Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

Mr R. C. J. Howlanda1 and R. C. Knighta2

a1 Professor of Mathematics, Emmanuel College, University College, Southampton

a2 Assistant Lecturer in Mathematics, University College, Southampton.

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.

(Received December 01 1932)

(Accepted May 01 1933)