Abstract
In this paper it is shown, using a numerical technique, that the boundary-layer equations for the flow near a continuously moving vertical plate with free convection are not unique. Further it is observed that when the buoyancy forces dominate the viscous forces there are no solutions. However, when the buoyancy forces oppose the motion of the plate, it is found that the numerical solution terminates in a singular manner which is of a different nature to any previously published results which have been obtained by solving non-linear ordinary differential equations where singular and dual solutions exist.
Zusammenfassung
In diesem Artikel wird mittels eines numerischen Verfahrens gezeigt, daß die Grenzschichtgleichungen für die Strömung in der Nähe einer kontinuierlich bewegten vertikalen Platte mit freier Konvektion nicht eindeutig sind.
Weiter wird beobachtet, daß es keine Lösungen gibt, wenn die Auftriebskräfte über die Zähigkeitskräfte dominieren.
Wenn jedoch die Auftriebskräfte der Plattenbewegung entgegentreten, wird herausgefunden, daß die numerische Lösung zu einer singulären Lösung wird, welche sich vor allen bisher veröffentlichten Resultaten unterscheidet, die durch Lösung der gewöhnlichen nichtlinearen Differentialgleichungen gefunden worden sind, bei denen singuläre und zweifache Lösungen existieren.
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Ingham, D.B. Singular and non-unique solutions of the boundary-layer equations for the flow due to free convection near a continuously moving vertical plate. Z. angew. Math. Phys. 37, 559–572 (1986). https://doi.org/10.1007/BF00945430
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DOI: https://doi.org/10.1007/BF00945430