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

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.

Research highlights
► 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.