On some rotational flows of non-integer order rate type fluids with shear stress on the boundary

Abstract

This article presents rotational flows of some rate type fluids with non-integer order derivatives. The fluid fills an infinite straight circular cylinder and its motion is generated by a time dependent torsion, applied to the surface of the cylinder. As novelty, the dimensionless governing equation related to the non-trivial shear tension is used and the first exact solutions analogous to a ramped shear stress on the surface are obtained using integral transforms. The results that have been obtained allow us to provide solutions for ordinary Oldroyd-B, non-integer order Maxwell and ordinary Maxwell fluids performing similar motions. In addition, the control of non-integer order framework on shear stress and velocity profiles is analyzed by numerical simulations and graphical interpretations. Keywords: Oldroyd-B fluid, Caputo derivatives, Velocity field, Shear stress, Circular cylinder