Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid
The problem of concentric pervious spheres carrying a fluid source 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 couple, rate of dissipated energy...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2009/740172 |
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| _version_ | 1832555568228728832 |
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| author | Deepak Kumar Srivastava |
| author_facet | Deepak Kumar Srivastava |
| author_sort | Deepak Kumar Srivastava |
| collection | DOAJ |
| description | The problem of concentric pervious spheres carrying a fluid source 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 couple, rate of dissipated energy is found analytically in the present situation. The expression of couple 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, and (iii) inner sphere rotates with uniform angular velocity Ω1, while outer sphere rotates at infinity with angular velocity Ω2, have been deduced. |
| format | Article |
| id | doaj-art-e1dfa4db853148ef822be8a1ed722d8d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e1dfa4db853148ef822be8a1ed722d8d2025-02-03T05:47:58ZengWileyJournal of Applied Mathematics1110-757X1687-00422009-01-01200910.1155/2009/740172740172Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous FluidDeepak Kumar Srivastava0Department of Mathematics, B.S.N.V. Post Graduate College, University of Lucknow, Lucknow 226001, IndiaThe problem of concentric pervious spheres carrying a fluid source 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 couple, rate of dissipated energy is found analytically in the present situation. The expression of couple 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, and (iii) inner sphere rotates with uniform angular velocity Ω1, while outer sphere rotates at infinity with angular velocity Ω2, have been deduced.http://dx.doi.org/10.1155/2009/740172 |
| spellingShingle | Deepak Kumar Srivastava Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid Journal of Applied Mathematics |
| title | Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid |
| title_full | Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid |
| title_fullStr | Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid |
| title_full_unstemmed | Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid |
| title_short | Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid |
| title_sort | slow rotation of concentric spheres with source at their centre in a viscous fluid |
| url | http://dx.doi.org/10.1155/2009/740172 |
| work_keys_str_mv | AT deepakkumarsrivastava slowrotationofconcentricsphereswithsourceattheircentreinaviscousfluid |