A boundary-layer in an elastico-viscous fluid

Zusammenfassung Die Prandtlsche Grenzschichttheorie wird verallgemeinert, so dass sie die Nollschen «einfachen Flüssigkeiten» erfasst. Es wird bewiesen, dass bei Flüssigkeiten mit geringem «Erinnerungsvermögen» die in der Grenzschicht vorhandenen Spannungen denjenigen ähnlich sind, welche bei einer einfachen Schubbeanspruchung vorkommen.     

Group properties and exact solutions for two-dimensional flow of a non-newtonian fluid

The Group Properties and the associated Lie Algebra are developed for the equations of motion of the unsteady two-dimensional flow of a non-Newtonian fluid in cartesian coordinates. Then by using the full one-parameter infinitesimal transformation group and its subgroups a number of exact solutions are obtained.     

MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux

The steady laminar magnetohydrodynamic (MHD) boundary-layer flow past a wedge with constant surface heat flux immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated in this paper. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by means of an implicit finite-difference scheme known as the Keller-box method. Numerical results show that micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

On a boundary-layer controversy

Zusammenfassung Frater hat kürzlich gewisse Grenzschichtrechnungen für viskoelastische Flüssigkeiten kritisiert. Es wird versucht, diese Kritik zu entkräften.     

A note on a boundary-layer collision on a rotating sphere

A recent study of the unsteady boundary layer near the equator of a spinning sphere provided strong numerical evidence that the solution develops a singularity a finite time after the motion is initiated. In this paper we reformulate and complete the asymptotic structure proposed to describe this singularity. It is then self-consistent and provides convincing evidence of the accuracy of the computations and of the existence of the singularity.

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Zusammenfassung Eine neuere Untersuchung über die nicht-stationäre Grenzschicht nahe am Äquator einer rotierenden Kugel ergab starke numerische Evidenz für das Auftreten einer Singularität in der Lösung nach einer endlichen Zeit, vom Beginn der Bewegung gerechnet. In dieser Arbeit wird die asymptotische Struktur zur Beschreibung der Singularität neu formuliert und ergänzt. Sie wird selbstkonsistent und gibt ein wichtiges Zeugnis für die Genauigkeit der Berechnungen und für die Existenz der Singularität.

     

Surface waves in a non-newtonian incompressible liquid film

The perturbation techniques of Friedrichs, Keller and Benney ar used to derive the governing equations of long wavelength surface waves in a liquid film of a fluid which obeys a generalized Norton type consititutive relationship. Motions are assumed to be small so that acceleration terms are negligible. It is shown that the form of the surface wave equation depends verystrongly on the stress-strain-rate relationship at very small strain rates. The result is that dispension is a secondary effect, if the material response is soft at low strain rates, but may be dominant, if it is stiff.

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Zusammenfassung Die Methode der singulären Strömungsrechnung von Friedrichs, Keller und Benney wird zur Herleitung der, lange Oberflächenwellen in Flüssigkeitsfilmen beschreibenden Differentialgleichung benutzt und zwar für eine, einem verallgemeinerten Nortonschen Fliessgesetz gehochende viskose Flüssigkeit. Die Bewegung se ein langsames kriechen, so dass Beschleunigungsterme vernachlässigbar sind. Es wird gezeigt, dass die Form der Oberflächenwellen-Gleichung stark von der Spannungs-Dehnungs-Beziehung abhängt, indem Dispersion einen kleinen Effekt darstellt, falls das Material sich für kleine Verzerrungsgeschwindigkeiten weich verhält, aber einen entscheidenden Einfluss ausübt, wenn es hart ist.

     

A method for optimal control in boundary-layer flow

A methodology for active flow control which couples unsteady flow fields and controls is described. Active-control methods are used to maintain laminar flow in a region in which the natural instabilities lead to turbulent flow. The simplest form of control which might achieve this objective is the wave-cancellation approach. The case of boundary layer instability suppression is considered as the initial validation and test case. Control is effected through the injection or suction of fluid through a single orifice on the boundary. The optimal control theory provides an approach which does not require a priori knowledge of the flow. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Second-order thermal boundary-layer on a blunted wedge

Second-order thermal boundary-layer solutions are obtained for flow past a blunted wedge with constant wall temperature. Contributions due to longitudinal curvature and displacement effect are obtained by employing the G?rtler power series method. The first five terms of the series for each of the effects are computed. Since the region of validity of the results thus obtained is restricted in the streamwise direction, Eulerization technique is used to extend the radius of convergence to infinity.     

Second-order thermal boundary-layer on a blunted wedge

Summary Second-order thermal boundary-layer solutions are obtained for flow past a blunted wedge with constant wall temperature. Contributions due to longitudinal curvature and displacement effect are obtained by employing the Görtler power series method. The first five terms of the series for each of the effects are computed. Since the region of validity of the results thus obtained is restricted in the streamwise direction, Eulerization technique is used to extend the radius of convergence to infinity.

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Zusammenfassung Die thermische Grenzschichtlösung zweiter Ordnung wurde für die Strömung an einem abgestumpften Keil mit konstanter Temperatur bestimmt. Die Beiträge wegen Krümmung und Verdrängungsdicke wurden erhalten; die Methode der Görtler'schen Reihe wurde verwendet. Für jeden Effekt wurden die fünf ersten Koeffizienten berechnet. Da die Gültigkeit der Ergebnisse für grosse Werte der Variablen in Strömungsrichtung begrenzt ist, wurde die Technik der Euler'schen Konvergenzverbesserung verwendet, um den Konvergenzradius bis ins Unendliche zu erstrecken.

     

Quadrature formulas for functions with a boundary-layer component

Quadrature formulas for one-variable functions with a boundary-layer component are constructed and studied. It is assumed that the integrand can be represented as the sum of a regular and a boundary-layer component, the latter having high gradients that reduce the accuracy of classical quadrature formulas, such as the trapezoidal and Simpson rules. The formulas are modified so that their error is independent of the gradients of the boundary-layer component. Results of numerical experiments are presented.     

Heat transfer in linearl flows of non-newtonian fluids

The average rate of heat transferred to the channel wall when a hot incompressible third-order fluid, in rectilinear motion, flows (i) between two infinite parallel plates and (ii) in a circular tube is studied. A heat transfer coefficient has been evaluated for several values of a non-Newtonian parameter which is a measure of non-linear effects in the fluid. Enhancement of the heat transfer coefficient is found for those fluids which exhibit large strain rate gradients in the region of the channel wall.

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Zusammenfassung Untersucht wird die durchschnittliche Wärmeübertragung an die Kanalwand für eine erhitzte inkompressible Flüssigkeit dritter Ordnung, die sich geradlinig bewegt (i) zwischen zwei unbegrenzten, parallelen Platten und (ii) in einem runden Rohr. Ein Wärmeübertragungskoeffizient ist für mehrere Werte eines nicht-Newtonischen Parameters berechnet worden, der ein Mass der nicht linearen Effekte in der Flüssigkeit darstellt. Es wird eine Vergrösserung des Wärmeübertragungskoeffizienten für jene Flüssigkeiten gefunden, die in der Nähe der Kanalwand grosse Gradienten der Verzerrungsgeschwindigkeit aufweisen.

     

A novel approach to the solution of boundary-layer problems

By replacing a differential equation boundary-layer problem by its discrete lattice equivalent we are able to treat the resulting equation as a regular perturbation problem. We obtain the solution on the lattice as a regular perturbation series in inverse powers of the lattice spacing. To obtain the answer to the continuum problem we extrapolate the solution to the lattice problem to zero lattice spacing. This extrapolation, which is a Padé-like procedure, yields good numerical results for a wide range of problems.     

On stationary problems in magnetohydrodynamics of non-newtonian media

Moscow. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 4, pp. 120–127, July–August, 1992.     

Multiple solutions of mixed convection boundary-layer approximations in a porous medium

This note deals with a theoretical analysis of the existence, non-uniqueness and non-existence of similarity solutions of the two-dimensional mixed convection boundary-layer flow over a vertical surface with a power law temperature. Here, it is assumed that the surface is embedded in a saturated porous media. The results depend on the power law exponent and the ratio of the Rayleigh to Péclet numbers. It is shown, under certain circumstance, that the problem has an infinite number of solutions.     

Random attractors of stochastic non-newtonian fluids

The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors ΛH(ω) in H; Secondly, we prove the existence of random attractors ΛV (ω) in V . Then we verify regularity of the random attractors by showing that ΛH(ω) = ΛV (ω), which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.     

Refined-mesh interpolation method for functions with a boundary-layer component

Linear and quadratic spline interpolation methods for a one-variable function with a boundary-layer component are examined. It is shown that the interpolation method for such a function leads to considerable errors when applied on a uniform mesh. The error of linear and quadratic spline interpolations on meshes that are refined in the boundary layer is estimated. Numerical results are presented.