A comparative study of three low-Reynolds-Number kappa-epsilon turbulence models was undertaken, to establish a model suitable for calculating turbulent-diffusion flames in radiant tubes. A turbulence model capable of accurately predicting the turbulent transport processes in the near-wall region is desirable for determining the local convective heat-transfer rate to the radiant-tube wall. In this study the three turbulence models were judged by assessment of their performance in simulating flows typically encountered in radiant tubes. Model predictions were compared against experimental data obtained in fully developed pipe flows, non-reacting, confined, co-axial-pipe flows and abrupt-expansion pipe flows with heat-transfer. The study indicated that the low-Reynolds-Number kappa-epsilon model proposed by Nagano & Hishida predicted near-wall effects much more accurately than the other two models considered. For abrupt-expansion pipe flows with heat-transfer, an additional source term in the epsilon equation was necessary for reducing near-wall length scales and improving the heat-transfer predictions by means of the low-Reynolds-Number kappa-epsilon turbulence models.