Stability analysis using multiple scales homotopy approach of coupled cylindrical interfaces under the influence of periodic electrostatic fields

Eldabe

Sayed

2019

Heat Trans. Asian Res.

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

Section: Stability Analysis In the Presence Of A Uniform Magnetic Fieldmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Eldabe

Sayed

2019

Heat Trans. Asian Res.

“…The resonance cases are explained in the following analysis. There could be a lot of resonance cases, sub-harmonic, and super-harmonic resonances, and they can be distinguished; for example, see Moatimid et al [41]. The following is a list of the possible cases:…”

Section: Stability Analysis and Approximate Solution Of The Resonance...mentioning

confidence: 99%

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

Sayed

Zekry

2022

Preprint

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.

“…The nonlinear EHD of capillary surface waves was investigated 6 . The effect of a longitudinal periodic field on a streaming flow passing through three coaxial vertical cylinders was investigated 7 . Coupled Mathieu equations were conducted in their approach.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear EHD instability of two viscoelastic fluids under the influence of mass and heat transfer

Zekry

Ibrahim

2023

Sci Rep

This study attempts to provide an approach to studying the nonlinear stability of a vertical cylindrical interface between two Oldroyd-B prototypes. An unchanged axial electric field influences the system, and porous medium, and the effects of heat and mass transfer (MHT) are considered. Hsieh's modulation and the viscous potential flow (VPT) are used to abbreviate the mathematical analysis. The viscoelastic Oldroyd-B model significant role in geothermal, engineering and industrial enhancement motivated us to carry out this in-depth investigation. The methodology of the nonlinear technique depends mainly on solving the linear equations of motion and applying the appropriate nonlinear boundary conditions. Numerous non-dimensional physical numbers are exposed using a non-dimensional technique. The stability conditions are theoretically achieved and numerically verified. As a limiting case, the linear dispersion equation is accomplished, and a set of stability diagrams is reachable. Together with the nonlinear stability method, a Ginzburg–Landau equation is derived. Subsequently, both theoretical and numerical methods are used to achieve the nonlinear stability criteria. Furthermore, a precise perturbed approach for surface deflection is achieved theoretically and numerically using the Homotopy perturbation method and the extended frequency conception. Along with the linear approach, it is found that the structure becomes unstable by the Laplace, Reynolds, Weber, and elasticity quantities as well as the linear MHT parameter. Furthermore, the stability zones are enhanced in the nonlinear instability approach.