Memory Effects in the Magnetohydrodynamic Axial Symmetric Flows of Oldroyd-B Fluids in a Porous Annular Channel

Abstract

In this article, we analytically investigate the isothermal magnetohydrodynamic axial symmetric flows of ordinary and fractional incompressible Oldroyd-B fluids through a porous medium in an annular channel. The fluid’s motion is generated by an outer cylinder, which moves along its symmetry axis with an arbitrary time-dependent velocity Vh(t). Closed-form expressions are established for the dimensionless velocity fields of both kinds of fluids, generating exact solutions for any motion of this type. To illustrate the concept, two particular cases are considered, and the velocity fields corresponding to the flow induced by the outer cylinder are presented in simple forms, with the results validated graphically. The motion of fractional and ordinary fluids becomes steady over time, and their corresponding velocities are presented as the sum of their steady and transient components. Moreover, the steady components of these velocities are identical. The influence of magnetic fields and porous media on the flow of fractional fluids is graphically depicted and discussed. It was found that a steady state is reached earlier in the presence of a magnetic field and later in the presence of a porous medium. Moreover, this state is obtained earlier in fractional fluids compared with ordinary fluids.