A model has been developed to simulate combustion and heat transfer in a porous matrix combustor-heater. The system consists of a packed bed in which a premixed natural gas-air mixture combusts. Radiative and convective heat transfer occurs from the flame zone to a fluid flowing through a bank of tubes embedded in the packed bed. Radiative heat transfer in the bed is modelled as a diffusion process, and the flow field and temperature distribution in the bed are calculated. The numerically obtained results are compared with available experimental data for a similar system.