Simultaneous Flow of Three Immiscible Fractional Maxwell Fluids ‎with the Clear and Hoamogeneous Porous Cylindrical Domain

One-dimensional transient flows of three layers immiscible fractional Maxwell fluids in a cylindrical domain have been investigated in the presence of a porous medium. In the flow, the domain is considered the concentric regions namely one clear region and other two annular regions are filled with a homogeneous porous medium saturated by a generalized Maxwell fluid. The studied problem is based on a mathematical model focused on the fluids with memory described by a constitutive equation with time-fractional Caputo derivative. Analytical solutions to the problem with initial-boundary conditions and interface fluid-fluid conditions are determined by employing the integral transform method (the Laplace transform, the finite Hankel transform and the finite Weber transform). The memory effects and the influence of the porosity coefficient on the fluid motion have been studied. Numerical results and graphical illustrations, obtained with the Mathcad software, have been used to analyze the fluid behavior. The influence of the memory on the fluid motion is significant at the beginning of motion and it is attenuated in time.