Nonlinear electrohydrodynamic Rayleigh–Taylor instability with mass and heat transfer: effect of a normal field

1994 ◽  
Vol 72 (9-10) ◽  
pp. 537-549 ◽  
Author(s):  
Abou El Magd A. Mohamed ◽  
Abdel Raouf F. Elhefnawy ◽  
Y. D. Mahmoud
Keyword(s):  
Heat Transfer ◽  
Multiple Scales ◽  
Landau Equation ◽  
Finite Thickness ◽  
Surface Charges ◽  
Stability Diagrams ◽  
Dielectric Fluids ◽  
Mass And Heat Transfer ◽  
The Stability ◽  
Cubic Nonlinear Schrödinger Equation

The nonlinear electrohydrodynamic stability of two superposed dielectric fluids with interfacial transfer of mass and heat is presented for layers of finite thickness. The fluids are subjected to a normal electric field in the absence of surface charges. Using a technique based on the method of multiple scales it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. When the mass and heat transfer are neglected, the cubic nonlinear Schrödinger equation is obtained. Further, it is shown that, near the marginal state, a nonlinear diffusion equation is obtained in the presence of mass and heat transfer. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained.

scholarly journals Stability analysis of magnetic fluids in the presence of an oblique field and mass and heat transfer

2020 ◽  
Vol 330 ◽  
pp. 01035
Author(s):  
Rabah Djeghiour ◽  
Bachir Meziani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Magnetic Fluids ◽  
Physical Parameters ◽  
Stability Diagrams ◽  
Stability And Instability ◽  
Mass And Heat Transfer ◽  
Model Equations ◽  
The Stability ◽  
Oblique Magnetic Field

In this paper, we investigate an analysis of the stability of a basic flow of streaming magnetic fluids in the presence of an oblique magnetic field is made. We have use the linear analysis of modified Kelvin-Helmholtz instability by the addition of the influence of mass transfer and heat across the interface. Problems equations model is presented where nonlinear terms are neglected in model equations as well as the boundary conditions. In the case of a oblique magnetic field, the dispersion relation is obtained and discussed both analytically and numerically and the stability diagrams are also obtained. It is found that the effect of the field depends strongly on the choice of some physical parameters of the system. Regions of stability and instability are identified. It is found that the mass and heat transfer parameter has a destabilizing influence regardless of the mechanism of the field.

Nonlinear Electrohydrodynamic Stability of Two Superposed Walters B′ Viscoelastic Fluids in Relative Motion Through Porous Medium

2013 ◽  
Vol 29 (4) ◽  
pp. 569-582 ◽  
Author(s):  
M. F. El-Sayed ◽  
N. T. Eldabe ◽  
M. H. Haroun ◽  
D. M. Mostafa
Keyword(s):  
Surface Tension ◽  
Porous Medium ◽  
Electric Fields ◽  
Multiple Scales ◽  
Landau Equation ◽  
Three Dimensions ◽  
Surface Charges ◽  
Fluid Velocities ◽  
Medium Permeability ◽  
The Stability

ABSTRACTA nonlinear stability of two superposed semi-infinite Walters B′ viscoelastic dielectric fluids streaming through porous media in the presence of vertical electric fields in absence of surface charges at their interface is investigated in three dimensions. The method of multiple scales is used to obtain a Ginzburg-Landau equation with complex coefficients describing the behavior of the system. The stability of the system is discussed both analytically and numerically in linear and nonlinear cases, and the corresponding stability conditions are obtained. It is found, in the linear case, that the surface tension and medium permeability have stabilizing effects, and the fluid velocities, electric fields and kinematic viscoelastici-ties have destabilizing effects, while the porosity of porous medium and kinematic viscosities have dual role on the stability. In the nonlinear case, it is found that the fluid velocities, kinematic viscosities, kinematic viscoelasticities, surface tension and porosity of porous medium have stabilizing effects; while the electric fields and medium permeability have destabilizing effects.

Nonlinear Analysis of Rayleigh–Taylor Instability of Cylindrical Flow With Heat and Mass Transfer

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Mukesh Kumar Awasthi
Keyword(s):  
Mass Transfer ◽  
Nonlinear Analysis ◽  
Heat And Mass Transfer ◽  
Landau Equation ◽  
Taylor Instability ◽  
Ginzburg Landau ◽  
Stability Diagrams ◽  
Rayleigh Taylor Instability ◽  
Mass And Heat Transfer ◽  
The Stability

We study the nonlinear Rayleigh–Taylor instability of the interface between two viscous fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The fluids are considered to be viscous and incompressible with different kinematic viscosities. The method of multiple expansions has been used for the investigation. In the nonlinear theory, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. The various stability criteria are discussed both analytically and numerically and stability diagrams are obtained. It has been observed that the heat and mass transfer has stabilizing effect on the stability of the system in the nonlinear analysis.

Weakly Nonlinear Stability Analysis of a Thin Liquid Film With Condensation Effects During Spin Coating

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
C. K. Chen ◽  
M. C. Lin
Keyword(s):  
Liquid Film ◽  
Spin Coating ◽  
Multiple Scales ◽  
Landau Equation ◽  
Thin Liquid Film ◽  
Kinematic Model ◽  
Circular Disk ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
The Stability

This paper investigates the stability of a thin liquid film with condensation effects during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. The weakly nonlinear dynamics of a film flow are studied by the multiple scales method. The Ginzburg–Landau equation is determined to discuss the necessary conditions of the various states of the critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that decreasing the rotation number and the radius of the rotating circular disk generally stabilizes the flow.

scholarly journals Synchronous and Asynchronous Boundary Temperature Modulations on Triple-Diffusive Convection in Couple Stress Liquid Using Ginzburg-Landau Model

2018 ◽  
Vol 7 (4.10) ◽  
pp. 645
Author(s):  
T. Sameena ◽  
S. Pranesh
Keyword(s):  
Heat Transfer ◽  
Couple Stress ◽  
Landau Equation ◽  
Temperature Modulation ◽  
Ginzburg Landau ◽  
Boundary Temperature ◽  
Stress Parameter ◽  
Diffusive Convection ◽  
Mass And Heat Transfer ◽  
Rayleigh Numbers

A nonlinear study of synchronous and asynchronous boundary temperature modulations on the onset of triple-diffusive convection in couple stress liquid is examined. Two cases of temperature modulations are studied: (a) Synchronous temperature modulation ( ) and (b) Asynchronous temperature modulation ( ). It is done to examine the influence of mass and heat transfer by deriving Ginzburg-Landau equation. The resultant Ginzburg-Landau equation is Bernoulli equation and it is solved numerically by means of Mathematica. The influence of solute Rayleigh numbers and couple stress parameter is studied. It is observed that couple stress parameter increases the mass and heat transfer whereas solute Rayleigh numbers decreases the mass and heat transfer. 

Nonlinear instability of two dielectric viscoelastic fluids

2004 ◽  
Vol 82 (12) ◽  
pp. 1109-1133 ◽  
Author(s):  
Galal M Moatimid
Keyword(s):  
Boundary Conditions ◽  
Electric Fields ◽  
Multiple Scales ◽  
Landau Equation ◽  
Equations Of Motion ◽  
Nonlinear Boundary Conditions ◽  
Interfacial Wave ◽  
Surface Evolution ◽  
Stability Diagrams ◽  
Viscoelastic Effects

A weakly nonlinear interfacial wave propagating between two dielectric fluids and influenced by an oblique electric field is studied. The analysis considers the surface tension and viscoelastic effects. Due to the presence of streaming and viscoelasticity, a mathematical simplification is considered. The viscoelastic contribution is demonstrated through the boundary conditions. Therefore, the equations of motion are solved in the absence of the viscoelastic effects. The solutions of the linearized equations of motion under the nonlinear boundary conditions lead to a nonlinear characteristic equation governing the surface evolution. This equation is accomplished by utilizing cubic nonlinearity. Taylor theory is adopted to expand the characteristic nonlinear equation in the light of the multiple-scales technique. The perturbation analysis produces two levels of the solvability conditions, which are used to construct the Ginzburg–Landau equation. Stability criteria are discussed both theoretically and computationally in which stability diagrams are obtained. Under appropriate data choices, we can recover some reported works as limiting cases. The effects of the orientation of the electric fields on the stability configuration in linear as well as nonlinear approaches are discussed. PACS Nos.: 47.65.+a, 47.20.–k, 47.50.+d

scholarly journals Nonlinear Stability of a Cylindrical Interface with Mass and Heat Transfer

2000 ◽  
Vol 55 (9-10) ◽  
pp. 837-842 ◽  
Author(s):  
Doo-Sung Lee
Keyword(s):  
Heat Transfer ◽  
Nonlinear Stability ◽  
Time Scale ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Cylindrical Interface ◽  
Liquid Phases ◽  
Region Of Stability ◽  
Mass And Heat Transfer ◽  
The Stability

Abstract The nonlinear Rayleigh-Taylor stability of a cylindrical interface between vapor and the liquid phases of a fluid is studied when the phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The method of multiple time scale expansion is used for the investigation. A simple nondimensional parameter is found to characterize the stability of the system. Using this parameter, the region of stability is displayed graphically.

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