Flow of visco-elastic fluid of Rivlin-Ericksen type between two inclined parallel planes in presence of gravity and uniform transverse magnetic field

In this paper, an attempt has been made to study the flow of Rivlin-Ericksen visco-elastic fluid between two inclined parallel planes in presence of gravity and uniform transverse magnetic field. It has been assumed that the lower plane is at rest and the upper plane is moving with a transient velocity in the first case, while in the second case it is moving longitudinally with a periodic velocity. In both cases the fluid velocity and flux of fluid have been obtained by variable separation technique. These results are then deduced for the case of visco-elastic Maxwell fluid taking the fluid to be electrically conducting and placed in presence of a uniform transverse magnetic field. Further, when the magnetic field is absent the corresponding results are obtained by passing to the limit as uniform magnetic field tending to zero. Moreover, the titled problem has also been solved in case of inviscid fluid in both cases of hydromagnetic flow and flow in absence of magnetic field. Thus the present problem is focused to a wide range of flow problems of different types of fluid models. (author)