Impact of induced magnetic field on magnetohydrodynamic (MHD) natural convection flow in a vertical annular micro-channel in the presence of radial magnetic field

This study is devoted to investigate the effect of induced magnetic field on fully developed magnetohydrodynamic (MHD) natural convection flow of electrically conducting fluid in a vertical annular micro-channel formed by two concentric cylinders in the presence of imposed radial magnetic field. The velocity slip and temperature jump at the annular micro-channel surfaces are taken into account. 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 under relevant boundary conditions. The expressions for velocity field, the induced magnetic field, temperature field, induced current density and skin friction have been obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity field, the induced magnetic field, temperature, induced current density, volume flow rate and skin friction are illustrated graphically to show interesting features of the radius ratio, rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number. During the course of investigation, it is found that for fixed value of Hartmann number, the skin friction profiles in the presence of induced magnetic field are higher compared to the case when the induced magnetic field is neglected.