On modelling of two-dimensional MHD flow with induced magnetic field: solution of peristaltic flow of a couple stress fluid in a channel

The aim of present paper is to provide mathematical modelling for the two-dimensional MHD flow with induced magnetic field. The flaws in the already existing equations have been pointed out. The results of low magnetic Reynolds number approximation are recovered as a special case from the developed equations. As an example, the peristaltic flow for a couple stress fluid in a channel is considered. For the solution of the problem the governing equations are simplified under the realistic assumption of long wavelength. Exact solution of the problem is presented and some features of peristaltic motion have been discussed. It is observed that the applied magnetic field increases the pressure rise in the pumping region. However, the presence of applied electric field reduced it in that region. It is also found that the stream function is independent of applied electric field.