Study on Kelvin–Helmholtz Instability With Heat and Mass Transfer

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Mukesh Kumar Awasthi
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stability Criterion ◽  
Relative Velocity ◽  
Critical Value ◽  
Helmholtz Instability ◽  
Stabilizing Effect ◽  
Vapor Fraction ◽  
The Stability ◽  
Liquid And Vapor Phases

The effect of heat and mass transfer on the Kelvin–Helmholtz instability between liquid and vapor phases of a fluid has been studied using three different theories: a purely irrotational theory based on the dissipation method, a hybrid irrotational-rotational theory, and an inviscid potential flow theory. These new results are compared with previous results from viscous irrotational theory. The stability criterion is given in terms of the critical value of relative velocity. The system is shown to be unstable when the relative velocity is greater than the critical value of relative velocity; otherwise, it is stable. It is observed that heat and mass transfer has a destabilizing effect on the stability of the system while vapor fraction has a stabilizing effect.

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.

The effect of a time harmonic-magnetic field on the stability of cylindrical ferrofluids in the presence of heat and mass transfer

1995 ◽  
Vol 73 (9-10) ◽  
pp. 595-601 ◽  
Author(s):  
Galal M. Moatimid
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Uniform Field ◽  
Periodic Field ◽  
Cylindrical Interface ◽  
Time Harmonic ◽  
General Dispersion ◽  
The Stability ◽  
Transition Curves

The stability of two ferrofluids separated by a cylindrical interface and pervaded by a time harmonic-magnetic field is considered. The magnetic fluids are sandwiched between two rigid cylindrical edges. The cylindrical interface allows heat and mass transfer. A general dispersion equation is obtained. Some previous studies are compared using appropriate data. The case of a uniform field has been studied before, the attention is thus focussed to the case of the periodic field. The transition curves are obtained by means of Whittaker's technique. The analytical results are confirmed numerically. It is found that heat and mass transfer and the frequency of the magnetic field have a destabilizing influence.

Viscous effects on Kelvin–Helmholtz instability in a channel

2011 ◽  
Vol 680 ◽  
pp. 398-416 ◽  
Author(s):  
H. KIM ◽  
J. C. PADRINO ◽  
D. D. JOSEPH
Keyword(s):  
Slug Flow ◽  
Kinematic Viscosity ◽  
Relative Velocity ◽  
Viscosity Ratio ◽  
Critical Value ◽  
Helmholtz Instability ◽  
Viscous Effects ◽  
Velocity Difference ◽  
Neutral Curves ◽  
Gas Fractions

The effects of viscosity on Kelvin–Helmholtz instability in a channel are studied using three different theories; a purely irrotational theory based on the dissipation method, an exact rotational theory and a hybrid irrotational–rotational theory. These new results are compared with previous results from a viscous irrotational theory. An analysis of the neutral state is conducted and its predictions are compared with experimental results related to the transition from a stratified-smooth to a stratified-wavy or slug flow. For values of the gas fraction greater than about 0.20, there is an interval of velocity differences for which the flow is unstable for an interval of wavenumbers between two cutoff wavenumbers, k− and k+. For unstable flows with a velocity difference above that interval or with gas fractions less than 0.20, k− = 0. The maximum critical relative velocity that determines the onset of instability can be found when the kinematic viscosity of the gas and liquid are the same. This critical value is surprisingly achieved when both fluids are inviscid. The neutral curves from the analyses of potential flow of viscous fluids and the hybrid method, the only theories that account for the viscosity of both fluids in this work, indicate that the critical velocity does not change with the viscosity ratio when the kinematic viscosity of the liquid is greater than a critical value. For smaller liquid viscosities, the critical relative velocity decreases.

scholarly journals Analysis of Heat and Mass Transfer for Second-Order Slip Flow on a Thin Needle Using a Two-Phase Nanofluid Model

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1176
Author(s):  
Siti Nur Alwani Salleh ◽  
Norfifah Bachok ◽  
Fadzilah Md Ali ◽  
Norihan Md Arifin
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Slip Flow ◽  
Second Order ◽  
Two Phase ◽  
Specific Domain ◽  
Transfer Rates ◽  
Similarity Transformations ◽  
The Stability ◽  
Good Agreement

The present paper concentrates on the second-order slip flow over a moving thin needle in a nanofluid. The combined effects of thermophoresis and Brownian motion are considered to describe the heat and mass transfer performance of nanofluid. The resulting system of equations are obtained using similarity transformations and being executed in MATLAB software via bvp4c solver. The physical characteristics of embedded parameters on velocity, temperature, concentration, coefficient of skin friction, heat and mass transfer rates are demonstrated through a graphical approach and are discussed in detail. The obtained outcomes are validated with the existing works and are found to be in good agreement. It is shown that, for a specific domain of moving parameter, dual solutions are likely to exist. The stability analysis is performed to identify the stability of the solutions gained, and it is revealed that only one of them is numerically stable. The analysis indicated that the percentage of increment in the heat and mass transfer rates from no-slip to slip condition for both thin and thick surfaces of the needle ( a = 0.1 and a = 0.2 ) are 10.77 % and 12.56 % , respectively. Moreover, the symmetric behavior is noted for the graphs of reduced heat and mass transfer when the parameters N b and N t are the same.

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