Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 16, Issue 7, Pages 2737-2744Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2010.10.006
Keywords
Generalized Oldroyd-B fluid; Velocity field; Shear stress; Fractional calculus; Integral transforms
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Considering a fractional derivative model the unsteady flow of an Oldroyd-B fluid between two infinite coaxial circular cylinders is studied by using finite Hankel and Laplace transforms. The motion is produced by the inner cylinder which is subject to a time dependent longitudinal shear stress at time t = 0(+). The solution obtained under series form in terms of generalized G and R functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, generalized and ordinary Maxwell, and Newtonian fluids are obtained as limiting cases of our general solutions. The influence of pertinent parameters on the fluid motion as well as a comparison between models is illustrated graphically. (C) 2010 Elsevier B.V. All rights reserved.
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