Abstarct: Nowadays, using natural convection phenomena in many types of science and engineering and scientific, such as solar energy storage and cooling nuclear reactors, cooling towers, power plants, oil and gas, Aerospace industry and so on is very important. The results show that the addition of nanoparticles to baxse fluids (such as water, oil and ethylene glycol) because of their impact on physical quantities, such as raising the thermal conductivity and heat transfer coefficient is raising the Brown motion. This thesis is devoted to simulation of Numerical investigation of unsteady natural convection heat transfer of nanofluids in an eccentric annulus. Alternating Direction Implicit method (ADI) and the Successive Over_Reiaxation (SOR) are used for discretizing equations. In addition to the effect of different quantities such as Rayleigh number, nanofluid volume fraction, Darcy number, porosity coefficient of the porous medium and ecentry ratio have been investigated in average Nusselt number, local Nusselt number, stream lines and isothermal lines.