Law of Maxwell fluid flowing in annuli with inner wall reciprocating axially

Key words:  viscoelastic fluid  annulus  axial reciprocating movement  Maxwell fluid

Abstract:

Based on the momentum equation and the constitutive equation, a mathmatical model for Maxwell viscoelastic fluid flowing in annuli with the inner wall reciprocating axially was set up. An analytical solution for the velocity was obtained by the method of eigen function. The results show that under the influence of the reciprocating movement of the inner wall, the velocity and the average velocity in annuli varied with time periodically. The influence of the fluid elasticity on the velocity and average velocity was similar to that of the oscillating frequency of the moving inner wall on them. The increase of fluid elasticity or movment frequency of inner wall would change the velocity profile in annuli at some moments. There existed an elastic coefficient or oscillating Reynold number which corresponded to the maximum variation of velocity and average velocity. The amplitude of reciprocating movement changed the extent of velocity and average velocity variation only. The parabolic distribution of velocity was leveled by the decrease in annular space, which also diminished the cyclic average velocity.