Journal of Prime Research in Mathematics
Vol. 1 (2009), Issue 1, pp. 139 – 148
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
Exact solutions of generalized Oldroyd-B fluid subject to a time-dependent shear stress in a pipe
Qammar Rubbab
Department of Mathematics, FAST National University of Computer & Emerging Sciences, Lahore, Pakistan.
Syed Muhammad Husnine
Department of Mathematics, FAST National University of Computer & Emerging Sciences, Lahore, Pakistan.
Amir Mahmood
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
\(^{1}\)Corresponding Author: rubabqammar@gmail.com
Copyright © 2009 Qammar Rubbab, Syed Muhammad Husnine, Amir Mahmood. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2009.
Abstract
The velocity field and the shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid in an infinite circular cylinder subject to a longitudinal time-dependent shear stress are determined by means of Hankel and Laplace transforms. The exact solutions, written in terms of the generalized \(G\)-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Oldroyd-B, ordinary and generalized Maxwell, ordinary and generalized second grade as well as for Newtonian fluids are obtained as limiting cases of our general solutions.
Keywords:
Exact solutions, generalized Oldroyd-B fluid, longitudinal shear stress.