Thermal convection in a Hele-Shaw cell

Hartline, Beverly Karplus; Lister, C. R. B.

doi:10.1017/s0022112077000202

Cited by 82 publications

(31 citation statements)

References 10 publications

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“…Such studies have been performed among others by Elder (1967), Hartline and Lister (1977), Koster and Miiller (1982), and recently by Biihler et al (1987). The latter authors presented experimental and numerical results of natural convection in a square Hele-Shaw cell, heated at the lower and cooled at the upper boundary.…”

Section: Introductionmentioning

confidence: 85%

Flow and temperature measurement of natural convection in a Hele-Shaw cell using a thermo-sensitive liquid-crystal tracer

Ozawa

Müller²,

Kimura

et al. 1992

Experiments in Fluids

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The temperature and flow field of natural convection in a Hele-Shaw cell is visualized by using a liquid-crystal tracer. The tracer photographs obtained by this method are compared with the interferograms of previous experiments using the same experimental setup, and the applicability of the present methods is validated. Quantitative data of the temperature and velocity were obtained by applying a colour-image-processing technique to the visualized images.

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Section: Introductionmentioning

confidence: 85%

Flow and temperature measurement of natural convection in a Hele-Shaw cell using a thermo-sensitive liquid-crystal tracer

Ozawa

Müller²,

Kimura

et al. 1992

Experiments in Fluids

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“…In summary, the study considered in the second formulation showed that the frequency ratio plays an important role in controlling the onset of convection. From a physical point of view, our motivation was based on the fact that the Hele-Shaw cells are widely used to simulate two-dimensions flows in porous media [31][32][33][34][35]. Therefore, this linear study can serve as model to investigate the influence of the quasi-periodic gravitational modulation on the threshold of convective instability in porous medium.…”

Section: Resultsmentioning

confidence: 99%

Effect of quasi-periodic gravitational modulation on the convective instability in Hele-Shaw cell

Boulal

Aniss

Belhaq

et al. 2008

International Journal of Non-Linear Mechanics

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The aim of the present paper is to examine the effect of a quasi-periodic gravitational modulation on the onset of convective instability in Hele-Shaw cell. The quasi-periodic modulation considered here consists in a modulation having two incommensurate frequencies. This study is an extension of a previous work by Aniss et al. [10] in which only a periodic gravitational modulation was considered. We have shown that for P r = O(1) or P r >> 1, the gravitational modulation has no effect on the convective threshold as expected. However, for P r = O(ǫ 2 ), it turns out that a modulation with two incommensurate frequencies has a stabilizing or a destabilizing effect strongly depending on the frequencies ratio.

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“…As reported by Hartline and Lister (1977), the Hele-Shaw cell could be a powerful tool for quantitative studies of two-dimensional flows in porous media by properly identifying the Hele-Shaw permeability, K , in terms of the slot width d and the cell width Y as…”

Section: Heat Transfer Measurementmentioning

confidence: 99%

Experimental Study on Oscillatory Natural Convection in a Hele-Shaw Cell due to Unstably Heated Side

2008

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The oscillatory motion of natural convection in a porous medium has been investigated experimentally using a Hele-Shaw cell technique. The cell has been heated on the lower half and cooled on the upper half along the same vertical sidewall. Flows have been visualized using the pH indicator method. Photographs of natural convection patterns as well as average Nusselt number data have been presented for different Rayleigh numbers. Oscillatory motion of natural convection has been observed for large enough Rayleigh numbers and the critical Rayleigh number has been estimated to be between 120 and 450. Scaling analysis has been conducted to understand the heat transfer and the oscillating mechanism. According to the scaling analysis, it has been found that the average Nusselt number is proportional to the square root of the Rayleigh number, and that the oscillation frequency is proportional to the Rayleigh number. Obtained experimental data support the scaling analysis.

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Thermal convection in a Hele-Shaw cell

Cited by 82 publications

References 10 publications

Flow and temperature measurement of natural convection in a Hele-Shaw cell using a thermo-sensitive liquid-crystal tracer

Flow and temperature measurement of natural convection in a Hele-Shaw cell using a thermo-sensitive liquid-crystal tracer

Effect of quasi-periodic gravitational modulation on the convective instability in Hele-Shaw cell

Experimental Study on Oscillatory Natural Convection in a Hele-Shaw Cell due to Unstably Heated Side

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