Motion of a spherical solid particle in Couette flow: exact solution vs. homotopy perturbation approximation with and without Pade approximants

The motion of a spherical solid particle in plane Couette flow is governed by a linear problem that has a simple exact solution. As such, there is no need for an approximate analytical representation of the solution; specially when it is tedious, complicated, and requires hairy terms to give accurate results only at small or moderate values of the time.