Flow of MHD micropolar fluid through porous medium: a hodograhic approach for exact solution

An analytical study of the motion of a steady, homogenous, incompressible, plane electrically conducting micropolar fluid flow through a porous medium subjected to a transverse magnetic field is carried out. The governing non linear partial differential equations describing the continuity, momentum and angular momentum are converted into a system of linear partial differential equations by means of hodograph transformation. Further the flow equations have been obtained in terms of Legendre transform function of the stream function. Results are summarized in the form of a theorem. Lastly two examples have been taken as application to illustrate the developed theory and exact solutions are determined. The expressions for velocity, micro-rotation, streamline and pressure distribution are obtained in each case. The streamline patterns are plotted and also the pressure variation with x and y  are studied for varying porous media parameter at constant density of fluid and also for varying density of different fluids at constant porous media parameter value.