Instability through porous media of three layers superposed conducting fluids

Zakaria, Kadry; Sirwah, Magdy A.; Alkharashi, Sameh A.

doi:10.1016/j.euromechflu.2008.08.002

Cited by 12 publications

(5 citation statements)

References 11 publications

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“…The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and nonlinear Ginzburg-Landau equation, for the higherorder problem, describing the behavior of the system in a nonlinear approach. In paper (Zakaria et al, 2009), the instability properties of streaming superposed conducting fluids through porous media under the influence of uniform magnetic field have been investigated, where the system is composed of a middle fluid sheet of finite thickness embedded between two semi-infinite fluids.…”

Section: Introductionmentioning

confidence: 99%

Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

AlHamdan¹,

Alkharashi²

2016

JMR

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The current study concerns, the effect of a horizontal magnetic field on the stability of three horizontal finite layers of immiscible fluids in porous media. The problem examines few representatives of porous media, in which the porous media are assumed to be uniform, homogeneous and isotropic. The dispersion relations are derived using suitable boundary and surface conditions in the form of two simultaneous Mathieu equations of damping terms having complex coefficients. The stability conditions of the perturbed system of linear evolution equations are investigated both analytically and numerically and stability diagrams are obtained. The stability diagrams are discussed in detail in terms of various parameters governing the flow on the stability behavior of the system such as the streaming velocity, permeability of the porous medium and the magnetic properties. In the special case of uniform velocity, the fluid motion has been displayed in terms of streamlines concept, in which the streamlines contours are plotted. In the uniform velocity motion, a fourth order polynomial equation with complex coefficients is obtained. According to the complexity of the mathematical treatments, when the periodicity of the velocity is taken into account, the method of multiple scales is applied to obtain stability solution for the considered system. It is found that a stability effect is found for increasing, the magnetic permeability ratio, the magnetic field, and the permeability parameter while the opposite influence is observed for increasing the upper layer velocity.

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Section: Introductionmentioning

confidence: 99%

Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

AlHamdan¹,

Alkharashi²

2016

JMR

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“…Here, the boundary constraints are information about the obtained solutions of the governing equations at certain places, such as the lower and the upper substrates, in addition the interface between the fluids (Shankar and Sharma (2004), Wu and Chou (2005), Ozen et al (2006), Zakaria et al(2009), Hayat et al (2016), Alkharashi and Gamiel (2017), Tomar et al (2007); Zakaria and Alkharashi (2017)).…”

Section: Boundary Conditionsmentioning

confidence: 99%

Performance Evaluation of Insoluble Surfactants on the Behavior of Two Electric Layers

Alkharashi¹,

Assaf²,

Alhamad³

et al. 2019

JAFM

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The purpose of this study is to establish the effects of insoluble surfactants on the stability of two layers flow down an inclined wall in the limit of Stokes and long-wavelength approximations. The dynamics of the liquid-liquid interface is described for arbitrary amplitudes by evolution equations derived from the basic hydrodynamic equations, in which the fluids are subjected to a uniform electric field. The principle aim of this work is to investigate the interfacial stability as well as the growth rate in the presence of insoluble surfactants. The parameters governing the flow system, such as Marangoni, Weber, capillary numbers and the inclined substrate strongly affect the waveforms and their amplitudes and hence the stability of the fluid. Approximate solutions of this system of linear evolution equations are performed. epending on the selected parameters, the phenomenon of the dual role is found with respect to the electric Weber number as well as the viscosity ratio. The interfacial waves will be more stable due to the growth of the Marangoni number while, while the opposite effect is found for the increase in capillary number. In the longwave perturbations, the stability process is found to confirm the stabilizing effect of the Marangoni number and the destabilizing influence of both capillary and Reynolds numbers, whereas the dual role is observed for the dielectric ratio.

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“…For recent surveys regarding the developments of linear and nonlinear electromagnetic flows in porous media, see refs. [26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Stability Characteristics of Finite Electrified Conducting Fluids Streaming through a Porous Medium

Metwaly

Gharsseldien

2020

Journal of Mathematics

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A novel procedure is utilized to investigate the surface waves between two finite conducting fluids streaming through a porous medium in the presence of a horizontal electric field. Normal mode analysis is applied to study two- and three-dimension disturbances cases. The quadratic dispersion equation of complex coefficients representing the system is derived and discussed. It is noted that based on appropriate data selections, the stability criteria do not depend on the medium permeability. It is found that electrical conductivities, viscosities, medium porosity, and surface tension enhance the stability of the system while the dimension and the fluid velocities decrease the stability of the system. Finally, the fluid depths have a dual role (stabilizing as well as destabilizing effects) on the system.

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Instability through porous media of three layers superposed conducting fluids

Cited by 12 publications

References 11 publications

Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

Performance Evaluation of Insoluble Surfactants on the Behavior of Two Electric Layers

Three-Dimensional Stability Characteristics of Finite Electrified Conducting Fluids Streaming through a Porous Medium

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