Critical study on rotational flow of a fractional Oldroyd-B fluid induced by a circular cylinder
type: Item
instance of: scholarly article
title: Critical study on rotational flow of a fractional Oldroyd-B fluid induced by a circular cylinder
zbMATH Open document ID: 1382.76283
DOI: 10.5402/2012/835398
author: D. Kharzeev
published in: ISRN Mathematical Physics
publication date: 2012-03-14T00:00:00Z
review text: Summary: We considered the unsteady flow of a fractional Oldroyd-B fluid through an infinite circular cylinder with the help of infinite Hankel and Laplace transforms. The motion of the fluid is produced by the cylinder that, at time \(t = 0^+\) is subject to a time-dependent angular velocity. The established solutions have been presented under series form in terms of the generalized \(G\) functions satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, ordinary and fractional Maxwell, ordinary and fractional second-grade, and Newtonian fluids, performing the same motion, are acquired as limiting cases of general solutions. The keynote points regarding this work to mention are that (1) we extracted the expressions for velocity field and shear stress corresponding to the motion of fractional second-grade fluid as a limiting case of general solutions; (2) the expressions for velocity field and shear stress are in the most simplified form in contrast with the studies of \textit{I. Siddique} and \textit{Z. Sajid} [Commun. Nonlinear Sci. Numer. Simul. 16, No. 1, 226--238 (2011; Zbl 1221.76023)], in which the expression for the velocity field involves the convolution product as well as the integral of the product of generalized \(G\) functions. Finally, numerical results are presented graphically and discussed in order to reveal some physical aspects of obtained results.
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 6014702
Wikidata QID: Q58692696
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/835398
OpenAlex ID: W2049012628
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description: scientific article; zbMATH DE number 6014702