Lattice Boltzmann Method is used to simulate mixed convection between two horizontal cylinders. This geometry is created using Smoothed Profile Method which produces proper fluid-solid interaction force as well as heat exchange. A two dimensional double distribution function lattice Boltzmann method is employed to simulate fluid flow and heat transfer simultaneously. In order to implement the velocity and temperature boundary conditions, the force term and heat source/sink are included in the evolution equations. While fixed Eulerian lattice nodes are employed, while different eccentricities are considered for inner cylinder. In order to simulate mixed convection, the radius ratio is set to be 2.5. Furthermore, the effect of Richardson number by choosing 0.01, 1, 100 and Prandtl number of 0.716 for air and 6.2 for water are investigated. Isotherms, streamlines and mean Nusselt numbers are given for each case. The results are in good agreement with previous related publications.