Nicht-Newtonsche Flüssigkeiten II. Drehströmungen Ostwald-de Waelescher nicht-Newtonscher Flüssigkeiten

Mitschka, P.

doi:10.1135/cccc19642892

Cited by 55 publications

(26 citation statements)

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“…As noted by Mitschka (1964), the leading-order boundary-layer equations admit a similarity solution in the form…”

Section: Formulationmentioning

confidence: 99%

“…However, in the limit of large Reynolds number some progress can be made as there is a readily available self-similar form which is a simple generalization of that presented by von Kármán (1921) to the case of a power-law fluid. This is the direction chosen by Mitschka (1964) and AKM and we follow the same approach here, albeit somewhat more formally. We shall proceed with a familiar boundary-layer methodology, assuming that Re 1.…”

Section: Formulationmentioning

confidence: 99%

“…We shall show that the results of AKM and Mitschka (1964) are in fact only accurate over a range of shear-thinning fluids and miss the fact that their solutions for shear-thickening fluids are non-differentiable at a critical location in the layer. Furthermore, the inconsistencies of the numerical work of AKM and Mitschka (1964) for highly shear-thinning fluids are again shown to be associated with an incorrect consideration of the far-field behaviour. Throughout § 3 we shall comment on the appropriateness of the boundary-layer solutions obtained in the broader context of the global flow field, that is, on the boundary-layer free-stream matching process.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Andersson, de Korte & Meland (2001) (subsequently referred to herein as AKM) have revisited the problem of the flow of a non-Newtonian fluid over a rotating disk, which was first considered by Mitschka (1964). The motivation of AKM was to address the 'accuracy' of the numerical solutions presented by Mitschka (1964) in the region of highly shear-thinning fluids and to extend the numerical results to a greater range of shear-thickening fluids.…”

Section: Introductionmentioning

confidence: 99%

“…The motivation of AKM was to address the 'accuracy' of the numerical solutions presented by Mitschka (1964) in the region of highly shear-thinning fluids and to extend the numerical results to a greater range of shear-thickening fluids. As we shall show, there are some issues to be addressed both in the assumptions and the analysis of the work of AKM.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic matching constraints for a boundary-layer flow of a power-law fluid

Denier

Hewitt

2004

J. Fluid Mech.

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We reconsider the three-dimensional boundary-layer flow of a power-law (Ostwaldde Waele) rheology fluid, driven by the rotation of an infinite rotating plane in an otherwise stationary system. Here we address the problem for both shear-thinning and shear-thickening fluids and show that there are some fundamental issues regarding the application of power-law models in a boundary-layer context that have not been mentioned in previous discussions. For shear-thickening fluids, the leading-order boundary-layer equations are shown to have no suitable decaying behaviour in the far field, and the only solutions that exist are necessarily non-differentiable at a critical location and of 'finite thickness'. Higher-order effects are shown to regularize the singularity at the critical location. In the shear-thinning case, the boundary-layer solutions are shown to possess algebraic decay to a free-stream flow. This case is known from the existing literature; however here we shall emphasize the complexity of applying such solutions to a global flow, describing why they are in general inappropriate in a traditional boundary-layer context. Furthermore, previously noted difficulties for fluids that are highly shear thinning are also shown to be associated with the imposition of incorrect assumptions regarding the nature of the far-field flow. Based on Newtonian results, we anticipate the presence of non-uniqueness and through accurate numerical solution of the leading-order boundary-layer equations we locate several such solutions. IntroductionThe flow induced by the rotation of an infinite impermeable plane submerged in a viscous incompressible Newtonian fluid is described by a long-standing and classical (exact) solution of the Navier-Stokes equations. The solutions and their extensions have found many uses in industrial devices and processes, and they provide a test bed for the development of three-dimensional cross-flow instability theories and have applications to geophysics in Ekman pumping models and the decay of geostrophic flows.A similarity reduction of the fully nonlinear governing partial differential equations was provided by von Kármán (1921) for the flow induced by a rotating disk in a stationary fluid. This was later extended by Bödewadt (1940) to the problem of a rigidly rotating fluid above a stationary disk, with the obvious later continuation of the solutions across the intervening range of the parameter space for a rotating disk in a rotating fluid.In terms of the characteristics of the solutions to the Newtonian rotating-disk equations, it is well known that an enormously rich and detailed structure exists, spanned

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“…As noted by Mitschka (1964), the leading-order boundary-layer equations admit a similarity solution in the form…”

Section: Formulationmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic matching constraints for a boundary-layer flow of a power-law fluid

Denier

Hewitt

2004

J. Fluid Mech.

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Coupled Mass and Heat Transfer between a Cone and a Power‐Law Fluid

Elperin

Fominykh

2004

Chem Eng & Technol

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Coupled mass and heat transfer between a cone and a non-Newtonian fluid was studied when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). Convective heat and mass transfer between a laminar flow and a stationary cone and between a rotating cone and a quiescent fluid is investigated. Solutions of both problems are found in the form of the dependencies of Sherwood number vs. Reynolds and Schmidt numbers. Coupled thermal effects during dissolution and solute concentration level effect on the rate of mass transfer are investigated. It is found that the rate of mass transfer between a cone and a non-Newtonian fluid increases with the increase of the solute concentration level. The suggested approach is valid for high Peclet and Schmidt numbers. Isothermal and nonisothermal cases of dissolution are considered whereby the latter is described by the coupled equations of mass and heat transfer. It is shown that for positive dimensionless heat of dissolution, K > 0, thermal effects cause the increase of the mass transfer rate in comparison with the isothermal case. On the contrary, for K < 0 thermal effects cause the decrease of the mass transfer rate in comparison with the isothermal case. The latter effect becomes more pronounced with the increase of the concentration level of the solute in a solvent.

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Schnell laufende Rührwerke bei laminarer Strömung. Teil II: Simulation des mechanischen Rührens durch einen rotierenden niedrigen Zylinder

Wichterle¹,

Prošková²,

Ulbrecht³

1971

Chemie Ingenieur Technik

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Ausgehend von den dynamischen Einwirkungen eines rotierenden niedrigen Zylinders auf eine Flüssigkeit werden verschiedene Eigenschaften des Geschwindigkeitsfeldes in der nahen Umgebung schnell laufender Rührwerke untersucht. Es wird eine Hypothese über die Additivität der Einflüsse der einzelnen Flächen eines rotierenden Köpers aufgestellt. Unter diesen Voraussetzungen kann die Abhängigkeit des Drehmomentes von Rührwerken von deren geometrischer Anordnung und dem Fließindex über die Kenntnis der Drehmomente bei der Rotation einfacher Körper bestimmt werden. Die theoretischen Schlußfolgerungen stimmen mit experimentellen Ergebnissen gut überein.

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Nicht-Newtonsche Flüssigkeiten II. Drehströmungen Ostwald-de Waelescher nicht-Newtonscher Flüssigkeiten

Cited by 55 publications

References 0 publications

Asymptotic matching constraints for a boundary-layer flow of a power-law fluid

Asymptotic matching constraints for a boundary-layer flow of a power-law fluid

Coupled Mass and Heat Transfer between a Cone and a Power‐Law Fluid

Schnell laufende Rührwerke bei laminarer Strömung. Teil II: Simulation des mechanischen Rührens durch einen rotierenden niedrigen Zylinder

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