MHD axial couette flows of burgers fluids in an infinite circular cylinder

Axial flow of incompressible Burgers fluids in an infinite circular cylinder that slides along its symmetry axis with an arbitrary time-dependent velocity is analytically and numerically investigated in the presence of a constant magnetic field. Analytic expressions are established for the dimensionless velocity field and the non-trivial shear stress. For validation, distinct expressions are determined for the fluid velocity and their equivalence in a concrete case is graphically proved. The influence of relaxation time and of Burgers and magnetic parameters on the fluid velocity is graphically highlighted and discussed. It was found that, outside a small vicinity of the symmetry axis of cylinder, the fluid flows slower in the presence of the magnetic field. The oscillatory translational movement of the cylinder induces a motion with oscillating velocity of the fluid. If the cylinder velocity tends to a constant value for large values of the time t, the fluid motion becomes steady in time and the corresponding steady solutions are determined.