In this paper, the effects of the number and arrangement of radial fins on laminar natural convection between horizontal circular and square cylinders has been investigated numerically with the lattice Boltzmann method. The Rayleigh number is varied from $ {\rm Ra}=10^3-10^6)$, the number of fins $ (N=2-8)$ and the Prandtl number $ (\Pr=0.7)$. The local Nusselt number profiles over the outer and inner cylinders and the average Nusselt number over the top, bottom and side walls of the outer cold square cylinder are obtained. The temperature and streamline contours are also depicted to investigate the heat and fluid flow behavior inside the computational domain.