Permanent solutions for some MHD motions of generalized Burgers fluids through a porous medium in cylindrical domains

Abstract

Some isothermal motions of the incompressible generalized Burgers fluids in cylindrical domains are investigated when the magnetic and porous effects are taken into consideration. Analytical expressions are established for the dimensionless steady-state velocity fields corresponding to motions between two infinite horizontal coaxial circular cylinders. The respective motions are generated by oscillatory or constant pressure gradients which act along the common axis of cylinders. Similar velocities for motions through an infinite circular cylinder are obtained as limiting cases of previous solutions. All results can be easily particularized to give similar solutions for the incompressible Burgers, Oldroyd-B, Maxwell, and Newtonian fluids. Finally, some numerical results are graphically represented and discussed. It was found that the fluid velocity diminishes with increasing values of the magnetic and porous parameters. It means the fluid moves slower in the presence of a magnetic field or porous medium.