In this paper, effects of anisotropic thermal conductivity and the Lorentz force in a ferro-nanofluid induced by external magnetic fields are investigated. The nanofluid is modeled as a non-linear single-phase fluid, where the viscosity is considered to depend on the nanoparticle concentration; the thermal conductivity shows anisotropy due to the existence of the magnetic field. The anisotropic thermal conductivity tensor, which depends on the magnetic field vector, is derived by considering the principle of material frame indifference of Continuum Mechanics. Numerical simulations are performed in a horizontal annulus enclosure. Effects of the nanoparticle concentration, magnetic distribution, and the dimensionless parameters, such as the Rayleigh number and the Hartmann number, are studied. The numerical results indicate that due to the anisotropic thermal conductivity, the isotherms become elliptic and deviate significantly from a circle which is a typical distribution with isotropic thermal conductivity; furthermore the elliptic shape changes as the direction of the magnetic field varies while the heat transfer is always much faster in the direction parallel to the magnetic field. For the range of the dimensionless parameters studied here, the Nusselt number increases significantly as the Rayleigh number (ranging from 2500 to 50,000) increases; depending on the situation, the magnetic field (the Hartmann number which ranges from 0 to 1) may enhance or diminish the thermal performance. In addition, the streamlines are more organized and less wavy when there exists a magnetic field; this could be attributed to the suppressive effect of the Lorentz force. (C) 2018 Elsevier Ltd. All rights reserved.