Hartmann problem for micropolar fluids

An analysis of the steady hydromagnetic channel flow between two parallel solid walls of an incompressible electrically conducting micropolar fluid, proposed by Eringen, in the presence of a transverse uniform magnetic field is given. With the usual assumptions of magnetohydrodynamics, the equations of motion for these flows called magneto micropolar flows are obtained. The flow field is governed by the micropolar parameters K, and the usual Hartmann number M. The solution is discussed in detail for a channel flow of magneto micropolar fluid. In general, for fixed values of the micropolar parameters K and lambda, the velocity profile is flattened with increase in the strength of the magnetic field while the velocity profile is a smaller with increase in K (or decrease in lambda) for a fixed M. The behaviour of the microrotation, surface traction, couple stress and current distribution is discussed in detail. Finally the effects of maximum micropolarity on the flow field are pointed out. (author)