A numerical simulation of an oscillation-controlled heat-transport coaxial pipe is carried out for studying the flow structure and heat transport characteristics. The heat-transport pipe connects the hot and cold reservoirs, and the cold and hot fluids are discharged with the anti-phase reciprocal waves through circular and annular openings at the ends of the chamber, respectively. By changing the diameter ratio of the circular opening to the inner tube, a unidirectionally circulating flow is observed to develop spontaneously. The flow rate of the unidirectional current is found to be approximately inversely-proportional to the diameter ratio. While the amount of transported heat increases with the flow rate of the unidirectional current (especially when generating strong vortices at the edge of the inner tube) for both cases of thermally-insulated and fully-conductive inner wall, the optimal heat transport performance is attained (not in association with the strongest unidirectional flow) when making zero-averaged vorticity in the cold-end region. For the case of the conductive inner wall, the heat loss across the wall is suppressed with decreasing the diameter ratio, due to the development of the strong jet and radially surrounding shear layer that separate the outer hot fluid from the inner cold fluid.