A numerical study of the Bénard cell

Cabelli, A.; Davis, G. de Vahl

doi:10.1017/s002211207100034x

Cited by 11 publications

(6 citation statements)

References 16 publications

(4 reference statements)

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“…After each half-time increment, an updated estimate was made of the stream function by solving Equation ( 15). A point over-relaxation procedure was used (Smith, 1971) with the over-relaxation parameter being empirically varied in successive solution processes to minimize the required number of iterations (Cabelli, 1970). A relative convergence criterion was used to terminate this stage.…”

Section: St-rt Modelmentioning

confidence: 99%

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The behavior of a power‐law fluid flowing through a sudden expansion: Part I. A numerical solution

1975

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The numerical solution was obtained using an Alternating Direction Implicit method. Both a stream tube-real tube and a real tube-real tube model were investigated. The conditions for significant diffusion of momentum upstream of the plane of expansion are specified. Eddy characteristics and flow field development are predicted as functions of the flow behavior index n and of the Reynolds number. Some results showing the influence of the expansion ratio are presented. Experimental data are presented to verify the numerical model. Streak photography was used for recording flow patterns and a multiple flash technique was used for point velocity measurement. Fluid properties were determined with an R16 Weissenberg Rheogoniometer. The measured reattachment lengths, the recorded flow patterns, and the developing axial velocity field all show excellent agreement with the numerical predictions.

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Section: St-rt Modelmentioning

confidence: 99%

“…Douglas (1962) showed that when a similar method is used, the overall accuracy improves from first to second order in time. An accelerated rate of convergence and a reduction in computation time of 10 to 15% was obtained by empirically varying the time step after each iteration (Cabelli, 1970).…”

Section: St-rt Modelmentioning

confidence: 99%

The behavior of a power‐law fluid flowing through a sudden expansion: Part I. A numerical solution

1975

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“…Among dissipative systems observed, Turing's reaction-diffusion and Rayleigh-Bénard (R-B) convection are the two representative systems for spatial pattern formation, and they have been actively studied because of their analytical and experimental accessibility. [13][14][15][16][17][18][19][20][21][22][23][24][25] Although the appeared structures either in scales or formation process are different for diverse dissipative systems, their morphologies are similar. 26 For example, line patterns, square-grid arrays, zig-zag patterns etc.…”

Section: Introductionmentioning

confidence: 99%

Turing patterns with high-resolution formed without chemical reaction in thin-film solution of organic semiconductors

Xiang

et al. 2022

Preprint

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Regular patterns can form spontaneously in chemical reaction-diffusion systems under non-equilibrium conditions as proposed by Alan Turing. Here, we found that regular patterns can be generated in uphill-diffusion solution systems without a chemical reaction process through both in-situ and ex-situ observations. Organic semiconductor solution is confined between two parallel plates with controlled micron/submicron-meter distance, to minimize convection of the liquid and avoid spinodal precipitation at equilibrium. The solvent evaporation concentrates the solution gradually into an oversaturated non-equilibrium condition, under which a phase-transition occurs and ordered concentration-waves are generated. By proper tuning of the experimental parameter, multiple regular patterns with micro/nano-meter scaled features (line, square-grid, zig-zag, and fence-like patterns etc.) were observed. We explain the observed phenomenon as Turing-pattern generation resulted from uphill-diffusion and solution oversaturation. The generated patterns in the solutions can be condensed onto substrates to form structured micro/nanomaterials. We have fabricated organic semiconductor devices with such patterned materials to demonstrate the potential applications. Our observation may serve as a milestone in the progress towards a fundamental understanding of pattern formation in nature, like in biosystem, and pave a new avenue in developing self-assembling techniques of micro/nano structured materials.

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“…Other data not available. Fick's Law apparently valid Very few collapse pressure and collapse rate data available, and these pertain to mono layers at the air-water interface [52 ] Measurements available for a variety of surfactants at the air-water and oil-water [55] interface, but little agreement amongst investigators useful in constructing semi -em pirical models of the developed convection for purposes of predicting heat or mass transfer accompanying interfacial convection [57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

Interfacial Hydrodynamics: An Over View

Berg¹

1982

Canadian Metallurgical Quarterly

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A fluid interface may promote spontaneous flow, or, particularly if laden with a surface-active agent, may act to suppress flow in its vicinity. In either event, the effect is the result of locally unbalanced forces at the interface. The resulting flows may be chaotic (interfacial turbulence) or orderly (cellular convection), steady, periodic or intermittent. They may significantly increase heat and mass transfer rates and alter contacting patterns in fluid-phase contacting equipment. Flow suppression due to surface-active agents may also assume a variety offorms and may significantly reduce transfer rates. These phenomena are classified, illustrated and rationalized in terms of hydrodynamic theory. Recent research developments and implications for metallurgical systems are given. Resume-Uneinterface fluide peut generer un ecoulement spontane, ou, si elle est recouverte par un agent tensio-actif, supprimer cet ecoulement. Dans les deux cas, l'effet observe est dfI a des forces locales non equilibrees it l'interface. Les ecoulements resultants peuvent etre irreguliers (turbulence interfaciale) ou ordonnes (convection localisee), stables, periodiques ou intermittents. Ils peuvent augmenter de fa<;on appreciable les taux de transfert de masse et de chaleur et modifier la nature du contact du fluide avec les equipements. Les agents tensio-actifs modifient grandement les profils des ecoulements et peuvent reduire de fa<;on marquee les taux de transfert de masse et de chaleur. Tous ces differents phenomenes sont classifies, illustres et analyses it l'aide de la theorie de l'hydrodynamique des fluides. De nouveaux developpements de recherche ainsi que les implications pour les systemes metallurgiques sont presentes.

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A numerical study of the Bénard cell

Cited by 11 publications

References 16 publications

The behavior of a power‐law fluid flowing through a sudden expansion: Part I. A numerical solution

The behavior of a power‐law fluid flowing through a sudden expansion: Part I. A numerical solution

Turing patterns with high-resolution formed without chemical reaction in thin-film solution of organic semiconductors

Interfacial Hydrodynamics: An Over View

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