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Slow motion of a rotating circular cylinder through a micropolar fluid

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Języki publikacji
EN
Abstrakty
EN
Presented is an analytical solution to creeping flow of a micropolar fluid past a rotating circular cylinder of infinite length in spanwise direction. The solution is decomposed into two parts; first, the flow past a stationary circular cylinder is solved by the use of matched asymptotic expansions method. Afterwards, the rotation of a circular cylinder in a stationary ocean of a micropolar fluid is investigated. Due to linearity of the governing equations, the principle of superposition is then recalled to construct the desired flow field. Ultimately, several kinematic and kinetic quantities of the flow are studied by the use of the obtained closed-form analytical solution.
Rocznik
Strony
199--220
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
autor
autor
  • Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, 16844 Tehran, Iran, aminmoosaie@gmail.com
Bibliografia
  • 1. G.G. STOKES, On the effect of the internal friction of fluids on the motion of pendulums, Trans. Cambridge Phil. Soc., 9, 8-106, 1851.
  • 2. C.W. OSEEN, Hydrodynamik, Akademische Verlagsgesellschaft, Leipzig 1927.
  • 3. H. LAMB, On the uniform motion of a sphere through a viscous fluid, Philos. Mag., 21, 112-212, 1911.
  • 4. H. FAXEN, Exakte Lösungen der Oseenschen DgL einer zähen Flüssigkeit für den Fall der Translationsbewegung eines Zylinders, Nova Acta Soc. Sei. Upsal. 4, 1-55, 1927.
  • 5. S. TOMOTIKA, T. Aoi, The steady flow of a viscous fluid past a sphere and circular cylinder at small Reynolds numbers, Quart. J. Mech. Appl. Math., 3, 140-161, 1950.
  • 6. T. PROUDMAN, J.R.A. PEARSON, Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech., 2, 237-262, 1957.
  • 7. S. KAPLUN, Low Reynolds number flow past a circular cylinder, J. Math. Mech., 6, 595-603, 1957.
  • 8. S. KAPLUN, P.A. LAGERSTROM, Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers, J. Math. Mech., 6, 585-593, 1957.
  • 9. P.A. LAGERSTROM, Note on the preceding two papers, J. Math. Mech., 6, 605-606, 1957.
  • 10. G. ATEFI, Analytische Lösung der Oseenschen Differentialgleichung des quer-ange-strömten drehenden Zylinders bei Schlupf, Dissertation, Technische Universität Berlin, 1990.
  • 11. G. ATEFI, Einfluß des slips auf das Wirbelfeld hinter dem schwach angeströmten Zylinder, Forschungsbericht Nr. 9, 2, Institut für Mechanik, Technische Universität Berlin, 1991.
  • 12. G. ATEFI, Quer angeströmter drehender Zylinder bei kleinen Reynoldszahlen und bei Schlupf, Arch. Appl. Mech., 61, 488-502, 1991.
  • 13. B.S. PADMAVATHI, T. AMARANATH, S.D. NIG AM, Stokes flow past a sphere with mixed slip-stick boundary conditions, Fluid Dyn., Res. 11, 229-234, 1993.
  • 14. E. COSSERAT, F. COSSERAT, Sur la mécanique générale, C. R. Acad. Sci. Paris, 145, 1139-1142, 1907.
  • 15. E. COSSERAT, F. COSSERAT, Théorie des Corps Déformables, Librairie Scientifique A. Herrnann et Fils, Paris, 1-221, 1909.
  • 16. D.W. CONDIFF, J.S. DAIILER, Fluid mechanical aspects of antisymmetric stress, Phys. Fluids, 7, 842-854, 1964.
  • 17. A.C. ERINGEN, Theory of micropolar fluids, J. Math. Mech., 16, 1-18, 1966.
  • 18. R, TROSTEL, Gedanken zur Konstruktion mechanischer Theorien II, Forschungsbericht Nr. 7, 2, Institut für Mechanik, Technische Universität Berlin, 1988.
  • 19. C. ALEXANDRU, Systematik nichtlokaler Kelvinhafter Fluide vom Grade zwei auf der Basis ernes COSSERAT Kontinuumsmodelles, Fortschrittberichte VDI, Reihe 18/Nr. 61, VDI-Verlag, Düsseldorf 1989.
  • 20. G. STOKES, Fluids with Micro structure, Birkhäuser, Boston 1999.
  • 21. G. LuKASZEWlCZ, Micropolar Fluids: Theory and Applications, Birkhäuser, Boston 1999.
  • 22. A,C. ERINGEN, Microcontinuum Field Theories II: Fluent Media, Springer, New York 2001.
  • 23. A. MOOSAIE, GH. ATEFI, Cosserat modeling of turbulent plane-Couette and pressure-driven channel flows, ASME J. Fluids Eng., 129, 806-810, 2007.
  • 24. A. MOOSAIE, GH. ATEFI, A COSSERAT continuum mechanical approach to steady flow of blood through arteries, J. Disper. Sci. Technol., 28, 765-768, 2007.
  • 25. A. MOOSAIE, GH. ATEFI, Analysis of concentrated suspension flow by utilizmg a Cosserat-type continuum theory, J. Disper. Sci. Technol., 28, 901-906, 2007.
  • 26. A. MOOSAIE, GH. ATEFI, Microstretch continuum mechanical description of concentrated suspension flow, J. Disper. Sci. Technol., 29, 2008, in press.
  • 27. H. RAMKISSOON, S.R. MAJUMDAR, Representations and fundamental singular solutions in micropolar fluid, ZAMM, 56, 197-203, 1976.
  • 28. H. RAMKISSOON, S.R. MAJUMDAR, Drag on an axially symmetric body in the Stokes flow of micropolar fluid, Phys. Fluids, 19, 16-21, 1976.
  • 29. H. RAMKISSOON, Plane interior boundary value problems in microcontinuum fluid mechanics, Int. J. Erig. Sci., 23, 809-820, 1985.
  • 30. C.V. EASWARAN, S.R. MAJUMDAR, Causal fundamental solutions for the slow flow of a micropolar fluid, Int. J. Eng. Sci., 28, 843-850, 1990.
  • 31. II. RAMKISSOON, Flow of a micropolar fluid past a Newtonian fluid sphere, ZAMM, 65, 635-637, 1985.
  • 32. H. POWER, H. RAMKISSOON, Stokes flow of a micropolar fluid exterior to several non-intersecting closed surfaces, but contained by an exterior contour, Math. Methods Appl. Sci., 17, 1115-1127, 1994.
  • 33. T. BUCHUKURI, R. CHICHINADZE, Two-dimensional problems of stationary flow of a noncompressible viscous fluid in the case of Oseen's linearization, Georgian Math. J., 1, 251-266, 1994.
  • 34. H. HAYAKAWA, Slow viscous flows in micropolar fluids, Phys. Rev., E 61, 5477-5492, 2000.
  • 35. M. VAN DYKE, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford 1975.
  • 36. J. KEVORKIAN, J.D. COLE, Multiple Scale and Singular Perturbation Methods, Springer, Berlin 1996.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0012-0035
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