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Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

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Stokes Flow Around Slowly Rotating Concentric Pervious Spheres

Deepak Kumar Srivastava
  • Department of Mathematics; B.S.N.V. Post Graduate College (University of Lucknow, Lucknow); Lucknow-226001, U.P., India
  • :
/ Raja Ram Yadav
  • Department of Mathematics, University of Lucknow, Lucknow (U.P.), India
  • :
/ Supriya Yadav
  • Department of Mathematics, University of Lucknow, Lucknow (U.P.), India
  • :
Published Online: 2013-07-05 | DOI: https://doi.org/10.2478/meceng-2013-0011

In this paper, the problem of concentric pervious spheres carrying a fluid sink at their centre and rotating slowly with different uniform angular velocities 1, 2 about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists and the torque, rate of dissipated energy is found analytically in the present situation. The expression of torque on inner sphere rotating slowly with uniform angular velocity 1, while outer sphere also rotates slowly with uniform angular velocity Ω2, is evaluated. The special cases like, (i) inner sphere is fixed (i.e. Ω1 = 0), while outer sphere rotates with uniform angular velocity Ω2, (ii) outer sphere is fixed (i.e. Ω2 = 0), while inner sphere rotates with uniform angular velocity Ω1, (iii.) inner sphere rotates with uniform angular velocity 1, while outer rotates at infinity with angular velocity 2; have been deduced. The corresponding variation of torque with respect to sink parameter has been shown via figures. AMS subject classification - 76 D07

Streszczenie

W artykule rozwaza sie problem koncentrycznych kul przepuszczalnych, ze zlewem płynu w centrum, które wiruja powoli wokół srednicy z jednostajnymi predkosciami katowymi Ω1 i Ω2. Analiza wykazała, ze istnieje tylko azymutalny składnik predkosci, a moment obrotowy i szybkosc rozpraszania energii sa w istniejacych warunkach wyznaczane analitycznie. Wyprowadzono wyrazenie na moment obrotowy na powierzchni wewnetrznej kuli powolnie wirujacej z jednostajna predkoscia katowa Ω1, podczas gdy kula zewnetrzna takze powolnie wiruje z jednostajna predkoscia katowa Ω2. Zbadano takze przypadki szczególne, takie jak: (i) kula wewnetrzna jest nieruchoma (tzn. Ω1 = 0), podczas gdy kula zewnetrzna wiruje z jednostajna predkoscia katowa Ω2, (ii) kula zewnetrzna jest nieruchoma (tzn. Ω2 = 0), podczas gdy kula wewnetrzna wiruje z jednostajna predkoscia katowa Ω1, (iii) kula wewnetrzna wiruje z jednostajna predkoscia katowa Ω1, podczas gdy kula zewnetrzna wiruje w nieskonczonej odległosci z predkoscia katowa Ω2. Na wykresach przedstawiono zaleznosci miedzy zmianami momentu obrotowego a parametrami zlewu.

Keywords : rotation of concentric spheres; fluid sink; slow viscous flow; Stokes approximation

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Published Online: 2013-07-05

Published in Print: 2013-06-01


Citation Information: Archive of Mechanical Engineering. Volume 60, Issue 2, Pages 165–219, ISSN (Print) 0004-0738, DOI: https://doi.org/10.2478/meceng-2013-0011, July 2013

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