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 Effects of Magnetic Field and Non-Uniform Basic Temperature Gradient

2002 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
S. Pranesh
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Conducting Fluid ◽  
Wave Number ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

The effects of a non-uniform temperature gradient and magnetic field on the onset of convection in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free/adiabatic boundary and a lower rigid/isothermal boundary have been considered. A linear stability analysis is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the Eigen values. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid without Suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

scholarly journals Effects of Controller and Nonuniform Temperature Profile on the Onset of Rayleigh-Bénard-Marangoni Electroconvection in a Micropolar Fluid

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
H. M. Azmi ◽  
R. Idris
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Micropolar Fluid ◽  
Marangoni Convection ◽  
Temperature Gradients ◽  
Temperature Profiles ◽  
Nonuniform Temperature ◽  
Onset Of Convection ◽  
Basic Temperature ◽  
Rayleigh Benard

Linear stability analysis is performed to study the effects of nonuniform basic temperature gradients on the onset of Rayleigh-Bénard-Marangoni electroconvection in a dielectric Eringen’s micropolar fluid by using the Galerkin technique. In the case of Rayleigh-Bénard-Marangoni convection, the eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal boundaries. The influence of various parameters has been analysed. Three nonuniform basic temperature profiles are considered and their comparative influence on onset of convection is discussed. Different values of feedback control and electric number are added up to examine whether their presence will enhance or delay the onset of electroconvection.

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} $.

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Thermal Instability of Compressible Micropolar Fluid in the Presence of Suspended Particles

2012 ◽  
Vol 28 (2) ◽  
pp. 239-246 ◽  
Author(s):  
N. Rani ◽  
S. K. Tomar
Keyword(s):  
Dispersion Relation ◽  
Rayleigh Number ◽  
Micropolar Fluid ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Stationary Convection ◽  
Presence And Absence ◽  
Number Curve

AbstractA problem of thermal instability of a compressible micropolar fluid layer heated from below in the presence of suspended particles has been investigated. Dispersion relation is derived and Rayleigh number curve is then plotted against the wavenumber at different values of compressibility parameter for a model example. Compressibility is found to be responsible to destabilize the system in the presence and absence of suspended particles for both stationary and over stationary convection.

Natural Convection in Horizontal Thin-Walled Honeycomb Panels

1973 ◽  
Vol 95 (4) ◽  
pp. 439-444 ◽  
Author(s):  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Layer ◽  
Convection Heat Transfer ◽  
Correlation Equation ◽  
Wave Number ◽  
Equivalent Wave ◽  
Side Walls ◽  
The Stability ◽  
Rayleigh Numbers

This paper presents an experimental study of the stability of and natural convection heat transfer through a horizontal fluid layer heated from below and constrained internally by a honeycomb. Examination of the types of boundary conditions exacted on the fluid at the cell side-walls has shown that there are three limiting cases: (1) perfectly conducting side-walls; (2) perfectly adiabatic side-walls; and (3) side-walls having zero thickness. Experiments described in this paper approach the latter category. The fluid used is air and the honeycomb used is square-celled. Measured critical Rayleigh numbers are found to be intermediate between those applying to cases (1) and (2), and consistent with an “equivalent wave number” of approximately 0.95 times that for case (1). The measured natural convective heat transfer after instability is found to be significantly less than that predicted by the Malkus-Veronis power integral technique. However, it is found to approach asymptotically the heat transfer which would take place through a similar fluid layer unconstrained by a honeycomb. A general correlation equation for the heat transfer is given.

Instability of a gravity-modulated fluid layer with surface tension variation

2001 ◽  
Vol 434 ◽  
pp. 243-271 ◽  
Author(s):  
J. RAYMOND LEE SKARDA
Keyword(s):  
Surface Tension ◽  
Fluid Layer ◽  
Modulation Frequency ◽  
Galerkin Approximation ◽  
Neutral Stability ◽  
Modulation Amplitude ◽  
Neutral Stability Curve ◽  
Stability Curve ◽  
The Stability ◽  
Rayleigh Benard

Gravity modulation of an unbounded fluid layer with surface tension variations along its free surface is investigated. The stability of such systems is often characterized in terms of the wavenumber, α and the Marangoni number, Ma. In (α, Ma) parameter space, modulation has a destabilizing effect on the unmodulated neutral stability curve for large Prandtl number, Pr, and small modulation frequency, Ω, while a stabilizing effect is observed for small Pr and large Ω. As Ω → ∞ the modulated neutral stability curves approach the unmodulated neutral stability curve. At certain values of Pr and Ω, multiple minima are observed and the neutral stability curves become highly distorted. Closed regions of subharmonic instability are also observed. In (1/Ω, g1Ra)-space, where g1 is the relative modulation amplitude, and Ra is the Rayleigh number, alternating regions of synchronous and subharmonic instability separated by thin stable regions are observed. However, fundamental differences between the stability boundaries occur when comparing the modulated Marangoni–Bénard and Rayleigh–Bénard problems. Modulation amplitudes at which instability tongues occur are strongly influenced by Pr, while the fundamental instability region is weakly affected by Pr. For large modulation frequency and small amplitude, empirical relations are derived to determine modulation effects. A one-term Galerkin approximation was also used to reduce the modulated Marangoni–Bénard problem to a Mathieu equation, allowing qualitative stability behaviour to be deduced from existing tables or charts, such as Strutt diagrams. In addition, this reduces the parameter dependence of the problem from seven transport parameters to three Mathieu parameters, analogous to parameter reductions of previous modulated Rayleigh–Bénard studies. Simple stability criteria, valid for small parameter values (amplitude and damping coefficients), were obtained from the one-term equations using classical method of averaging results.

scholarly journals A theoretical and numerical study of thermosolutal convection: stability of a salinity gradient solar pond

2011 ◽  
Vol 15 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Dalila Akrour ◽  
Mouloud Tribeche ◽  
Djamel Kalache
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Numerical Study ◽  
Salinity Gradient ◽  
Thermosolutal Convection ◽  
Separation Coefficient ◽  
Onset Of Convection ◽  
Solar Pond ◽  
Negative Case ◽  
The Stability

A theoretical and numerical study of the effect of thermodiffusion on the stability of a gradient layer is presented. It intends to clarify the mechanisms of fluid dynamics and the processes which occur in a salinity gradient solar pond. A mathematical modelling is developed to describe the thermodiffusion contribution on the solar pond where thermal, radiative, and massive fluxes are coupled in the double diffusion. More realistic boundary conditions for temperature and concentration profiles are used. Our results are compared with those obtained experimentally by authors without extracting the heat flux from the storage zone. We have considered the stability analysis of the equilibrium solution. We assumed that the perturbation of quantities such as velocity, temperature, and concentration are infinitesimal. Linearized equations satisfying appropriate prescribed boundary conditions are then obtained and expanded into polynomials form. The Galerkin method along with a symbolic algebra code (Maple) are used to solve these equations. The effect of the separation coefficient y is analyzed in the positive and negative case. We have also numerically compared the critical Rayleigh numbers for the onset of convection with those obtained by the linear stability analysis for Le = 100, ?a = 0.8, and f = 0.5.

Rayleigh–Bénard instability generated by a diffusion flame

2013 ◽  
Vol 736 ◽  
pp. 464-494 ◽  
Author(s):  
P. Pearce ◽  
J. Daou
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Diffusion Flame ◽  
Damkohler Number ◽  
Benard Convection ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe investigate the Rayleigh–Bénard convection problem within the context of a diffusion flame formed in a horizontal channel where the fuel and oxidizer concentrations are prescribed at the porous walls. This problem seems to have received no attention in the literature. When formulated in the low-Mach-number approximation the model depends on two main non-dimensional parameters, the Rayleigh number and the Damköhler number, which govern gravitational strength and reaction speed respectively. In the steady state the system admits a planar diffusion flame solution; the aim is to find the critical Rayleigh number at which this solution becomes unstable to infinitesimal perturbations. In the Boussinesq approximation, a linear stability analysis reduces the system to a matrix equation with a solution comparable to that of the well-studied non-reactive case of Rayleigh–Bénard convection with a hot lower boundary. The planar Burke–Schumann diffusion flame, which has been previously considered unconditionally stable in studies disregarding gravity, is shown to become unstable when the Rayleigh number exceeds a critical value. A numerical treatment is performed to test the effects of compressibility and finite chemistry on the stability of the system. For weak values of the thermal expansion coefficient $\alpha $, the numerical results show strong agreement with those of the linear stability analysis. It is found that as $\alpha $ increases to a more realistic value the system becomes considerably more stable, and also exhibits hysteresis at the onset of instability. Finally, a reduction in the Damköhler number is found to decrease the stability of the system.

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