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    Yang, J. Wolgemuth, C. W. and Huber, G. 2013. Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses. Physics of Fluids, Vol. 25, Issue. 5, p. 051901.

    Champmartin, Stéphane Ambari, Abdelhak and Roussel, Nicolas 2007. Flow around a confined rotating cylinder at small Reynolds number. Physics of Fluids, Vol. 19, Issue. 10, p. 103101.

    Meleshko, VV 2003. Selected topics in the history of the two-dimensional biharmonic problem. Applied Mechanics Reviews, Vol. 56, Issue. 1, p. 33.

    Goodier, J.N. 1934. XLVI.An analogy between the slow motions of a viscous fluid in two dimensions, and systems of plane stress. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 17, Issue. 113, p. 554.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 29, Issue 2
  • May 1933, pp. 277-287

Slow rotation of a circular cylinder in a viscous fluid bounded by parallel walls

  • R. C. J. Howland (a1) and R. C. Knight (a2)
  • DOI:
  • Published online: 24 October 2008

Solutions of the bi-harmonic equation valid in the region bounded externally by parallel lines and internally by a circle midway between the lines have been given by one of the Authors in a recent paper [2]. These solutions were adapted to the requirements of certain problems in the theory of elasticity, but modified solutions satisfying the boundary conditions characteristic of viscous fluid motion are easily derived. These modified solutions will here be given and will be used to find the stream function corresponding to the slow rotation of a cylinder placed symmetrically between parallel walls.

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1.R. C. J. Howland ; Proc. Roy. Soc., A, 124 (1929), 89119.

2.R. C. J. Howland ; Phil. Trans., A, 229 (1930), 4986.

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Mathematical Proceedings of the Cambridge Philosophical Society
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  • EISSN: 1469-8064
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