We investigate the natural convective flow in a reactor bounded by two concentric cylinders and filled with fluid-saturated porous media. The fluid is supposed to generate heat by an exothermic reaction. The problem is described using the non-Darcy model that includes the friction resulted from the macroscopic shear and the flow inertia. We solve the transformed equations using finite difference method. A detailed study of the flow and thermal fields and the heat transfer at the inner and outer walls of the annulus has been conducted for a wide range of the physical parameters, such as, the Darcy number, Forchheimer drag parameter, Frank-Kamenetskii number, Rayleigh number and outer radius of the annulus. Two counter-rotating vortices are generated in each half of the annulus. It is found from the variations of the streamlines and isotherms that for higher values of the physical parameters the outer vortices go upward and the maximum temperature is built up at the top of the annulus. However, for lower values of them the inner and outer vortices occur on the same line and the isotherms become nearly concentric. With the increase of the Darcy number and Rayleigh number, the maximum value of the magnitude of Nusselt number at the inner and outer walls increases whereas its minimum value decreases. As a result, the Nusselt number curves intersect each other. Besides the magnitude of Nusselt number at the inner and outer walls appreciably decreases due to the increase of the Frank-Kamenetskii number and outer radius of the annulus. These findings could be used for the advancement of the existing technology or the development of new technology, especially when an exothermic reaction plays a key role in the convection process in enclosed porous media. (C) 2018 Elsevier Ltd. All rights reserved.