Hydromagnetic flow of an incompressible viscous conducting fluid between two permeable beds (Q1082213)

The hydrodmagnetic flow of an incompressible viscous conducting fluid in a channel sandwiched between two permeable beds is investigated in the presence of a uniform transverse magnetic field. The slip boundary condition postulated by \textit{Beavers} and \textit{Joseph} [J. Fluid Mech. 30, 197 ff. (1967)] is assumed at the interfaces between the channel and the two permeable beds and the lower bed is assumed to move with a uniform velocity parallel to the channel. Assuming the flow in the permeable beds to be governed by Darcy's law, the thicknesses of the two boundary layers near the above two interfaces are calculated. The effects of the magnetic field, slip and porosity parameters on the velocity and temperature distributions are investigated after including viscous and Joule dissipation in the heat transfer equation. I find to my utter dismay that although many results are reported, there is no attempt to interpret any one of these by physical arguments. Further the problem appears to me rather artificially contrived without having bearing on any specific physical situation.