Net heat current at zero mean temperature gradient

The existence of a net heat current conductive thermal waves is demonstrated even in the absence mean temperature gradient. This effect, which we called shuttling, generated by temperature-dependent conductivity materials excited with excitation periodically modulated time. We show that this modulation gives rise to superimposed on one gradient, enhances transport when increases temperature. By contrast, if decreases as increases, thermal-wave inverts its direction and reduces total flux. reported shutting effect sensitive amplitude periodic excitation, can facilitate observation application harvest energy from variations environment.