Summary
The behavior of laminar free-convection boundary layers at large Prandtl number is considered. Plane and axisymmetric flows are treated simultaneously in terms of a unified formulation. Flow and heat-transfer quantities are expressed in terms of expansions within an inner and an outer layer, both of which lie inside the Prandtl's viscous layer. The first two approximations are given in general and the first three approximation for self-similar flows. The inner solutions provide information on skin friction and heat transfer, whereas the outer solutions determine the mass flow rate induced by buoyancy. Numerical results are given for the selfsimilar flows.
Zusammenfassung
Das Verhalten von laminaren Grenzschichten bei freier Konvektion wird für grosse Prandtl-Zahlen behandelt. Strömungs-und Wärmeübergangs-Grössen werden ausgedrückt mit Hilfe einer Entwicklung in einer inneren und äusseren Schicht, die beide innerhalb der Prandtlschen Reibungsschicht liegen. Die zwei ersten Näherungen des allgemeinen Falles werden angegeben, sowie die ersten drei Glieder für ähnliche Lösungen. Die innere Lösung ergibt die Reibung und den Wärmeübergang, während die äussere Lösung den durch Auftrieb induzierten Massenstrom liefert. Numerische Ergebnisse werden für Ähnlichkeits-Lösungen angegeben.
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Eshghy, S. Free-convection layers at large prandtl number. Journal of Applied Mathematics and Physics (ZAMP) 22, 275–292 (1971). https://doi.org/10.1007/BF01591411
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DOI: https://doi.org/10.1007/BF01591411