A two dimensional mathematical model has been developed to simulate the coupled heat and mass transfer in a porous medium undergoing a strong exothermic reaction. The problem has received a lot of interest due to its relevance in a wide variety of engineering applications such heat pipes, nuclear reactors, drying technologies, catalytic reactors and others. The fluid flow is modelled via the Darcy-Brinkman-Forchheimer equation. This model is solved numerically by the finite volume method, and the code is validated by comparing with previously published works. The influence of the exothermic chemical reaction on the heat and mass transfer in the porous medium is discussed. The effects of pertinent parameters such as the Biot number, the Reynolds number and the Frank-Kamenetskii number were analyzed. Quantitative and qualitative results are presented. Comparisons with other works in the literature are performed and excellent agreement between the results is obtained.