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Perturbation methods applied to the helical flow of a Casson fluid

Chiera C., Connell H. J., Shepherd J. J.

International Journal of Applied Mechanics and Engineering

2005

Vol. 10, no 1

39-51

The helical flow of a Casson fluid between infinitely long coaxial cylinders is analyzed, when the inner cylinder has a given constant angular velocity, and a constant axial flow rate is imposed. Perturbation methods are applied in two circumstances of physical interest - that of low axial flow rates; and that of small intercylindrical gap width - to yield approximate expressions describing the fluid velocity field; and the Reiner-Riwlin equation, the fundamental relationship linking the angular velocity of the inner cylinder, the torque experienced there, and the given axial flow rate. The accuracy of these expressions is tested by comparison with solutions generated using numerical computation.

Multiscaling analysis of a nonlinear boundary value problem in lubrication theory

Aliu E., Shepherd J. J., Connell H. J.

International Journal of Applied Mechanics and Engineering

2004

Vol. 9, no 3

455-470

The method of multiple scales, a long standing alternative to the method of matched expansions, is applied to the nonlinear boundary value problem modelling the operation of a one-dimensional gas lubricated slider bearing, at large values of the bearing number. Approximate expansions for the pressure profile, load bearing capacity and the location of the centre of pressure are obtained, and compared with the results of applying matched expansions and numerical techniques.