This work is concerned with domestic boilers burning solid fuels. Time-dependent coal combustion in the counter-current fixed-bed has been investigated using both measurements and mathematical modeling. Three-dimensional, time-dependent model of the fixed-bed has been developed as a submodel to a computational fluid dynamics (CFD)-based model of the whole boiler. The overall 0.0177 kg/(m(2) s) and 0.0266 kg/(m(2) s) coal combustion rates have been observed for air velocities of 0.17 m/s and 0.26 m/s, respectively. Two temperature peaks have been observed: one propagating downward the bed and the other one moving upward from the bed bottom. The developed three-dimensional model has demonstrated good agreement with the measured data. The char oxidation rate is paramount in predicting the temperature-time history of the bed. A 20% increase in its rate has resulted in a 20% increase in the overall combustion rate. A 20% increase in the fuel density has slowed down the combustion rate by around 5%. A 20% increase in the effective thermal conductivity of the fixed-bed has resulted in minor changes.