The objective of present study is to analyze a concentric triple-passage heat exchanger for an optimal design of a continuous hot steel-tube cooling system, where a hot-steel tube line is passing through an antioxidant gas with a constant speed. Velocities and temperatures of the inert gas flowing between inner and outer tubes are calculated theoretically for laminar and numerically for turbulent flow regimes. From their profiles Nusselt numbers and friction factors are calculated (or various ratios of inner/outer tube radii and relative velocities. With these Nusselt numbers triple-passage heat exchangers are investigated for their thermal characteristics. 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 local heat transfer coefficients for flows through an annulus are dependent on local wall heat flux ratios.