Magnetohydrodynamic natural convection flow in a vertical micro-porous-channel in the presence of induced magnetic field

In this work, the exact solution for fully developed magnetohydrodynamic natural convection flow of viscous, incompressible, electrically conducting fluid in vertical micro-porous-channel formed by electrically non-conducting infinite vertical parallel porous plates in presence of induced magnetic field is investigated. Effects of velocity slip and temperature jump conditions are taken into account due to their counter effects both on the volume flow rate and the rate of heat transfer. The governing coupled equations responsible for present physical situation 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 subject to the relevant boundary conditions. The expressions for the induced current density and skin friction at the micro-porous-channel surfaces are also obtained. A parametric study of some 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 suction/injection, rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number. Result reveals that, for a fixed value of the Hartmann number, the skin frictions at micro-porous-channel surfaces in the presence of induced magnetic field are higher compared to the case when the induced magnetic field is neglected.