Investigating Magnetohydrodynamic Motions of Oldroyd-B Fluids through a Circular Cylinder Filled with Porous Medium

Abstract

We analytically investigated the magnetohydrodynamic motions of electrically conductive, incompressible Oldroyd-B fluids through an infinite circular cylinder filled with a porous medium. A general expression was established for the dimensionless velocity of fluid as a cylinder moves along its symmetry axis with an arbitrary velocity; the expression can generate exact solutions for any motion of this fluid type, solving the discussed problem. Special cases were considered and validated through graphical investigation to illustrate important characteristics of fluid behavior. In application, this is the first presentation of an exact general expression for non-trivial shear stress related to the magnetohydrodynamic motions of Oldroyd-B fluids when a longitudinal time-dependent shear stress is applied to the fluid by a cylinder. Solutions for the motions of rate-type fluids are lacking. The graphical representations show that in the presence of a magnetic field or porous medium, fluids flow more slowly and the steady state is reached earlier.