Combined Effects of Hall Current and Rotation on Unsteady Couette Flow in a Porous Channel

Abstract

The combined influences of Hall currents and rotation on the MHD Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel porous plates channel in a rotating system in the presence of a uniform transverse magnetic field have been carried out. The solutions for the velocity field as well as shear stresses have been obtained for small time as well as for large times by Laplace transform technique. It is found that for large times the Hall currents accelerates primary flow whereas it retards secondary flow while the rotation retards the primary flow whereas it accelerates the secondary flow. It is also found that the velocity components converge more rapidly for small time solution than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of magnetic parameter <i>M</i>², rotation parameter <i>K</i>² and Reynolds number <i>R</i>_<i>e</i>. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the layer increases with increase in either Hall parameter <i>m</i> or Reynolds number <i>R</i>_<i>e</i> while it decreases with increase in Hartmann number <i>M</i>. It is interesting to note that for large values of <i>M</i>² , the boundary layer thickness is independent of the rotation parameter.