Effect of Induced Magnetic Field on Natural Convection in Vertical Concentric Annuli Heated/Cooled Asymmetrically

In the present paper, the fully developed laminar free convective flow of a viscous incompressible and electrically conducting fluid between two concentric vertical cylinders is considered in the presence of a radial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The expressions for the temperature, velocity, induced magnetic field, induced current density, skin-friction and Nusselt number are obtained in a closed form under more general boundary conditions for the induced magnetic field. The influence of the Hartmann number and buoyancy force distribution parameter on the fluid velocity, induced magnetic field and induced current density have been analyzed by using the graphs while the values of the skin-friction, Nusselt number, induced current flux and mass flux are given in the tabular form. It is observed that the fluid velocity and induced magnetic field are rapidly decreasing with increase in the value of Hartmann number in the case when one of the cylinders is conducting compared with the case when both cylinders are non-conducting. The effect of the induced magnetic field is to increase the velocity profiles in comparison to the case of neglecting the induced magnetic field. The buoyancy force distribution parameter has tendency to increase the fluid velocity, induced magnetic field, temperature field and induced current flux.