Unsteady longitudinal flow of a generalized Oldroyd-B fluid in cylindrical domains

• Published in: Communications in nonlinear science & numerical simulation Vol. 16; no. 7; pp. 2737 - 2744
• Main Authors: Nazar, M., Sultan, Qamar, Athar, M., Kamran, M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2011
• Subjects: Computational fluid dynamics; Cylinders; Derivatives; Fluid flow; Fluids; Fractional calculus; Generalized Oldroyd-B fluid; Integral transforms; Mathematical analysis; Mathematical models; Shear stress; Velocity field; Shear stress; Integral transforms; Velocity field; Fractional calculus; Generalized Oldroyd-B fluid
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2010.10.006

► The aim of this paper is to establish exact solutions for the velocity field and the adequate shear stress corresponding to the unsteady flow of an incompressible generalized Oldroyd-B fluid between two infinite coaxial circular cylinders induced by a time-dependent shear. ► The motion of the fluid is produced by the inner cylinder, which at time t = 0 + begins to slide along its axis with a time-dependent shear stress. ► The solutions presented under series form in terms of the generalized G and R functions, are established by means of the finite Hankel and Laplace transforms, satisfy all imposed initial and boundary conditions. ► Similar solutions for the Oldroyd-B, generalized Maxwell, ordinary Maxwell, and Newtonian fluids are obtained as limiting cases. ► The influence of pertinent parameters on the fluid motion as well as a comparison between models is illustrated graphically. 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.