Onset of Thermal Convection in a Fluid Layer Subjected to Transient Heating From Below

1984 ◽  
Vol 106 (4) ◽  
pp. 817-823 ◽  
Author(s):  
M. Kaviany
Keyword(s):  
Fluid Layer ◽  
Sudden Change ◽  
Onset Time ◽  
Lower Surface ◽  
Analytical Prediction ◽  
Rigid Boundary ◽  
Transient Heating ◽  
Onset Of Convection ◽  
Analytical Results ◽  
Heating From Below

The onset of convection in a horizontal layer of fluid subject to time-dependent heating from below is studied both experimentally and analytically. The fluid layer is confined by a rigid boundary at the bottom and a shear-free surface at the top. The fluid, which is initially quiescent, is heated by increasing the temperature of the lower surface at a constant time-rate. The experimental observation of the time of the onset of convection is made through the sudden change in variation of the temperature of the lower surface with respect to time. The onset is also observed through the sudden change in the fringe pattern created by holographic interferometry. Various layer depths are considered in order to observe the influence of this variable on the onset time. The analytical prediction is made by application of the linear amplification theory subject to boundary conditions similar to those of the experiment. Good agreement is found between the experimental and analytical results. Comparisons are also made with the experimental and analytical results available in the literature.

Effect of Solute Concentration Gradients on the Onset of Convection: Uniform and Nonuniform Initial Gradients

1986 ◽  
Vol 108 (4) ◽  
pp. 776-782 ◽  
Author(s):  
M. Kaviany ◽  
M. Vogel
Keyword(s):  
Temperature Gradient ◽  
Concentration Gradient ◽  
Fluid Layer ◽  
Onset Time ◽  
Solute Concentration ◽  
Concentration Gradients ◽  
Linear Amplification ◽  
Onset Of Convection ◽  
Gradient Layer ◽  
Good Agreement

The time of the onset of convection in a fluid layer, which is initially stably stratified and then heated from below in a transient manner, is determined experimentally and analytically. The initial stratification is due to the presence of a solute concentration gradient. In addition to initial linear solute concentration distributions two other specific initial solute concentration distributions are considered. In Case 1, a zero gradient layer is located underneath a nonzero and uniform gradient layer. In Case 2, the zero gradient layer is on the top. The linear amplification theory is applied to the prediction of the onset time. Interferometry is used as a means of determining the onset time experimentally. It is shown that since the adverse temperature gradient is concentrated near the bottom, any nonuniformity in the solute concentration gradient in this region reduces the effectiveness of the gradient in delaying the onset. Experimental and predicted results are in good agreement.

The Effect of Spatially Nonuniform Internal Heating on the Onset of Convection in a Horizontal Fluid Layer

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
A. V. Kuznetsov ◽  
D. A. Nield
Keyword(s):  
Fluid Layer ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Source Strength ◽  
Linear Quadratic ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Special Cases ◽  
Basic Temperature ◽  
Horizontal Fluid Layer

In this paper, we investigated the onset of natural convection in a horizontal fluid layer due to nonuniform internal heat generation, which is relevant to a number of geophysical situations. We investigated a number of special cases, which we believe are paradigmatic. Those include linear, quadratic, concentrated, and exponential source strength distributions. Our results show that those situations that lead to a reduction/increase in the size of the region in which the basic temperature gradient is destabilizing lead to an increase/decrease in stability.

scholarly journals Penetrative convection in a fluid saturated Darcy-Brinkman porous media with LTNE via internal heat source

2019 ◽  
Vol 8 (1) ◽  
pp. 546-558 ◽  
Author(s):  
Amit Mahajan ◽  
Reena Nandal
Keyword(s):  
Porous Media ◽  
Heat Generation ◽  
Fluid Layer ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Heat Extraction ◽  
Graphical Form ◽  
Nonlinear Stability Analysis ◽  
Penetrative Convection ◽  
Onset Of Convection

Abstract The present work involves the study of penetrative convection in an incompressible fluid-saturated porous media with local thermal non-equilibrium. The onset of convection evaluated linearly and nonlinearly for the system influenced by heat extraction and heat generation. Darcy-Brinkman law is employed to model the momentum equation and four type of internal heat generating function are considered which leads to thermo-convective instability within the fluid layer. Linear analysis carried out by using normal mode technique and nonlinear stability analysis has been done by energy method. Due to heat generation within the fluid layer and heat extraction through boundary, the subcritical instability may exist with higher possibility. Effects of various parameters as: inter-phase heat transfer parameter, Darcy-Brinkman number, porosity-modified conductivity ratio, and heat parameter are explored on Darcy-Rayleigh number by Chebyshev pseudospectral method as numerical form and graphical form.

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.

Throughflow effects on convective instability in superposed fluid and porous layers

1991 ◽  
Vol 231 ◽  
pp. 113-133 ◽  
Author(s):  
Falin Chen
Keyword(s):  
Porous Layer ◽  
Convective Instability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Vertical Direction ◽  
Single Layer ◽  
Layer Depth ◽  
Onset Of Convection ◽  
Precise Control ◽  
Porous Layers

We implement a linear stability analysis of the convective instability in superposed horizontal fluid and porous layers with throughflow in the vertical direction. It is found that in such a physical configuration both stabilizing and destabilizing factors due to vertical throughflow can be enhanced so that a more precise control of the buoyantly driven instability in either a fluid or a porous layer is possible. For ζ = 0.1 (ζ, the depth ratio, defined as the ratio of the fluid-layer depth to the porous-layer depth), the onset of convection occurs in both fluid and porous layers, the relation between the critical Rayleigh number Rcm and the throughflow strength γm is linear and the Prandtl-number (Prm) effect is insignificant. For ζ ≥ 0.2, the onset of convection is largely confined to the fluid layer, and the relation becomes Rcm ∼ γ2m for most of the cases considered except for Prm = 0.1 with large positive γm where the relation Rcm ∼ γ3m holds. The destabilizing mechanisms proposed by Nield (1987 a, b) due to throughflow are confirmed by the numerical results if considered from the viewpoint of the whole system. Nevertheless, from the viewpoint of each single layer, a different explanation can be obtained.

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).

Convection in a rotating cylinder. Part 2. Linear theory for low Prandtl numbers

1994 ◽  
Vol 262 ◽  
pp. 293-324 ◽  
Author(s):  
H. F. Goldstein ◽  
E. Knobloch ◽  
I. Mercader ◽  
M. Net
Keyword(s):  
Vertical Cylinder ◽  
Rigid Boundary ◽  
Onset Of Convection ◽  
Helium 4 ◽  
Carbon Dioxide Gas ◽  
Different Types ◽  
Concentric Pattern ◽  
Prandtl Numbers ◽  
The Relationship ◽  
Linear Stability Problem

The onset of convection in a low-Prandtl-number fluid confined in a uniformly rotating vertical cylinder heated from below is studied. The linear stability problem is solved for perfectly conducting stress-free or rigid boundary conditions at the top and bottom; the sidewalls are taken to be insulating and rigid. For these Prandtl numbers axisymmetric overstability leads to an oscillating concentric pattern of rolls. When the instability breaks axisymmetry the resulting pattern must in addition precess. The relationship between these two types of oscillatory behaviour is explored in detail. The complex interaction between different types of neutrally stable modes is traced out as a function of the Prandtl and Taylor numbers, as well as the aspect ratio. A qualitative explanation is provided for the multiplicity of modes of a given azimuthal wavenumber and its dependence on the parameters. Specific predictions are made for the Prandtl numbers 0.025, 0.49 and 0.78, corresponding to mercury, liquid helium 4 and compressed carbon dioxide gas.

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