Abstract: This paper may be the first attempt to solve the flow-field of homogeneous fluid between concentric cones (narrow gap) with equal angular velocities of rotation by using a boundary perturbation method, and the hydrodynamic stability of blood flow in the cone-type blood processor is verified, under conditions of the narrow gap between the cones and small axial Re numbers. This paper also verifies the hydrodynamic stability between concentric cylinders (narrow gap) with equal angular velocities of rotation by using a new mathematical technic.These theoretical analyses are in agreement with the experimental observations, which have been made by Shanghai Medical Instruments Institute.

Key words: nonlinear input, unknown parameter, uncertainty, finite-time control, non-autonomous chaotic gyroscope