The objective of present study is to analyze a hot steel-tube cooling system as a kind of concentric triple-passage heat exchanger, whose inner tube is moving with a constant speed. Velocities and temperatures of an antioxidant gas flowing between inner and outer tubes are calculated theoretically for both laminar and turbulent flow regimes and used to give Nusselt numbers and friction factors with respect to various radius ratios and velocity ratios. In addition, it is shown that heat transfer coefficients based on ratios of average heat fluxes from inner and outer tubes might result in great errors for the temperature distributions of the flows, since the local heat transfer coefficients are dependent on the local heat flux ratios.