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.

Bubble Formation in Superposed Magnetic Fluids in the Presence of Heat and Mass Transfer

1995 ◽  
Vol 50 (9) ◽  
pp. 805-812 ◽  
Author(s):  
Gurpreet K. Gill ◽  
R.K. Chhabra ◽  
S.K. Trehan
Keyword(s):  
Mass Transfer ◽  
Nonlinear Analysis ◽  
Heat And Mass Transfer ◽  
Bubble Formation ◽  
Magnetic Fluids ◽  
Taylor Instability ◽  
Linear Case ◽  
Explosive Instability ◽  
Normal Field ◽  
Rayleigh Taylor Instability

Abstract In this paper we study the nonlinear Rayleigh-Taylor instability in the case of magnetic fluids in the presence of heat and mass transfer. We find that there is a normal field instability in the linear case. The behaviour of the bubbles in the nonlinear analysis is the same as if they were leaving the surface when the liquid is superheated. The criterion for "Explosive Instability" is also examined.

scholarly journals Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mukesh Kumar Awasthi ◽  
Vineet K. Srivastava
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Electric Field ◽  
Heat And Mass Transfer ◽  
Taylor Instability ◽  
Wave Number ◽  
Physical Parameters ◽  
Tangential Electric Field ◽  
Rayleigh Taylor Instability ◽  
The Stability

The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.

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 Electrohydrodynamic Interfacial Stability Conditions in the Presence of Heat and Mass Transfer and Oblique Electric Fields

1999 ◽  
Vol 54 (8-9) ◽  
pp. 470-476
Author(s):  
Mohamed Fahmy El-Sayed
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Electric Field ◽  
Heat And Mass Transfer ◽  
Electric Fields ◽  
Stability Criterion ◽  
Dielectric Constants ◽  
Interfacial Stability ◽  
Mass And Heat Transfer ◽  
The Stability

A novel mathematical formulation to deal with interfacial stability problems of the Kelvin-Helmholtz type with heat and mass transfer in the presence of oblique electric fields is presented. The perturbed system is composed of two homogeneous, inviscid, incompressible, dielectric, and streaming fluids sep-arated by a horizontal interface, and bounded by two rigid planes. The effect of a phase transition on the instability is considered, and the linear dispersion relations are obtained and discussed. It is found that the electric field has a major effect and can be chosen to stabilize or destabilize the flow. For Ray-leigh-Taylor instability problems of a liquid-vapor system it is found that the effect of mass and heat transfer enhances the stability of the system when the vapor is hotter than the liquid, although the clas-sical stability criterion is still valid. For Kelvin-Helmholtz instability problems, however, the classical stability criterion is found to be substantially modified due to the effects of the electric field, mass and heat transfer. A new stability condition relating the magnitude and orientation of the electric field and the dielectric constants is obtained. Oblique electric fields are found to have stabilizing effects which are reduced by the normal components of the electric fields. The effects of orientation of the electric fields and fluid depths on the stability configuration are also discussed.

Viscous Corrections for the Viscous Potential Flow Analysis of Rayleigh–Taylor Instability With Heat and Mass Transfer

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Mukesh Kumar Awasthi
Keyword(s):  
Mass Transfer ◽  
Normal Stress ◽  
Heat And Mass Transfer ◽  
Potential Flow ◽  
Flow Analysis ◽  
Viscous Potential Flow ◽  
Stabilizing Effect ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Viscous Pressure

Viscous corrections for the viscous potential flow analysis of Rayleigh–Taylor instability of two viscous fluids when there is heat and mass transfer across the interface have been considered. Both fluids are taken as incompressible and viscous with different kinematic viscosities. In viscous potential flow theory, viscosity enters through a normal stress balance and the effects of shearing stresses are completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface of the two fluids. It has been observed that heat and mass transfer has a stabilizing effect on the stability of the system. It has been shown that the irrotational viscous flow with viscous corrections gives rise to exactly the same dispersion relation as the dissipation method in which no pressure term is required and the viscous effect is accounted for by evaluating viscous dissipation using irrotational flow. It has been observed that the inclusion of irrotational shearing stresses has a stabilizing effect on the stability of the system.

Sign in / Sign up

Export Citation Format

Share Document