An exact solution for the Rayleigh-Benard convective flow with quadratic heating at the upper boundary of a fluid layer

2020 ◽  
Author(s):  
V. V. Privalova ◽  
E. Yu. Prosviryakov
Keyword(s):  
Exact Solution ◽  
Convective Flow ◽  
Fluid Layer ◽  
Rayleigh Benard ◽  
Upper Boundary

Stabilization of the no-motion state in the Rayleigh–Bénard problem

1994 ◽  
Vol 447 (1931) ◽  
pp. 587-607 ◽  
Keyword(s):  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Control Flow ◽  
Feedback Controller ◽  
Linear Stability Theory ◽  
Motion State ◽  
Conduction State ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

Using linear stability theory and numerical simulations, we demonstrate that the critical Rayleigh number for bifurcation from the no-motion (conduction) state to the motion state in the Rayleigh–Bénard problem of an infinite fluid layer heated from below and cooled from above can be significantly increased through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid’s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary’s temperature or velocity are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behaviour at relatively low Rayleigh numbers.

scholarly journals Toward understanding the multiscale spatial spectrum of solar convection

2012 ◽  
Vol 8 (S294) ◽  
pp. 361-363
Author(s):  
A. V. Getling ◽  
O. S. Mazhorova ◽  
O. V. Shcheritsa
Keyword(s):  
Convective Instability ◽  
Convective Flow ◽  
Large Scale ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Spatial Spectrum ◽  
Small Scale ◽  
Two Dimensional ◽  
Solar Convection

AbstractConvection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

Marangoni convection of a viscous fluid over a vibrating plate

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190214
Author(s):  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Viscous Dissipation ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Plane Waves ◽  
Internal Heat ◽  
Runge Kutta Method ◽  
Insight Into ◽  
Unstable Temperature ◽  
Upper Boundary ◽  
Vibrating Plate

This research presents a new insight into Marangoni convection through investigating, both numerically and analytically, the surface tension driven instability activated by a coupled effect of a vibrating plate and viscous dissipation. A horizontal, thin fluid layer is bounded from below by an impermeable, adiabatic plate that vibrates in the horizontal direction. The upper boundary is modelled by a free surface subject to a thermal boundary condition of the third kind (Robin). The internal heat generation due to viscous dissipation yields a vertical, potentially unstable temperature gradient. The linear stability analysis of the stationary terms of the basic state is performed. The perturbed flow, in the form of plane waves, is superimposed onto the basic state. The obtained system of ordinary differential equations is solved numerically by means of the Runge–Kutta method coupled with the shooting method. For the two limiting cases, the isothermal upper boundary and adiabatic upper boundary, the analytical solutions of the eigenvalue problem are obtained. The values of the critical parameter, which identifies the threshold for the onset of Marangoni convection, are presented.

Dissipative Structures in Demixing Binary Liquid Systems

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1309-1316 ◽  
Author(s):  
Roland Zander ◽  
Michael Dittmann ◽  
Gerhard M. Schneider
Keyword(s):  
Fluid Layer ◽  
Synergetic Effect ◽  
Sample Volume ◽  
Dissipative Structures ◽  
Vertical Temperature ◽  
Convective Structures ◽  
Liquid Systems ◽  
Convective Pattern ◽  
Rayleigh Benard ◽  
Horizontal Fluid Layer

AbstractThe demixing of a horizontal fluid layer of far-critical composition in the presence of a vertical temperature gradient can cause the formation of dissipative structures and thereby lead to a regular distribution of the precipitate. The occurrence of these convective structures is explained with the model of a Rayleigh-Benard instability (RBI) which is driven by parallel gradients of temperature and concentration. The distribution of the precipitate is a synergetic effect of the macroscopic convective pattern and the local action of the Marangoni flow at the surfaces of the drops. If boundary conditions prohibit an RBI, the distribution of the precipitate also becomes inhomogeneous in course of time; however, in this case no regular pattern is observable and the inhomogeneities develop mainly due to the Marangoni convection near the surfaces of the larger drops that have settled at the boundary of the sample volume

Identification of Rayleigh-Bénard Convection on Physical Model of Electric Furnace

2008 ◽  
Vol 39-40 ◽  
pp. 481-484
Author(s):  
Antonín Lisý ◽  
Josef Smrček
Keyword(s):  
Physical Model ◽  
Convective Flow ◽  
Electric Energy ◽  
Melting Furnace ◽  
Melting Tank ◽  
Bénard Convection ◽  
Reducing Ability ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The released electric energy in the melting tank, the distribution of temperatures in the glass melt and by them generated the flow influences a quality of the manufactured glass melt especially their homogeneity. Between those places where the energy releases and where the energy consumes generates natural convection, called Rayleigh-Bénard convection. This type of the convective flow is forming by the volumetric releasing of energy and this flow is also present in electric glass melting furnaces. In the melting tank of the furnace is released energy transported to colder areas for heating and melting of the batch. Experiments on the physical model were carried out with cooling the surface and heating the room below it. The temperature gradient area rises in the horizontal layer below the batch. From this layer the cooler blobs divide off and fall. Theirs velocities are depended on RaI 0,33 and it is less than the dependence of the flow velocity measured by Dubois and Bergé with RaI 0,50. The results of the electric energy releasing in the physical model of the melting furnace showed that with decreasing depth of the tank is forming more smaller cells of Rayleigh-Bénard convective flow and also by them is reducing ability of the blobs flow generating.

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.

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