Comment on "On a class of exact solutions of the equations of motion of a second grade fluid" by C. Fetecau and J. Zierep (Acta Mech. 150, 135-138, 2001)

TL;DR

This paper critiques a 2001 study on second grade fluid flow, clarifying that the original solution was incorrect due to a computational error, and highlights the importance of correct mathematical procedures in fluid dynamics solutions.

Contribution

It clarifies the inaccuracies in Fetecau and Zierep's 2001 solution and emphasizes the correct approach established by Puri in 1984 for Stokes' first problem.

Findings

Fetecau and Zierep's solution is generally incorrect.

The error was due to incorrect computation of the distributional derivative.

The correct solution was provided by Puri in 1984.

Abstract

In a 2001 article, Fetecau and Zierep [1] considered Stokes' first problem for a second grade (SG) fluid, unaware that it had already been solved (correctly) by Puri [2] in 1984. These authors used the Fourier sine transform to obtain, what they believed to be, the exact solution of the resulting initial-boundary-value problem (IBVP). Unfortunately, due to their incorrect computation of the distributional derivative of the Heaviside function, an omission of a critical term in the subsidiary equation occurred, an elementary mistake (gracefully explained in [3]) apparently not uncommon in the literature. Therefore, the solution given in [1] is, generally speaking, incorrect.