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)

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.

arXiv comment3 pages, 1 figure (2 images); v2 corrects a few typos. The final publication is available at http://www.springerlink.com

Cited by in corpus (7)

• Stokes' first problem for some non-Newtonian fluids: Results and mistakes
• Stress retardation versus stress relaxation in linear viscoelasticity
• On a difficulty in the formulation of initial and boundary conditions for eigenfunction expansion solutions for the start-up of fluid flow
• Comments on: "Starting solutions for some unsteady unidirectional flows of a second grade fluid," [Int. J. Eng. Sci. 43 (2005) 781]
• Comments on: "Energetic balance for the Rayleigh--Stokes problem of an Oldroyd-B fluid" [Nonlinear Anal. RWA 12 (2011) 1]
• Comment on "The velocity field due to an oscillating plate in an Oldroyd-B fluid" by C.C. Hopkins and J.R. de Bruyn [Can. J. Phys. 92, 533 (2014)]
• Comment on: "Stokes' first problem for heated flat plate with Atangana--Baleanu fractional derivative" [Chaos Solitons Fractals 117 (2018) 68]