Boundary of monotonic and oscillatory convective stability of a horizontal fluid layer

1992 ◽  
Vol 32 (6) ◽  
pp. 861-866
Author(s):  
V. I. Yudovich
Keyword(s):  
Fluid Layer ◽  
Convective Stability ◽  
Horizontal Fluid Layer

Onset of thermal convection in a horizontal fluid layer under ramp heating

2002 ◽  
Author(s):  
Dae Jun Yang ◽  
Jake Kim ◽  
Chang Kyun Choi ◽  
In Gook Hwang
Keyword(s):  
Thermal Convection ◽  
Fluid Layer ◽  
Horizontal Fluid Layer

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.

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.

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).

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