This report presents analytical results on the effects of heat transfer between the tube walls and the liquid column on the effective thermal diffusivity in the liquid column region of bundles of two-dimensional oscillation-controlled heat transport tubes. The analytical results are derived for two types of bundle. The first is a novel inverted oscillation-phase (IO) type in which the phase difference of oscillation between adjacent liquid columns is π/ω. The second is the conventional synchronized oscillation (SO) type in which the phase difference is 0. The comparison between the effective thermal dlffusivities of the two types shows that, in the case of thin walls, the IO type has effective thermal diffusivities much higher than those of the SO type.