Nonlinear Ehd Instability of a Cylindrical Interface Between Two Walters B' Fluids in Porous Media

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.

Section: Linear Stability Methodologysupporting

confidence: 57%

“…Henceforth, all fundamental amounts will be unrestricted with the angular position. A similar problem with the Walters-B fluids has been recently analyzed 41 . For more explanation, Fig.…”

Section: Methodology Of the Modelmentioning

confidence: 99%

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

Zekry

Ibrahim

2023

Sci Rep

“…It was demonstrated that the perpendicular magnetic field component always has a destabilizing effect. Two Walters' B-type type viscoelastic fluids were involved in a cylindrical shape contact, and the nonlinear EHD instability of this contact was investigated [19]. An interface movement nonlinear characteristic equation was produced via the nonlinear stability approach.…”

Section: Greek Symbols English Symbolsmentioning

confidence: 99%

“…In order to systematize the problem construction, the overall solutions of the functions j  and j  that are specified by Eqs. (14)(15)(16) and (17)(18)(19) must be calculated completely in light of convenient boundary conditions. Consequently, one needs to determine the profiles of functions that are time-dependent and given in these formulas.…”

Section: Boundary Conditionsmentioning

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.

“…One of them is referred to as the linear part which must have an exact solution, whereas the other is known as the nonlinear part. The nonlinear EHD stability of a cylinder-shaped interface between two Walters' B-type viscoelastic liquids was examined in a permeable media 30 . The extended frequency theory was merged with the HPM to produce a distribution of the surface displacement in an analytical periodical approximation.…”

Section: Introductionmentioning

confidence: 99%

Heat and mass flux through a Reiner–Rivlin nanofluid flow past a spinning stretching disc: Cattaneo–Christov model

Mohamed

Elagamy

2022

Sci Rep

Self Cite

The current work scrutinizes a non-Newtonian nanofluid free convective flow induced by a rotating stretchable disc. The examination surveys the Stefan blowing and Cattaneo–Christov mass and heat fluxes, as a precise illustrative model. The innovative aspects of the ongoing project include the analysis of the border sheet nanofluid flow near a revolving disc through thermophoresis, Reiner–Rivlin prototype features, and random nanoparticle motion. The Reiner–Rivlin non-Newtonian model is considered together with the effect of an unvarying axial magnetic strength. The constitutive formulae of a Reiner–Rivlin liquid have been reproduced in the cylindrical coordinates. Through implementing the applicable relationship transformations, the controlling partial differential equations are transferred to ordinary differential equations (ODE). This procedure yields a group of coupled nonlinear ordinary differential equations in relation to speed, heat, and nanoparticle concentration profiles that are impacted by several physical characteristics. These equations are analyzed by using the homotopy perturbation method (HPM). Due to the analytical solution given by HPM, the current work enables us to take the infinity of the layer as a parameter of the problem and discuss its variation in the obtained distributions. Consequently, a physical significant graphical visualization of the data is emphasized. The rates of mass and temperature transmission are examined to understand if any of the relevant parameters may improve these rates. Additionally, the Stefan blowing causes extra particles diffusion, which enhances heat transfer and raises the nanoparticles concentration and could be useful in some medical therapies. Furthermore, the stretching of the rotating disc is concluded, which improves the fluid heat transfer.