The hydromagnetic flow of a dusty visco-elastic fluid between two infinite parallel plates

An initial value investigation is made on the motion of an incompressible visco-elastic (Rivlin-Ericksen) fluid with small particles between two infinite moving parallel plates in the presence of a transverse magnetic field. The flow is generated in the fluid particle system due to time dependent pressure gradient and also the motion of the plates in the presence of an external imposed transverse magnetic field. By Laplace transform technique, the velocity distribution and wall shear stress have been obtained for four different cases, when the pressure gradient and both the plate velocities are 1. (i) decreasing exponentially with time,2. (ii) varying periodically with time,3. (iii) impulsive type, and4. (iv) acting for a finite time. In each case, shear stresses at the boundary plates are also calculated.