Effect of nonlinear temperature and concentration profiles on the stability of a layer of fluid with chemical reaction

2020 ◽  
Author(s):  
Amit Mahajan ◽  
Vinit Kumar Tripathi
Keyword(s):  
Chemical Reaction ◽  
Piecewise Linear ◽  
Finite Amplitude ◽  
Step Function ◽  
Thermosolutal Convection ◽  
Concentration Gradients ◽  
Non Linear ◽  
Nonlinear Temperature ◽  
Basic Temperature ◽  
The Stability

Investigation of the onset of thermosolutal convection with chemical reaction is carried out for different types of basic temperature and concentration gradients using linear theory and energy method. An unconditional non-linear stability with exponential decay of finite amplitude perturbations is achieved and the Galerkin technique is utilized to solve the resulting Eigen-value problem obtained from linear and non-linear analysis. The numerical scheme is validated with existing results and the results are obtained for linear, parabolic, inverted parabolic, piecewise linear, oscillatory and step-function profiles of temperature and concentration gradients. The linear and non-linear results show the existence of subcritical instability.

Thermal Convection Induced by an Infinitesimally Thin and Unstably Stratified Layer

2016 ◽  
Vol 41 (4) ◽  
Author(s):  
Layachi Hadji ◽  
Rishad Shahmurov ◽  
Noufe H. Aljahdaly
Keyword(s):  
Piecewise Linear ◽  
Bottom Layer ◽  
Step Function ◽  
Finite Domain ◽  
Hyperbolic Tangent ◽  
Flow Features ◽  
Basic Temperature ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Function Profile

AbstractWe examine the linear stability analysis of the equations governing Rayleigh–Bénard convection flows when the basic temperature profile is unstably stratified solely over a thin horizontal slice of the fluid region. We conduct both asymptotic and numerical analyses on three distinct shapes of the basic temperature: (i) a hyperbolic tangent profile, (ii) a piecewise linear profile and (iii) a step-function profile. In the first two cases, the thin unstably stratified layer is centrally located. The presence of stably stratified regions below and above the central layer diminishes the effect of the velocity and thermal boundary layers that form at the plates. This in turn allows for the analysis of the convection process without the constraints of the horizontal boundaries to be simulated in a finite domain. We obtain expressions for the threshold parameters for convection onset as well as flow features as function of the thickness of the unstably stratified layer. In the limit of a vanishingly small thickness, the hyperbolic tangent profile tends to a step-function profile with a heavy top layer overlying a lighter bottom layer. These two layers are separated by an interface where a jump in density occurs. This situation resembles the Rayleigh–Taylor instability of a horizontal interface except that neither is the interface free nor is the buoyancy diffusion absent. The exploration of this case uncovers new instability threshold values and flow patterns. Finally, we discuss some relevant applications.

The stability of a water drop oscillating with finite amplitude in an electric field

1971 ◽  
Vol 50 (3) ◽  
pp. 417-430 ◽  
Author(s):  
P. R. Brazier-Smith
Keyword(s):  
Electric Field ◽  
Water Drop ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Step Function ◽  
Uniform Electric Field ◽  
Spheroidal Shape ◽  
Spheroidal Drop ◽  
The Stability ◽  
Approximate Equations

By assuming that an uncharged drop situated in a uniform electric fieldEretains a spheroidal shape while oscillating about its equilibrium configuration, two approximate equations of motion are derived for the deformation ratio γ expressed as the ratioa/bof the major and minor axis of the drop. Solutions of these equations of motion indicate that the stability of a drop of undistorted radiusRand surface tensionTdepends uponE(R/T)½and the initial displacement of γ from its equilibrium value. The predictions of the two equations are compared to assess the accuracy of the spheroidal assumption as applied to such a dynamical situation. The analysis is used to determine the stability criterion of a drop subject to a step function field. Finally, the limit of validity of the spheroidal assumption is discussed in terms of Rayleigh's criterion for the stability of charged spherical drops. By applying Rayleigh's criterion to the poles of a spheroidal drop, the stage at which the drop departs from spheroidal form to form conical jets was approximately determined.

Evolution of Weakly Non-Linear Perturbations in Gas Suspension with Chemical Reaction

2011 ◽  
Vol 6 (3) ◽  
pp. 21-32
Author(s):  
Oleg V. Sharypov ◽  
Igor S. Anufriev
Keyword(s):  
Chemical Reaction ◽  
Homogeneous Medium ◽  
Finite Amplitude ◽  
Solid Particles ◽  
Two Phase ◽  
Non Linear Equation ◽  
Non Linear ◽  
Phase Medium ◽  
Nonequilibrium Chemical Reaction ◽  
Kinetics Of Reaction

Dynamics of weak finite-amplitude perturbations in two-phase homogeneous medium (gas + solid particles) with nonequilibrium chemical reaction in gas is studied theoretically. Weakly non-linear model of plane perturbation evolution is substantiated by the instrumentality of asymptotic approach. The model takes into account wave-kinetic interaction and dissipation effects, including inter-phase heat and momentum transfer. Stability conditions for uniform state of the system are analyzed. Non-linear equation describing evolution of plane perturbations is derived under weak dispersion and dissipation effects. Solutions of evolution equation are obtained numerically in form of steady-state oscillations. Its parameters are determined by effect of nonlinearity and by relation between dissipative property of two-phase medium and given modeling characteristics of kinetics of reaction

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

A novel approach for the stability problem in non-linear dynamical systems

2003 ◽  
Vol 155 (1) ◽  
pp. 21-30 ◽  
Author(s):  
Tarcı́sio M. Rocha Filho ◽  
Iram M. Gléria ◽  
Annibal Figueiredo
Keyword(s):  
Dynamical Systems ◽  
Stability Problem ◽  
Linear Dynamical Systems ◽  
Novel Approach ◽  
Non Linear ◽  
The Stability
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