Mathematical Analysis of the Slip Flow due to a Cylinder Oscillating in Different Directions with Independent Amplitudes

Source abstract

This study examines the incompressible viscous fluid flow in an infinitely long cylinder, with slip occurring at the cylinder’s surface, undergoing longitudinal and torsional oscillations of independent amplitudes. The proposed governing equations are solved subject to the Basset slip condition. Analytical expressions for the velocity field, shear stresses, drag force on the cylinder, work done and the drag coefficient are obtained. Velocity components, drag and work done are illustrated graphically. The magnitude of the velocity increases as slip decreases and as the frequency of oscillations increases. Drag increases in both directions as the slip decreases and as the frequency of oscillations increases. Work done increases as slip decreases and as the ratio of the amplitude of torsional to longitudinal oscillations increases. These results which aid in the interpretation of drag forces and energy dissipation (work done) contribute to the understanding of engineering systems, such as vibration dampers, tuned liquid dampers, energy harvesting systems and acoustic devices. This study also has a wide variety of applications in industrial mixing and processing, aerospace and marine engineering and the automotive and transportation industries.