to obtain two parametrically a) E-mail: gal_moa@hotmail.com b) E-mail: dr_elham_alali@hotmail.com c) E-mail: hoda_ali_1@hotmail.com nonlinear Schrôdinger equations to describe the elevation of weakly nonlinear capillary waves. As a recent work, in this topic, Moatimid et al 9 discussed the KHI for flow in porous media under the influence of an oblique magnetic field.…”

Section: Introductionmentioning

confidence: 98%

“…Funada and Joseph 12 have done the viscous potential flow analysis of the KHI in a channel and found that the stability criterion for viscous potential flow is given by the critical value of the relative velocity. Moatimid et al 9 applied the viscous potential theory to analyze the KHI with heat and mass transfer. They observed that heat and mass transfer has a destabilizing effect.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium

2014

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Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted for different sets of physical parameters. A new stability as well as instability region, in the parameter space, appears due to the nonlinear effects.

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“…The combined study of magnetic field and porous medium on Kelvin-Helmholtz instability in plane geometry in the presence of heat and mass transfer was considered by Awasthi et al 15 Moatimid et al 16 considered the effect of oblique magnetic field on the Kelvin-Helmholtz instability in plane geometry in the presence of heat and mass transfer. Moatimid and Hassan 17 studied the effect of tangential electric field on the Kelvin-Helmholtz instability in cylindrical flow with permeable boundaries including heat and mass transfer in porous media and found that tangential electric field has stabilizing effect.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional magnetohydrodynamic Kelvin–Helmholtz instability of cylindrical flow with permeable boundaries

Awasthi

2014

Physics of Plasmas

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We study the linear magnetohydrodynamic Kelvin–Helmholtz instability of the interface between two viscous, incompressible, and electrically conducting fluids. The phases are enclosed between two coaxial cylindrical porous layers with the interface through which mass and heat transfer takes place. The fluids are subjected to a constant magnetic field parallel to the streaming direction, and the suction/injection velocities for the fluids at the permeable boundaries are also taken into account. Here, we use an irrotational theory in which the motion and pressure are irrotational, and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. We consider both asymmetric and axisymmetric disturbances in our analysis. A quadratic dispersion relation is deduced and stability criterion is given in terms of a critical value of relative velocity, as well as, magnetic field. It has been observed that in the case of permeable boundaries, heat and mass transfer phenomena play a dual in the stability analysis. The flow through porous medium is more stable than the pure flow.

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Kelvin-Helmholtz instability for flow in porous media under the influence of oblique magnetic fields: A viscous potential flow analysis

Cited by 18 publications

References 29 publications

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium

Three-dimensional magnetohydrodynamic Kelvin–Helmholtz instability of cylindrical flow with permeable boundaries

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