Laminar film flow over a sphere

Gyure, Dale C.; Krantz, William B.

doi:10.1021/i100012a009

Cited by 30 publications

(3 citation statements)

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“…First of all, inertial effects have been neglected in the solution of the momentum equations. In a recent work, Gyure and Krantz (1983) showed that inertial effects were of extreme importance in the problem of free sur-face flow over a sphere. They point out that inertia results in a significant thinning of the liquid film thickness.…”

Section: Aiche Journalmentioning

confidence: 99%

The hydrodynamics of trickling flow in packed beds. Part I: Conduit models

1986

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The hydrodynamics of trickling flow in packed beds is modeled by representing the porous medium as an array of parallel conduits of circular cross section.First, a straight tube model is developed and analytical solutions are obtained for the relative permeabilities of the gas and liquid phases. Then a periodically constricted tube model is proposed and the equations of motion are solved numerically t o determine the effect that surface tension forces have on the relative permeabilities. The constricted tube model predicts that the relative permeabilities of the phases are appreciably sensitive to surface tension forces, a prediction that seems at odds with experimental observations. This discrepancy may be caused by the assumption of fully wetted surface area of particles employed in the model. The straight tube model confirms experimental results indicating that the liquid phase relative permeability is, for practical purposes, insensitive to the gas flow rate and to the gas-to-liquid density and viscosity ratios. Both conduit models show that the gas phase relative permeability curves are strong functions of the gas phase Reynolds number when this parameter is small. For large gas Reynolds numbers, a single curve for the relative permeability as a function of saturation is obtained. These trends are observed in previous experimental studies.

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Section: Aiche Journalmentioning

confidence: 99%

The hydrodynamics of trickling flow in packed beds. Part I: Conduit models

1986

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“…However previous studies of thin film flow over a sphere were confined purely to the hydrodynamic problem. Gyure & Krantz [14] used a perturbation analysis for low Reynolds numbers. Gribben [15] obtained an approximation by using the Pohlhausen integral momentum technique [16], which assumed an approximate velocity profile across the thickness of the film.…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer in the Flow of a Cold, Axisymmetric Jet Over a Hot Sphere

Shu¹,

Wilks

2013

Journal of Heat Transfer

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The heat transfer characteristics of thin film flow over a hot sphere resulting from a cold vertical jet of liquid falling onto the surface has been investigated. The underlying physical features have been illustrated by numerical solutions of high accuracy based on the modified Keller box method. The solutions for film thickness distribution are good agreement with those obtained approximately by using the Pohlhausen integral momentum technique and observed experimentally by using water as working fluid, thus providing a basic confirmation of the validity of the results presented.

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“…However previous studies of thin film flow over a sphere were confined purely to the hydrodynamic problem. Gyure & Krantz [1] used a perturbation analysis for low Reynolds numbers. Gribben [2] obtained an approximation using the Pohlhausen integral momentum technique, which assumed an approximate velocity profile across the thickness of the film; Hunt [3] obtained a numerical solution using the modified Keller box method, which accommodated the outer, free boundary.…”

Section: Introductionmentioning

confidence: 99%