In this study, free convection heat transfer in a concentric annulus between a cold square and heated elliptic cylinders in presence of magnetic field is investigated. The square and elliptic cylinders are maintained at uniform temperatures and it is assumed that the walls are insulating magnetic field. Lattice Boltzmann method is applied to solve the governing equations. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo-Kleinstreuer-Li) correlation. In this model effect of Brownian motion on the effective thermal conductivity is considered. The numerical investigation is carried out for different governing parameters namely; the Hartmann number, Rayleigh number and nanoparticle volume fraction. Also a correlation of Nusselt number corresponding to active parameters is presented. The results reveal that average Nusselt number is an increasing function of nanoparticle volume fraction and Rayleigh number, while it is a decreasing function of Hartmann number. Moreover it can be found that the enhancement in heat transfer increases as Hartmann number increases but it decreases with increase of Rayleigh number. (C) 2013 Elsevier Ltd. All rights reserved.