Abstarct: Natural convection heat transfer in concentric annulus is one of the most interesting problems for researchers in theoretical and practical area. One of the existing restrictions in maximum heat transfer between horizontal concentric pipes is heat transfer surface, which in this case is restricted to internal and external cylinders. There are several typical methods to increase heat transfer including, heat transfer surface increasing, flow velocity increasing, magnetic field, solid particle adding to baxse fluid and etc. In natural convection heat transfer, solid particle adding to baxse fluid and also considering of a porous media will change stream field, temperature distribution and Nusselt number, substantially. In this study, unsteady natural convection heat transfer in a porous concentric horizontal annulus with an Alumina–Water nanofluid is numerically investigated. The main governing equations on fluid flow including continuity, momentum and energy equations have been discretized with finite difference method. For discretizing equations using the Alternating Direction Implicit method (ADI) and the Successive Over_Reiaxation method (SOR), and obtained algebraic equations system are solved through Tomas algorithm (TDMA). The effect of different quantities such as Rayleigh number, nanofluid volume friction, Darcy number, frequency and amplitude temperature, and porosity coefficient of porous media are investigated on average Nusselt number, local Nusselt number, isothermal lines and stream lines by the means of numerical solution. The results of simulation indicate that an increase in Rayleigh number leads to an increase in average Nusselt number of inner cylinder surface, because of the difference in isothermal and streamlines, which makes the better thermal performance of natural convection in higher Rayleigh number. The effect of nanoparticles volume friction enhancement on increasing the average Nusselt number is more illustrious in low Rayleigh numbers, such that in Ra=۱۰^۳ the ۴% increase of nanoparticles volume friction, caused ۱۱.۸% increase of the average Nusselt number, while in Ra=۱۰^۵ increased ۷.۲%. The decrease of Darcy number decreases permeability of porous media, which in Da=۱۰^(-۴) this decrease is so much that the fluid behaves like a solid body and even with increasing of Rayleigh number, there is no significant effect on increasing Nusselt number and thus decreases heat transfer. The increase in porosity coefficient cause the flow to accelerate and increase in average Nusselt number, which is negligible in lower Rayleigh number (Ra=۱۰^۳).