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Stratification effects on transient Stokes flow in the presence of a permeable boundary

Schichtenbildungseffekte von Stokes Strömungen in Gegenwart von durchlässigen Begrenzungen

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Abstract

The transient unbounded flow of a stratified viscous fluid over an oscillating permeable boundary has been considered. The viscosity and the density of the fluid have been assumed to decay exponentially in the direction normal to the bounding permeable wall. The initial value problem associated with the resulting diffusion equation, subject to the Beavers-Joseph boundary condition, has been solved analytically. The solution for the transient velocity has been expressed in terms of error and exponential functions of complex arguments. The effects of fluid stratification and the bounding porous medium on the fluid velocity have been analyzed.

Zusammenfassung

Die eingeschwungene, freie Strömung eines geschichteten viskosen Fluids über einer schwingenden, durchlässigen Begrenzung wird in dieser Arbeit betrachtet. Die Viskosität und die Dichte des Fluids wird dabei als exponentiell abnehmend in Richtung der Flächennormalen der durchlässigen Begrenzung angesetzt. Das Anfangswertproblem, welches mit der sich aus der Beavers-Joseph-Randbedingung ergebenden Diffusionsgleichung verknüpft ist, wird auf analytischem Wege gelöst. Die Lösung für das Geschwindigkeitsfeld wird in Abhängigkeiten der Error- und exponentieller Funktionen mit komplexen Argumenten dargestellt. Die Einflüsse der Schichtenbildung und der durchlässigen Begrenzung auf die Geschwindigkeit des Fluids werden analysiert.

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Authors and Affiliations

  1. Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    Ashok K. Singh

  2. Department of Mathematics & Statistics, College of Science, Sultan Qaboos University, P.O.Box 36, Al Khod, Muscat, Oman

    Nirmal C. Sacheti & Pallath Chandran

Authors
  1. Ashok K. Singh
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  2. Nirmal C. Sacheti
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  3. Pallath Chandran
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Correspondence to Nirmal C. Sacheti.

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Singh, A., Sacheti, N. & Chandran, P. Stratification effects on transient Stokes flow in the presence of a permeable boundary. Forsch Ingenieurwes 70, 67–73 (2005). https://doi.org/10.1007/s10010-005-0012-2

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  • DOI: https://doi.org/10.1007/s10010-005-0012-2

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