A note on longitudinal and torsional oscillations of a rod in a generalized non-Newtonian fluid

The rotational and torsional oscillations of a rod in a fluid has relevance to several applications. Stokes recognized that the rotational oscillations in a Navier–Stokes fluid allows one to obtain an exact solution. This seminal work has been extended by Casarella and Laura to find an exact solution to both the rotational and torsional oscillations in a Navier–Stokes fluid. This work has been generalized to the case of several non-Newtonian fluids by subsequent authors. In this study we analyze the solution that corresponds to two classes of non-Newtonian fluids, the constitutive relation put forth by Carreau and Yasuda, and a relatively new constitutive relation due to Garimella et al. that mimics viscoplastic flow exhibited by many materials.