Effect of Modulation on Thermal Convection Instability

2000 ◽  
Vol 55 (11-12) ◽  
pp. 957-966 ◽  
Author(s):  
P. K. Bhatia ◽  
B. S. Bhadauria
Keyword(s):  
Fourier Series ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Stability Problem ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Time Dependent ◽  
The Stability ◽  
Linear Stability Problem ◽  
Oscillatory Temperature

Abstract The linear stability problem for a fluid in a classic Benard configuration is considered. The applied temperature gradient is the sum of a steady component and a time-dependent periodic component. Only infinitesimal disturbances are considered. The time-dependent perturbation is expressed in Fourier series. The shift in critical Rayleigh number is calculated and the modulating effect of the oscillatory temperature gradient on the stability of the fluid layer is examined. Some comparison is made with known results.

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 Concordancing in ESP Class Rooms

2014 ◽  
Vol 4 (3) ◽  
pp. 434-439
Author(s):  
Sameh Benna ◽  
Olfa Bayoudh
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Analysis ◽  
Wave Number ◽  
Gravity Modulation ◽  
Non Linear ◽  
The Stability ◽  
Time Periodic

The effect of time periodic body force (or g-jitter or gravity modulation) on the onset of Rayleigh-Bnard electro-convention in a micropolar fluid layer is investigated by making linear and non-linear stability analysis. The stability of the horizontal fluid layer heated from below is examined by assuming time periodic body acceleration. This normally occurs in satellites and in vehicles connected with micro gravity simulation studies. A linear and non-linear analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. The linear theory is based on normal mode analysis and perturbation method. Small amplitude of modulation is used to compute the critical Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation. The non-linear analysis is based on the truncated Fourier series representation. The resulting non-autonomous Lorenz model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat transport.

scholarly journals Effects of modulation on Rayleigh-Benard convection. Part I

2004 ◽  
Vol 2004 (19) ◽  
pp. 991-1001 ◽  
Author(s):  
B. S. Bhadauria ◽  
Lokenath Debnath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Horizontal Layer ◽  
Time Dependent ◽  
Steady Temperature ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The linear stability of a horizontal layer of fluid heated from below and above is considered. In addition to a steady temperature difference between the walls of the fluid layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. Some comparisons have been made with the known results.

Linear Stability Analysis

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stability Problem ◽  
Linear Codes ◽  
Linear Equations ◽  
Critical Rayleigh Number ◽  
Linear Solution ◽  
Linear Stability Problem

This chapter describes a linear stability analysis (that is, solving for the critical Rayleigh number Ra and mode) that allows readers to check their linear codes against the analytic solution. For this linear analysis, each Fourier mode n can be considered a separate and independent problem. The question that needs to be addressed now is under what conditions—that is, what values of Ra, Prandtl number Pr, and aspect ratio a—will the amplitude of the linear solution grow with time for a given mode n. This is a linear stability problem. The chapter first introduces the linear equations before discussing the linear code and explaining how to find the critical Rayleigh number; in other words, the value of Ra for a and Pr that gives a solution that neither grows nor decays with time. It also shows how the linear stability problem can be solved using an analytic approach.

Instabilities of convection rolls with stress-free boundaries near threshold

1984 ◽  
Vol 146 ◽  
pp. 115-125 ◽  
Author(s):  
F. H. Busse ◽  
E. W. Bolton
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Limited Range ◽  
Finite Domain ◽  
Free Boundaries ◽  
Prandtl Numbers ◽  
The Stability ◽  
Convection Rolls ◽  
Horizontal Fluid Layer

The stability properties of steady two-dimensional solutions describing convection in a horizontal fluid layer heated from below with stress-free boundaries are investigated in the neighbourhood of the critical Rayleigh number. The region of stable convection rolls as a function of the wavenumber α and the Rayleigh number R is bounded towards higher α by the monotonic skewed varicose instability, while towards low wavenumbers stability is limited by the zigzag instability or by the oscillatory skewed varicose instability. Only for a limited range of Prandtl numbers, 0·543 < P < ∞, does a finite domain of stability exist. In particular, convection rolls with the critical wavenumber αc are always unstable.

The instability of a fluid layer with time-dependent heating

1965 ◽  
Vol 21 (3) ◽  
pp. 565-576 ◽  
Author(s):  
Wilbert Lick
Keyword(s):  
Temperature Gradient ◽  
Approximate Method ◽  
Fluid Layer ◽  
Time Dependent ◽  
Method Of Solution ◽  
The Stability

The problem of the stability and growth of disturbances in a fluid with time-dependent heating is investigated. The analysis is restricted to the case when the temperature gradient is large in a layer which is narrow by comparison with the overall depth of the fluid. An approximate method of solution is presented. Results of computations are also presented which illustrate the method of solution and the essential features of the problem.

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.

Effect of Modulation on Rayleigh-Benard Convection-II

2003 ◽  
Vol 58 (2-3) ◽  
pp. 176-182
Author(s):  
B. S. Bhadauria
Keyword(s):  
Rayleigh Number ◽  
Temperature Gradient ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Periodic Part ◽  
Prandtl Numbers ◽  
Rigid Walls ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Horizontal Fluid Layer

The linear stability of a horizontal fluid layer, confined between two rigid walls, heated from below and cooled from above is considered. The temperature gradient between the walls consists of a steady part and a periodic part that oscillates with time. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained for various Prandtl numbers and for various values of the frequency. Some comparisons with known results have also been made.

Stability of Heat Pipes in Vapor-Dominated Systems

1999 ◽  
Author(s):  
Pouya Amili ◽  
Yanis C. Yortsos
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Oil Recovery ◽  
Critical Rayleigh Number ◽  
Stability Limit ◽  
Wave Number ◽  
Nuclear Waste Repository ◽  
Geothermal Systems ◽  
Dimensionless Numbers ◽  
The Stability

Abstract We study the linear stability of a two-phase heat pipe zone (vapor-liquid counterflow) in a porous medium, overlying a superheated vapor zone. The competing effects of gravity, condensation and heat transfer on the stability of a planar base state are analyzed in the linear stability limit. The rate of growth of unstable disturbances is expressed in terms of the wave number of the disturbance, and dimensionless numbers, such as the Rayleigh number, a dimensionless heat flux and other parameters. A critical Rayleigh number is identified and shown to be different than in natural convection under single phase conditions. The results find applications to geothermal systems, to enhanced oil recovery using steam injection, as well as to the conditions of the proposed Yucca Mountain nuclear waste repository. This study complements recent work of the stability of boiling by Ramesh and Torrance (1993).

Stability and Convection in Impulsively Heated Porous Layers

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
M. J. Kohl ◽  
M. Kristoffersen ◽  
F. A. Kulacki
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Axisymmetric Flow ◽  
Temperature Fluctuations ◽  
Lower Surface ◽  
Onset Of Convection ◽  
Upward Moving ◽  
The Stability

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η−0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

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