Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli 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 transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli. The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening tendency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.