In the present report, the effect of liquid properties on the effective thermal diffusivity of the oscillation-controlled heat transport tube (the so-called dream pipe) is investigated. First, a slip flow model is presented to investigate the fundamental mechanism and the governing quantities of this phenomena. Results of the analyses show that cascade heat transport between the stagnant boundary layer and the core liquid, which is caused by phase shift between the radial conduction heat-flux and the oscillation, is the fundamental mechanism of the phenomena. Next, it is found that the effective thermal diffusivity reaches a maximum at a value of the thermal diffusivity of the liquid because the phase shift increases with increasing thermal diffusivity. Finally, it is shown that water is one of the desirable operating liquids of the heat transport tube of this type.