The effect of thermal dispersion on the steady free convection flow of a nanofluid in a vertical channel is investigated numerically using a single phase model. Considering the laminar and fully developed flow regime a simplified mathematical model is obtained. In the particular cases when solid phase and thermal dispersion effects are neglected the problem was solved analytically. The numerical solution is shown to be in excellent agreement with the close form analytical solution. Nusselt number enhancement with the Grashof number, volume fraction and thermal diffusivity constant increasing has been found.