Role of induced magnetic field on MHD natural convection flow in vertical microchannel formed by two electrically non-conducting infinite vertical parallel plates

The present work consists of theoretical investigation of MHD natural convection flow in vertical microchannel formed by two electrically non-conducting infinite vertical parallel plates. The influence of induced magnetic field arising due to the motion of an electrically conducting fluid is taken into consideration. The governing equations of the motion are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field. The expressions for the induced current density and skin friction have also been obtained. The effects of various non-dimensional parameters such as rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number on the velocity, the induced magnetic field, the induced current density, and skin friction have been presented in graphical form. It is found that the effect of Hartmann number and magnetic Prandtl number on the induced current density is found to have a decreasing nature at the central region of the microchannel.