Magnetic and porous effects on steady state and flow resistance of Burgers fluids between parallel plates

Abstract

Abstract Some motion problems of Burgers fluids between parallel plates are analytically and numerically investigated when magnetic and porous effects are taken into account and a differential expression of the non-trivial shear stress is prescribed on the lower plate. Closed-form expressions are determined for the non-dimensional steady state velocity and shear stress fields and the corresponding Darcy’s resistances. They are the first exact solutions for hydromagnetic motions of Burgers fluids through porous media when a differential expression of shear stress is given on the boundary. The results that have been obtained are used to get the necessary time to reach the steady state and to bring to light the influence of magnetic field and porous medium on the flow resistance of the fluid. They can immediately be particularized to provide exact solutions for similar motions of Oldroyd-B, Maxwell, second grade and Newtonian fluids. It was found that the steady state is rather obtained in the presence of a magnetic field or porous medium. In addition, the flow resistance of the fluid declines in the presence of a magnetic field and, as expected, increases through porous media.