A series of direct numerical simulations (DNS) are performed to study the natural convection heat transfer between concentric cylinders at several Rayleigh and Hartmann numbers. The buoyant flow is driven by the temperature difference between the inner and the outer walls, with the inner wall being at lower temperature, while an external transverse magnetic field is imposed. Both laminar and turbulent flows are observed depending on the magnitude of the Rayleigh and Hartmann numbers. The resulting flow structures of the cases studied were both laminar and turbulent. The results show the 3D nature of turbulence and the tendency of the magnetic field to form narrow Hartmann layers, 3D jets and wakes at specific azimuthal angles. Some particular features of the turbulent regime as well as the heat transfer are also investigated. The magnetic field effect on the convective heat transfer is assessed via the Nusselt number showing that conduction dominates as the Hartmann number increases. (C) 2007 Elsevier Ltd. All rights reserved.