A reciprocal flow filtration combustor with embedded heat exchangers is numerically studied. In this system the combustion of methane and air mixture is stabilized in a: transient porous media combustor by periodical switching the, direction of the flow. Two heat exchangers are placed in the terminal sections of the porous matrix, constraining the reaction in the. central insulated zone. The predicted temperature profile inside the reactor has a typical trapezoidal shape. The central plateau temperature ranges between 1300 and 1600 K as the equivalence ratio varies from 0.15 to 0.7 and the filtration velocity from 15 to 45 cm/s. The efficiency spans the range of 50-80% being higher for higher equivalence ratios and filtration velocities.