Effects of a Magnetic Modulation on the Stability of a Magnetic Liquid Layer Heated From Above

2001 ◽  
Vol 123 (3) ◽  
pp. 428-433 ◽  
Author(s):  
Saı¨d Aniss ◽  
Mohamed Belhaq ◽  
Mohamed Souhar
Keyword(s):  
Floquet Theory ◽  
Fluid Layer ◽  
Mathieu Equation ◽  
Magnetic Liquid ◽  
Damping Term ◽  
Onset Of Convection ◽  
First Order ◽  
Gravitational Forces ◽  
Sinusoidal Magnetic Field ◽  
The Stability

The effect of a time-sinusoidal magnetic field on the onset of convection in a horizontal magnetic fluid layer heated from above and bounded by isothermal non magnetic boundaries is investigated. The analysis is restricted to static and linear laws of magnetization. A first order Galerkin method is performed to reduce the governing linear system to the Mathieu equation with damping term. Therefore, the Floquet theory is used to determine the convective threshold for the free-free and rigid-rigid cases. With an appropriate choice of the ratio of the magnetic and gravitational forces, we show the possibility to produce a competition between the harmonic and subharmonic modes at the onset of convection.

scholarly journals Effects of Suction–Injection–Combination (SIC) on the onset of Rayleigh–Bénard Electroconvection in a Micropolar Fluid

2015 ◽  
Vol 14 (3) ◽  
pp. 23-42 ◽  
Author(s):  
S Pranesh ◽  
Tarannum Sameena ◽  
Baby Riya
Keyword(s):  
Stability Analysis ◽  
Micropolar Fluid ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Wave Number ◽  
Critical Wave Number ◽  
Onset Of Convection ◽  
Temperature Boundary ◽  
The Stability ◽  
Rayleigh Benard

The effect of Suction – injection combination on the onset of Rayleigh – Bénard electroconvection micropolar fluid is investigated by making a linear stability analysis. The Rayleigh-Ritz technique is used to obtain the eigenvalues for different velocity and temperature boundary combinations. The influence of various parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles.

scholarly journals Onset of Buoyancy and Surface-Tension Driven Instabilities in Presence of Random Vibrations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1235-1240
Author(s):  
B. S. Dandapat
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Fluid Layer ◽  
Heat Conducting ◽  
Rigid Plate ◽  
Stability Zone ◽  
Random Vibrations ◽  
White Noise Process ◽  
Onset Of Convection ◽  
The Stability

AbstractOnset of thermal convection in an incompressible fluid layer bounded between a perfectly heat conducting lower rigid plate and an upper free surface is analysed when the layer is subject to random vibrations. It is shown that when the vibrations are characterized by a white noise process, they hasten the onset of convection. Further it is shown that the stability zone is demarcated by an inverted parabola in the (R, M) plane.

scholarly journals On Stability of Periodic Solutions of Lienard Type Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Zijian Yin ◽  
Hongbin Chen
Keyword(s):  
Asymptotic Behavior ◽  
Periodic Solutions ◽  
Exponential Decay ◽  
Floquet Theory ◽  
Linear Growth ◽  
Liénard Equation ◽  
Damping Term ◽  
Restoring Force ◽  
Stable Periodic ◽  
The Stability

We use the Floquet theory to analyze the stability of periodic solutions of Lienard type equations under the asymptotic linear growth of restoring force in this paper. We find that the existence and the stability of periodic solutions are determined primarily by asymptotic behavior of damping term. For special type of Lienard equation, the uniqueness and stability of periodic solutions are obtained. Furthermore, the sharp rate of exponential decay of the stable periodic solutions is determined under suitable conditions imposed on restoring force.

Instability of an oscillatory fluid layer with insoluble surfactants

2008 ◽  
Vol 595 ◽  
pp. 461-490 ◽  
Author(s):  
PENG GAO ◽  
XI-YUN LU
Keyword(s):  
Floquet Theory ◽  
Critical Reynolds Number ◽  
Fluid Layer ◽  
Travelling Waves ◽  
Chebyshev Collocation Method ◽  
Insoluble Surfactant ◽  
Wide Range ◽  
The Stability ◽  
Bounded Below ◽  
First Time

The linear stability of an infinite fluid layer with a deformable free surface covered by an insoluble surfactant and bounded below by a horizontal rigid plate oscillating in its own plane is studied based on the Floquet theory. The differential system governing the stability problem for perturbations of arbitrary wavenumbers is solved numerically by a Chebyshev collocation method. Stability boundaries are obtained in a wide range of amplitude and frequency of the modulation as well as surfactant elasticity. Results show that the presence of the surfactant may significantly stabilize (destabilize) the flow by raising (lowering) the critical Reynolds number associated with the onset of instability. The effect of the surfactant plays a stabilizing role for small surfactant elasticity and a destabilizing one for relatively large surfactant elasticity. The destabilizing effect of the surfactant on the stability of flows with a zero-shear surface is found for the first time. The disturbance modes in the form of travelling waves may be induced by the surfactant and dominate the instability of the flow.

scholarly journals Thermosolutal Natural Convection in Partially Porous Domains

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Dominique Gobin ◽  
Benoît Goyeau
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat And Mass Transfer ◽  
Fluid Layer ◽  
Horizontal Layer ◽  
Clear Fluid ◽  
Onset Of Convection ◽  
The Stability ◽  
Double Diffusive

In many industrial processes or natural phenomena, coupled heat and mass transfer and fluid flow take place in configurations combining a clear fluid and a porous medium. Since the pioneering work by Beavers and Joseph (1967), the modeling of such systems has been a controversial issue, essentially due to the description of the interface between the fluid and the porous domains. The validity of the so-called one-domain approach—more intuitive and numerically simpler to implement—compared to a two-domain description where the interface is explicitly accounted for, is now clearly assessed. This paper reports recent developments and the current state of the art on this topic, concerning the numerical simulation of such flows as well as the stability studies. The continuity of the conservation equations between a fluid and a porous medium are examined and the conditions for a correct handling of the discontinuity of the macroscopic properties are analyzed. A particular class of problems dealing with thermal and double diffusive natural convection mechanisms in partially porous enclosures is presented, and it is shown that this configuration exhibits specific features in terms of the heat and mass transfer characteristics, depending on the properties of the porous domain. Concerning the stability analysis in a horizontal layer where a fluid layer lies on top of a porous medium, it is shown that the onset of convection is strongly influenced by the presence of the porous medium. The case of double diffusive convection is presented in detail.

scholarly journals TEMPERATURE MODULATION IN RAYLEIGH–BÉNARD CONVECTION

2008 ◽  
Vol 50 (2) ◽  
pp. 231-245 ◽  
Author(s):  
JITENDER SINGH ◽  
RENU BAJAJ
Keyword(s):  
Floquet Theory ◽  
Fluid Layer ◽  
Temperature Modulation ◽  
Bénard Convection ◽  
Benard Convection ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Horizontal Fluid Layer ◽  
Time Periodic

AbstractThe stability characteristics of an infinite horizontal fluid layer excited by a time-periodic, sinusoidally varying free-boundary temperature, have been investigated numerically using the Floquet theory. It has been found that the modulation of the temperature gradient across the fluid layer affects the onset of the Rayleigh–Bénard convection. Modulation can give rise to instability in the subcritical conditions and it can also suppress the instability in the supercritical cases. The instability in the fluid layer manifests itself in the form of either a harmonic or subharmonic flow, controlled by thermal modulation.

Reducibility and Analysis of Linear Quasi-Periodic Systems Via Normal Forms

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Peter M. B. Waswa ◽  
Sangram Redkar
Keyword(s):  
Periodic System ◽  
Constant Coefficient ◽  
Floquet Theory ◽  
Normal Forms ◽  
Time History ◽  
Mathieu Equation ◽  
Periodic Systems ◽  
State Augmentation ◽  
The Stability ◽  
Averaging Techniques

Abstract This article introduces a technique to accomplish reducibility of linear quasi-periodic systems into constant-coefficient linear systems. This is consistent with congruous proofs common in literature. Our methodology is based on Lyapunov–Floquet transformation, normal forms, and enabled by an intuitive state augmentation technique that annihilates the periodicity in a system. Unlike common approaches, the presented approach does not employ perturbation or averaging techniques and does not require a periodic system to be approximated from the quasi-periodic system. By considering the undamped and damped linear quasi-periodic Hill-Mathieu equation, we validate the accuracy of our approach by comparing the time-history behavior of the reduced linear constant-coefficient system with the numerically integrated results of the initial quasi-periodic system. The two outcomes are shown to be in exact agreement. Consequently, the approach presented here is demonstrated to be accurate and reliable. Moreover, we employ Floquet theory as part of our analysis to scrutinize the stability and bifurcation properties of the undamped and damped linear quasi-periodic system.

scholarly journals Thermosolutal Natural Convection in Partially Porous Domains

2010 ◽  
Author(s):  
Dominique Gobin ◽  
Benoiˆt Goyeau
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat And Mass Transfer ◽  
Fluid Layer ◽  
Clear Fluid ◽  
Open Problems ◽  
Onset Of Convection ◽  
The Stability ◽  
Double Diffusive

In many industrial processes or natural phenomena coupled heat and mass transfer and fluid flow take place in configurations combining a clear fluid and a porous medium. Since the pioneering work by Beavers and Joseph (1967), the modelling of such systems has been a controversial issue, essentially due to the description of the interface between the fluid and the porous domains. The validity of the so-called one-domain approach — more intuitive and numerically simpler to implement — compared to a two-domain description where the interface is explicitly accounted for, is now clearly assessed. This paper reports recent developments and the current state of the art on this topic, concerning the numerical simulation of such flows as well as the stability studies. The continuity of the conservation equations between a fluid and a porous medium are examined and the conditions for a correct handling of the discontinuity of the macroscopic properties are analyzed. A particular class of problems dealing with thermal and double diffusive natural convection mechanisms in partially porous enclosures is presented, and it is shown that this configuration exhibits specific features in terms of the heat and mass transfer characteristics, depending on the properties of the porous domain. From the viewpoint of the stability of convection in a horizontal layer where a fluid layer lies on top of a porous medium, the analysis shows that the onset of convection is strongly influenced by the presence of the porous medium. The case of thermal convection is fully detailed and many open problems arise in the field of double diffusive convection.

Heat transfer by rapidly rotating Rayleigh–Bénard convection

2012 ◽  
Vol 691 ◽  
pp. 568-582 ◽  
Author(s):  
E. M. King ◽  
S. Stellmach ◽  
J. M. Aurnou
Keyword(s):  
Heat Transfer ◽  
Fluid Layer ◽  
Scaling Law ◽  
Critical Rayleigh Number ◽  
Onset Of Convection ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Adequate Agreement ◽  
Exact Scaling

AbstractTurbulent, rapidly rotating convection has been of interest for decades, yet there exists no generally accepted scaling law for heat transfer behaviour in this system. Here, we develop an exact scaling law for heat transfer by geostrophic convection, $\mathit{Nu}= \mathop{ (\mathit{Ra}/ {\mathit{Ra}}_{c} )}\nolimits ^{3} = 0. 0023\hspace{0.167em} {\mathit{Ra}}^{3} {E}^{4} $, by considering the stability of the thermal boundary layers, where $\mathit{Nu}$, $\mathit{Ra}$ and $E$ are the Nusselt, Rayleigh and Ekman numbers, respectively, and ${\mathit{Ra}}_{c} $ is the critical Rayleigh number for the onset of convection. Furthermore, we use the scaling behaviour of the thermal and Ekman boundary layer thicknesses to quantify the necessary conditions for geostrophic convection: $\mathit{Ra}\lesssim {E}^{\ensuremath{-} 3/ 2} $. Interestingly, the predictions of both heat flux and regime transition do not depend on the total height of the fluid layer. We test these scaling arguments with data from laboratory and numerical experiments. Adequate agreement is found between theory and experiment, although there is a paucity of convection data for low $\mathit{Ra}\hspace{0.167em} {E}^{3/ 2} $.

scholarly journals Bleaching of chlorophylls by UV irradiation in vitro: The effects on chlorophyll organization in acetone and n-hexane

2008 ◽  
Vol 73 (3) ◽  
pp. 271-282 ◽  
Author(s):  
Jelena Zvezdanovic ◽  
Dejan Markovic
Keyword(s):  
Uv Irradiation ◽  
Photosynthetic Pigments ◽  
Energy Input ◽  
First Order ◽  
First Order Kinetics ◽  
Uv Photons ◽  
The Stability ◽  
Major Factors

The stability of chlorophylls toward UV irradiation was studied by Vis spectrophotometry in extracts containing mixtures of photosynthetic pigments in acetone and n-hexane. The chlorophylls underwent destruction (bleaching) obeying first-order kinetics. The bleaching was governed by three major factors: the energy input of the UV photons, the concentration of the chlorophylls and the polarity of the solvent, implying different molecular organizations of the chlorophylls in the two solvents.

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