This paper presents some of the results of the simulation in the radiation section of an industrial boiler using an advanced mathematical model. Calculations are described for the flow, heat transfer, and chemical reaction processes occurring within a gas-fired cylindrical furnace. The calculation procedure is a two dimensional one in which the main hydrodynamic variables are the velocity and stream functions. The turbulence formulae are used for this purpose. Mass transfer and chemical reactions are calculated from the model which assumes a single-step chemical reaction. Heat transfer is determined hy the solution of differential equations for the specific enthalpy, and for the radiative fluxes for each of the co-ordinate directions. The resulting system of coupled. non linear, elliptic, partial differential equations gives the velocity and temperature gradients inside the furnace. The results are compared with those reported in the literature and good agreements between them were found.