MHD effects on the channel flow of a fractional viscous fluid through a porous medium: An application of the Caputo-Fabrizio time-fractional derivative

This research article considers the exact solutions and theoretical aspects of the channel flow of a fractional viscous fluid which is electrically conducing and flowing through a porous medium. Joint Laplace and Fourier transform techniques are used to solve the momentum equation. The Caputo-Fabrizio time fractional derivative is used in the constitutive equations. Exact solutions for an arbitrary velocity are obtained, and then in the limiting cases over a bottom plate three types of flow are considered: that is, the impulsive, accelerating and oscillating motion of the fluid. The case where the flow of the fractional fluid is unaffected by the side walls, is correspondingly taken into account. For oscillating flow the solutions are separated into steady and transient parts for both sine and cosine oscillations. Moreover these solutions are captured graphically, and the effect of the Reynolds number "Re", fractional parameter "alpha", effective permeability "K-eff" and the time "t", on the fluid's motion are observed.