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Upper and lower bounds for the pressure error in the rectilinear flow along a slot with a pressure gradient

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Summary

The rectilinear flow of a second-order fluid is considered between two infinitely wide and long parallel plates. The bottom plate is at rest and has a longitudinal slot in the direction of the flow, while the top plate moves in the flow direction with a constant speed. Upper and lower bounds for the pressure error are obtained by the use of the maximum principle applied to harmonic functions.

Zusammenfassung

Es wird die geradlinige Strömung einer Flüssigkeit zweiter Ordnung zwischen zwei unendlich ausgedehnten parallelen Platten untersucht. Die mit einer rechteckigen, in Strömungsrichtung orientierten Nute versehene Grundplatte befindet sich in Ruhe, wohingegen die glatte Deckplatte sich mit konstanter Geschwindigkeit in Strömungsrichtung bewegt. Untere und obere Schranken für die Abweichung des Druckes infolge der Nute (“pressure error”) werden durch Anwendung des Maximumprinzips auf harmonische Funktionen berechnet.

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Authors and Affiliations

  1. Department of Applied Mechanics and Engineering Science, University of Michigan, 48 109, Ann Arbor, Mich., USA

    K. R. Rajagopal

  2. School of Mathematical Sciences, Flinders University, 5042, Bedford Park, S.A., Australia

    R. R. Huilgol

Authors
  1. K. R. Rajagopal
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  2. R. R. Huilgol
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Rajagopal, K.R., Huilgol, R.R. Upper and lower bounds for the pressure error in the rectilinear flow along a slot with a pressure gradient. Rheol Acta 18, 456–462 (1979). https://doi.org/10.1007/BF01736951

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  • DOI: https://doi.org/10.1007/BF01736951

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