ANALYTIC SOLUTIONS FOR THE UNSTEADY LONGITUDINAL FLOW OF AN OLDROYD-B FLUID WITH FRACTIONAL MODEL

• Published in: Chemical engineering communications Vol. 199; no. 2; pp. 290 - 305
• Main Authors: Nazar, M., Mahmood, A., Athar, M., Kamran, M.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01.02.2012; Taylor & Francis Ltd
• Subjects: Boundary conditions; Computational fluid dynamics; Cylinders; Derivatives; Exact solutions; Fluid flow; Fluids; Fractional calculus; Generalized Oldroyd-B fluid; Integral transforms; Laplace transforms; Mathematical models; Shear stress; Unsteady; Velocity field
• ISSN: 0098-6445; 1563-5201
• DOI: 10.1080/00986445.2011.590164

The unsteady flow of an Oldroyd-B fluid with fractional derivative model, between two infinite coaxial circular cylinders, is studied by using finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t = 0 + , is subject to a time-dependent longitudinal shear stress. The solutions that have been obtained, presented under series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B and generalized and ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.