Stabilization of the No-Motion State of a Horizontal Fluid Layer Heated From Below With Joule Heating

1995 ◽  
Vol 117 (2) ◽  
pp. 329-333 ◽  
Author(s):  
J. Tang ◽  
H. H. Bau
Keyword(s):  
Joule Heating ◽  
Fluid Layer ◽  
Control Strategies ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Small Perturbations ◽  
Motion State ◽  
Conduction State ◽  
Rayleigh Numbers ◽  
Horizontal Fluid Layer

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–Be´nard problem of an infinite fluid layer heated from below with Joule heating and cooled from above can be significantly increased through the use of feedback control strategies effecting small perturbations in the boundary data. The bottom of the layer is heated by a network of heaters whose power supply is modulated in proportion to the deviations of the temperatures at various locations in the fluid from the conductive, no-motion temperatures. Similar control strategies can also be used to induce complicated, time-dependent flows at relatively low Rayleigh numbers.

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.

The Effect of Suction on the Stability of Fluid between Horizontal Plates at Differing Temperatures

1985 ◽  
Vol 199 (2) ◽  
pp. 145-151 ◽  
Author(s):  
M M Sorour ◽  
M A Hassab ◽  
F A Elewa
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Stability Criteria ◽  
Thermal Boundary Conditions ◽  
Wide Range ◽  
Fluid Layers ◽  
The Stability ◽  
Horizontal Fluid Layer

The linear stability theory is applied to study the effect of suction on the stability criteria of a horizontal fluid layer confined between two thin porous surfaces heated from below. This investigation covers a wide range of Reynolds number 0 ≥ Re ≥ 30, and Prandtl number 0.72 ≥ Pr ≥ 100. The results show that the critical Rayleigh number increases with Peclet number, and is independent of Pr as far as Re < 3. However, for Re > 3 the critical Rayleigh number is function of both Pr and Pe. In addition, the analysis is extended to study the effect of suction on the stability of two special superimposed fluid layers. The results in the latter case indicate a more stabilizing effect. Furthermore, the effect of thermal boundary conditions is also investigated.

Natural Convection in a Horizontal Fluid Layer With Volumetric Energy Sources

1975 ◽  
Vol 97 (2) ◽  
pp. 204-211 ◽  
Author(s):  
F. A. Kulacki ◽  
M. E. Nagle
Keyword(s):  
Natural Convection ◽  
Fluid Layer ◽  
Lower Boundary ◽  
Linear Stability Theory ◽  
Volumetric Heating ◽  
Aspect Ratios ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Steady Heat ◽  
Horizontal Fluid Layer

Natural convection with volumetric heating in a horizontal fluid layer with a rigid, insulated lower boundary and a rigid, isothermal upper boundary is experimentally investigated for Rayleigh numbers from 114 to 1.8 × 106 times the critical value of linear stability theory. Joule heating by alternating current passing horizontally through the layer provides the volumetric energy source. Layer aspect ratios are kept small to minimize the effects of side walls. A correlation for mean Nusselt number is obtained for steady heat transfer, and data are presented on fluctuating temperatures at high Rayleigh numbers and on developing temperature distributions when the layer is subjected to a step change in power.

Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below

1989 ◽  
Vol 207 ◽  
pp. 311-321 ◽  
Author(s):  
Falin Chen ◽  
C. F. Chen
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Convective Stability ◽  
Onset Of Convection ◽  
Temperature Distributions ◽  
Critical Wavelength ◽  
Crystal Film ◽  
Flux Curve

Experiments have been carried out in a horizontal superposed fluid and porous layer contained in a test box 24 cm × 12 cm × 4 cm high. The porous layer consisted of 3 mm diameter glass beads, and the fluids used were water, 60% and 90% glycerin-water solutions, and 100% glycerin. The depth ratio ď, which is the ratio of the thickness of the fluid layer to that of the porous layer, varied from 0 to 1.0. Fluids of increasingly higher viscosity were used for cases with larger ď in order to keep the temperature difference across the tank within reasonable limits. The top and bottom walls were kept at different constant temperatures. Onset of convection was detected by a change of slope in the heat flux curve. The size of the convection cells was inferred from temperature measurements made with embedded thermocouples and from temperature distributions at the top of the layer by use of liquid crystal film. The experimental results showed (i) a precipitous decrease in the critical Rayleigh number as the depth of the fluid layer was increased from zero, and (ii) an eightfold decrease in the critical wavelength between ď = 0.1 and 0.2. Both of these results were predicted by the linear stability theory reported earlier (Chen & Chen 1988).

Unsteady Heating of Rayleigh-Benard Convection

2004 ◽  
Vol 59 (4-5) ◽  
pp. 266-274
Author(s):  
B. S. Bhadauria
Keyword(s):  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Dependent Part ◽  
Prandtl Numbers ◽  
Periodic Temperature ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Unsteady Heating ◽  
Horizontal Fluid Layer ◽  
Time Periodic

The linear thermal instability of a horizontal fluid layer with time-periodic temperature distribution is studied with the help of the Floquet theory. The time-dependent part of the temperature has been expressed in Fourier series. Disturbances are assumed to be infinitesimal. Only even solutions are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. It is found that the disturbances are either synchronous with the primary temperature field or have half its frequency. - 2000 Mathematics Subject Classification: 76E06, 76R10.

The effect of heating rate on the stability of stationary fluids

1967 ◽  
Vol 29 (2) ◽  
pp. 337-347 ◽  
Author(s):  
I. G. Currie
Keyword(s):  
Rayleigh Number ◽  
Surface Temperature ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Lower Surface ◽  
Published Data ◽  
Heating Rates ◽  
Lower Surface Temperature ◽  
The Stability ◽  
Horizontal Fluid Layer

A horizontal fluid layer whose lower surface temperature is made to vary with time is considered. The stability analysis for this situation shows that the criterion for the onset of instability in a fluid layer which is being heated from below, depends on both the method and the rate of heating. For a fluid layer with two rigid boundaries, the minimum Rayleigh number corresponding to the onset of instability is found to be 1340. For slower heating rates the critical Rayleigh number increases to a maximum value of 1707·8, while for faster heating rates the critical Rayleigh number increases without limit.Two specific types of heating are investigated in detail, constant flux heating and linearly varying surface temperature. These cases correspond closely to situations for which published data exist. The results are in good qualitative agreement.

scholarly journals Rayleigh-Bénard convection with magnetic field

2003 ◽  
pp. 29-40 ◽  
Author(s):  
Jürgen Zierep
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Fluid Layer ◽  
Wave Length ◽  
Critical Rayleigh Number ◽  
Black Spots ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Horizontal Fluid Layer ◽  
The Magnetic Field

We discuss the solution of the small perturbation equations for a horizontal fluid layer heated from below with an applied magnetic field either in vertical or in horizontal direction. The magnetic field stabilizes, due to the Lorentz force, more or less Rayleigh-B?nard convective cellular motion. The solution of the eigenvalue problem shows that the critical Rayleigh number increases with increasing Hartmann number while the corresponding wave length decreases. Interesting analogies to solar granulation and black spots phenomena are obvious. The influence of a horizontal field is stronger than that of a vertical field. It is easy to understand this by discussing the influence of the Lorentz force on the Rayleigh-B?nard convection. This result corrects earlier calculations in the literature.

Nonlinear interaction of magnetic field and convection

1975 ◽  
Vol 71 (1) ◽  
pp. 193-206 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Finite Amplitude ◽  
Magnetic Reynolds Number ◽  
Convection Rolls ◽  
Rayleigh Numbers ◽  
Horizontal Fluid Layer ◽  
Chandrasekhar Number

The interaction between convection in a horizontal fluid layer heated from below and an ambient vertical magnetic field is considered. The analysis is based on the Boussinesq equations for two-dimensional convection rolls and the assumption that the amplitude A of the convection and the Chandrasekhar number Q are small. It is found that the magnetic energy is amplified by a factor of order R½m, where Rm is the magnetic Reynolds number. The ratio between the magnetic and kinetic energies can reach values much larger than unity. Although the magnetic field always inhibits convection, this influence decreases with increasing amplitude of convection. Thus finite amplitude onset of steady convection becomes possible at Rayleigh numbers considerably below the values predicted by linear theory.

Convective instabilities in a closed vertical cylinder heated from below. Part 1. Monocomponent gases

1979 ◽  
Vol 92 (4) ◽  
pp. 609-629 ◽  
Author(s):  
J. M. Olson ◽  
F. Rosenberger
Keyword(s):  
Critical Rayleigh Number ◽  
Vertical Cylinder ◽  
Quantitative Agreement ◽  
Linear Stability Theory ◽  
Mean Flow ◽  
Sensor Arrangement ◽  
Convective Instabilities ◽  
Multiple Sensor ◽  
Vertical Cylinders ◽  
Rayleigh Numbers

Kr, Xe and SiCI4have been investigated for convective instabilities in closed vertical cylinders with conductive walls heated from below. Critical Rayleigh numbersNiRafor the onset of various convective modes (including the onset of marginally stable and periodic flow) have been determined with a high resolution differential temperature sensing method. Flow patterns were deduced from a multiple sensor arrangement. For the three lowest modes (i= 1, 2, 3) good quantitative agreement with linear stability theory is found. Stable oscillatory modes (periodic fluctuations of the mean flow) with a period of approximately 5 s are found for a relatively narrow range ofNRa. The critical Rayleigh numberNoscRafor the onset of oscillatory temperature fluctuations is 1348 ± 50 for an aspect ratio (height/radius) of 6.

Instabilities of convection rolls in a fluid of moderate Prandtl number

1979 ◽  
Vol 91 (2) ◽  
pp. 319-335 ◽  
Author(s):  
F. H. Busse ◽  
R. M. Clever
Keyword(s):  
Prandtl Number ◽  
Fluid Layer ◽  
Experimental Methods ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
Convection Rolls ◽  
Rayleigh Numbers ◽  
Horizontal Fluid Layer

The instabilities of two-dimensional convection rolls in a horizontal fluid layer heated from below are investigated in the case when the Prandtl number is seven or lower. Two new mechanisms of instability are described theoretically as well as experimentally. The knot instability causes the transition to spoke-pattern convection at higher Rayleigh numbers while the skewed varicose instability accomplishes a change to larger horizontal wavelengths of the convection rolls. Both instabilities disappear in the limits of small and large Prandtl number. Although the experimental methods fail in realizing closely the infinitely conducting boundaries assumed in the theory, the observations agree in all qualitative aspects with the theoretical predictions.

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