The turbulent flow of steam moving through the thermal entrance region of a concentric annulus and a circular tube, is heated by an inner pipe wall of the annulus and the circular tube wall, respectively. An analysis of this was made so as to study unsteady heat transfer combined with thermal radiation and turbulent flow. At the time this study was carried out, we took into consideration the influence of temperature-dependent thermophysical properties, and restricted ourselves to the optically thin limit, using the Planck mean coefficient, K_p(T). The influence from the radius ratio of the annulus and the temperature ratio were examined through numerical calculations of the finite difference methods. In particular, the unsteady states with consideration directed to the temperature-dependent properties of steam are emphasized in this paper.