The influence of fractional time-derivative on the helical flows of generalized multi-layer immiscible second grade fluids in a cylindrical domain

The problem of flow through layered media finds applications in various fields of science and engineering. Examples of these flows are the flow of ground water, oil, and gas flow in the ground layers. The helical flow of incompressible, unsteady, laminar and simultaneous multi-layer immiscible fractional second-grade fluids in a circular cylindrical pipe has been studied. The helical flow of fluids is caused by the translational as well as rotational motion of the cylinder along its axis in the presence of a time-dependent pressure gradient in the axial direction. The integral transform methods (Laplace, Hankel and Weber transformations) are used to find an exact analytical solution to a problem with the generic initial boundary and interface fluid-fluid conditions. The numeric reversal of the Laplace transform was performed using Talbot's technique. The impact of memories on the fluid motion have been investigated for the particular case of three fractional second grade fluids. The fluid behaviour has been studied using the graphical depictions produced using the Mathcad software. It is found that for increasing values of the fractional parameter the fluid velocity is decreasing. The memory effects have a stronger influence on the velocity of the second and the third layers. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams Uni-versity. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).