Effect of magnetic field on natural convection in a vertical cylindrical annulus

Natural convection of a low Prandtl number electrically conducting fluid (Pr = 0.054) under the influence of either axial or radial magnetic field in a vertical cylindrical annulus has been numerically studied. The inner and outer cylinders are maintained at uniform temperatures and the horizontal top and bottom walls are thermally insulated. A finite difference scheme consisting of alternating direction implicit (ADI) method and successive line over relaxation (SLOR) method is used to solve the vorticity stream function formulation of the problem. Detailed numerical results of heat transfer rate, temperature and velocity fields have been presented for 1 ⩽ λ ⩽ 10, 0.5 ⩽ A ⩽ 2, 103 ⩽ Ra ⩽ 106 and 0 ⩽ Har, Hax ⩽ 102. The computational results reveal that in shallow cavities the flow and heat transfer are suppressed more effectively by an axial magnetic field, whereas in tall cavities a radial magnetic field is more effective. It is also found that the flow oscillations can be suppressed effectively by imposing an external magnetic field. The average Nusselt number increases with radii ratio but decreases with the Hartmann number. Further, the present numerical results are shown to be in good agreement with the available benchmark solutions under the limiting conditions.