Similarity solutions of a class of laminar three-dimensional boundary layer equations of power law fluids

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Abstract

An analysis of the possibility of finding similarity solutions to the three-dimensional, steady, incompressible, boundary layer equations in rectangular coordinates for a power law fluid is investigated. It is found that, in general, the two components of the mainstream flow must differ by at most a multiplicative constant and that these components are powers or exponentials of the x'-coordinate.

By assuming small cross-flows, the cross flow component may be generalized and found to be representable by a polynomial in the through flow variable, x'.

Résumé

On analyse la possibilité de trouver des solutions de similitude aux équations, dans un système de coordonnées trirectangulaires, de la couche limite d'un fluide incompressible en mouvement permanent obéissant à une fonction puissance. On trouve qu'en général les deux composantes du flux principal doivent différer par au plus une constante multiplicative et que ces composantes sont des puissances ou des exponentielles de la coordonnée de la direction du flux direct.

En supposant que les flux transversaux sont petits, la composante transversale peut être généralisée et on trouve qu'elle est représentée par un polynôme dans la variable du flux direct.

Zusammenfassung

Es wird die Möglichkeit untersucht, Ähnlichketslösungen zu den dreidimensionalen, stationären, inkompressiblen Grenzschichtsgleichungen in rechtwinkligen Koordinaten für eine Flüssigkeit zu finden, die einem Potenzgesetz unterliegt. Es ergibt sich, dass sich die zwei Komponenten der Hauptströmung im allgemeinen durch höchstens eine multiplikative Konstante unterscheiden müssen, und dass diese Komponenten Potenz-öder Exponentialfunktionen der Koordinate darstellen, die in die Durchstromungsrichtung weist.

Durch die Annahme kleiner Kreuzströmung kann die Kreuzströmungskomponente verallgemeinert werden. Sie lässt sich dann durch ein Polynom in der Durchflüssvariablen darstellen.

Реферат

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