Stokes flow around slowly rotating concentric previous spheres

• Autorzy: Srivastava D. K. , Yadav R. R. , Yadav S.

Identyfikatory

DOI

10.2478/meceng-2013-0011

Warianty tytułu

PL

Przepływ stokesowski wokół powolnie wirujących koncentrycznych kul przepuszczalnych

• Języki publikacji: EN

Abstrakty

EN

In this paper, the problem of concentric pervious spheres carrying a fluid sink at their centre and rotating slowly with different uniform angular velocities Ω₁, Ω₂ 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 Ω₁, 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 Ω₁, while outer rotates at infinity with angular velocity Ω₂; have been deduced. The corresponding variation of torque with respect to sink parameter has been shown via figures. AMS subject classification – 76 D07.

PL

W artykule rozważa się problem koncentrycznych kul przepuszczalnych, ze zlewem płynu w centrum, które wirują powoli wokół średnicy z jednostajnymi prędkościami kątowymi Ω₁ i Ω₂. Analiza wykazała, że istnieje tylko azymutalny składnik prędkości, a moment obrotowy i szybkość rozpraszania energii są w istniejących warunkach wyznaczane analitycznie. Wyprowadzono wyrażenie na moment obrotowy na powierzchni wewnętrznej kuli powolnie wirującej z jednostajną prędkością kątową Ω₁, podczas gdy kula zewnętrzna także powolnie wiruje z jednostajną prędkością kątową Ω₂. Zbadano także przypadki szczególne, takie jak: (i) kula wewnętrzna jest nieruchoma (tzn. Ω₁ = 0), podczas gdy kula zewnętrzna wiruje z jednostajną prędkością kątową Ω₂, (ii) kula zewnętrzna jest nieruchoma (tzn. Ω₂ = 0), podczas gdy kula wewnętrzna wiruje z jednostajną prędkością kątową Ω₁, (iii) kula wewnętrzna wiruje z jednostajną prędkością kątową Ω₁, podczas gdy kula zewnętrzna wiruje w nieskończonej odległości z prędkością kątową Ω₂. Na wykresach przedstawiono zależności między zmianami momentu obrotowego a parametrami zlewu.

Słowa kluczowe

EN

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

PL

wirowanie kul koncentrycznych; zlew płynu; lepki powolny przepływ; aproksymacja Stokes'a

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2013
• Tom: Vol. LX, nr 2
• Strony: 165--184
• Opis fizyczny: Bibliogr. 55 poz., rys.

Twórcy

autor

Srivastava D. K.

• Department of Mathematics; B.S.N.V. Post Graduate College (University of Lucknow, Lucknow); Lucknow-226001, U.P., India

autor

Yadav R. R.

• Department of Mathematics, University of Lucknow, Lucknow (U.P.), India

autor

Yadav S.

• Department of Mathematics, University of Lucknow, Lucknow (U.P.), India

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Uwagi

EN

[from author] I acknowledge my sincere thanks to the anonymous referees for their invaluable comments and suggestions to improve the quality of the manuscript. I also express my thanks and gratitude to the authorities of B.S.N.V. Post Graduate College, Lucknow (Uttar Pradesh), India, for providing the basic infra structure facilities throughout the preparation of this work at the department of mathematics. Third author (SY) is thankful to University Grants Commission, New Delhi, to provide Junior Research Fellowship.