This work presents a numerical study of natural convection in a two-dimensional, rectangular, porous medium, differentially heated from its vertical walls. A finite-volume procedure is used to solve the Darcy-Brinkman-Forchheimer model with one energy equation. The purpose of the study is to analyze the effect of thermal dispersion, considering that the effective thermal conductivity of the porous medium depends on the local filtration velocity. The introduction of thermal dispersion in the classical Darcy-Brinkman-Forchheimer model leads to a significant increase in the overall heat transfer and to better agreement with the experimental data, particularly when the thermal conductivities of the fluid and the solid matrix are similar.