Laminar Flow of a Viscous Incompressible Fluid Between Two Eccentric Rotating Spheres with Non-Uniform Transpiration

摘要

The effects of non-uniform transpiration on the laminar flow of a Newtonian, viscous, incompressible fluid confined between two eccentric rotating spheres, which can rotate with constant angular velocities, are investigated. The unsteady-state Navier-Stokes equations in the dimensionless form are solved by the implicit finite difference method. The transpiration is considered as a step function of time. The flow patterns are presented for various values of rotational Reynolds number Re, time-dependent Reynolds number of injection/suction Re_w, and different ratios of the angular velocities of the spheres. The effects of transpiration and eccentricity on the viscous torque are also studied. The results show that the eddies created by the centrifugal effect generated by the rotation of the spheres will be removed in the annulus with an increase in transpiration. In addition, it is found that eccentricity has no significant effect on viscous torque on the inner and outer spheres whereas the transpiration can have a considerable effect on the magnitude of viscous torque.