Comments on: "Starting solutions for some unsteady unidirectional flows of a second grade fluid," [Int. J. Eng. Sci. 43 (2005) 781]

TL;DR

This paper identifies and corrects a mathematical error in a highly-cited study on unsteady flows of second-grade fluids, demonstrating the corrected solutions' agreement with numerical simulations and highlighting the prevalence of similar errors in related literature.

Contribution

It provides a correction to a key mathematical error in a previous influential paper and verifies the corrected solutions against numerical results.

Findings

Corrected solutions match numerical simulations.

Original solutions contained a significant mathematical error.

Many recent papers have similar errors.

Abstract

A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree identically with numerical ones generated by a finite-difference scheme, while the original ones of Fetecau & Fetecau do not. A list of other recent papers in the literature that commit the error corrected in this Comment is compiled. Finally, a summary of related erroneous papers in this journal is presented as an Appendix.