A two-dimensional axisymmetric model has been developed for combusting, reacting and radiating flows in radiant tubes. To account for possible relaminarisation of the flow in the tube, turbulent mixing of the co-axial streams of fuel and air in the radiant tube is modelled by means of the low-Reynolds-Number k-epsilon turbulence model proposed by Nagano & Hishida. The combustion process is represented by a one-step chemical reaction between the fuel and oxidant, and the assumption of infinitely fast reaction kinetics is employed to predict local species concentration. The fluctuations in mixture fraction are modelled by solution of an additional differential equation for the variance of mixture fraction, and fluctuations in scalar properties are accounted for by use of a double-delta probability density function for the mixture fraction. A modified weighted sum-of-grey-gases model is employed for spectral radiative transfer calculations using the S4 discrete-ordinates approach. Calculated velocity and temperature fields from the two-dimensional mathematical model developed for the radiant tube are found to be in reasonable agreement with experimental measurements obtained in gas-turbine combustor flows.