Analytical solutions for the axisymmetric flow inside a cylindrical container with a rod along the axis at low Reynolds numbers

The axisymmetric flow inside a cylindrical container with a rod along its symmetry axis is studied. The flow is produced by the rotation of one of the cylinder end walls, of both end walls, or of the sidewall. Analytical expressions (for low Reynolds numbers) of the azimuthal velocity field are presented, thus extending the solutions of the case without rod. Graphics of constant azimuthal velocity lines are obtained for two configurations (both end walls in rotation, one end wall in rotation). The calculations are based on summations with different number of terms. The introduction of Lanczos factors in the summations is shown to play an important role improving their convergence.