On hydromagnetic channel flow of an Oldroyd-B fluid induced by rectified sine pulses

The unsteady unidirectional motion of an incompressible electrically conducting Oldroyd-B fluid in a channel bounded by two infinite rigid non-conducting parallel plates in presence of an external magnetic field acting in a direction normal to the plates has been discussed in this paper. The flow is supposed to generate impulsively from rest due to rectified sine pulses applied periodically on the upper plate with the lower plate held fixed. There is no external electric field imposed on the system and the magnetic Reynolds number is very small. Exact solution of the problem is obtained both by the methods of Fourier analysis and the Laplace transforms. The enquiries are made about the velocity field and the skin-friction on the walls. The influence of the magnetic field and the elasticity on the flow as well as on the skin-friction are examined quantitatively. Finally, it is shown that the expressions for the fluid velocity obtained by the method of Fourier analysis and by the method of Laplace transforms coincide to provide the same exact solution of the problem.