A numerical study of the combustion of lean methane/air mixtures in a porous media burner is performed using novelty geometry, cylindrical annular space. The combustion process takes place in the porous space located between two pipes, which are filled with alumina beads of 5.6 mm diameter forming a porosity of 0.4. The outer tube diameter of 3.82 cm is isolated; meanwhile the inner tube of 2 cm in diameter is covered by a continuous set of thermoelectric elements (TE) for transforming heat energy into electricity. To achieve and maintain the proper temperature gradient on TE, convective heat losses are considered from the TE. Computer simulations focus on the two-dimensional (2D) temperature analysis and displacement dynamics of the combustion front inside the reactor, depending on the values of the filtration velocity (0.1 to 1.0 m/s), the heat loss coefficient from the internal cylinder (400-1500 W/m(2)/K), and the fuel equivalence ratio (0.06- 0.5). The conditions that maximized the overall performance of the process of energy conversion are: 0.7 m/s of the filtration velocity, 0.363 of the fuel equivalence ratio and 1500 W/(m(2 center dot)K) of the heat transfer coefficient from the internal cylinder, to obtain 2.05 V electrical potential, 21 W of electrical power, and 5.64% of the overall process efficiency. The study shows that the cylindrical annular geometry can be used for converting the energy of combustion from lean gas mixtures into electricity, with a performance similar to the specified by manufacturers of thermoelectric elements (TE).