The Rayleigh–Stokes problem for an edge in an Oldroyd-B fluid

• Published in: Comptes rendus. Mathématique Vol. 335; no. 11; pp. 979 - 984
• Main Author: Fetecau, Constantin
• Format: Journal Article
• Language: English
• Published: Paris Elsevier SAS 01.12.2002; Elsevier
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Mathematical analysis; Mathematics; Ordinary differential equations; Physics; Sciences and techniques of general use; Rayleigh problem; Fourier transformation; Sinuses; Initial condition; Fluid dynamics; Stokes problem; Navier Stokes equation; Differential equation; Oldroyd fluid; Maxwell fluid; Limit
• ISSN: 1631-073X; 1778-3569; 1778-3569
• DOI: 10.1016/S1631-073X(02)02577-3

The velocity fields corresponding to an incompressible fluid of Oldroyd-B type subject to a linear flow within an infinite edge are determined for all values of the relaxation and retardation times. The well known solution for a Navier–Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appears as a limiting case of our solutions. To cite this article: C. Fetecau, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 979–984. Les champs de vitesses correspondant à un fluide de type Oldroyd-B qui exécute un mouvement linéaire dans un dièdre infini sont déterminés pour toutes les valeurs des temps de relaxation et de retard. La solution bien connue pour le fluide de Navier–Stokes, les solutions correspondant à un fluide de Maxwell et à un fluide de grade deux apparaissent comme un cas limite de nos solutions. Pour citer cet article : C. Fetecau, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 979–984.