Heat conduction rectifier is attracting more attention due to its potential application to process thermal currents independently and convert them into electronic signals. This work reports an investigation by molecular dynamics simulation on the heat conduction rectification effect in the nanostructure whose cross-section have step change along the heat flux. It is found that thermal resistance is different with reversed heat flux direction, which is called the heat conduction rectification. The heat conduction rectification depends on the temperature difference. By reducing temperature difference across the nanostructure, the rectification could be reversed. When the temperature difference is small enough, the thermal resistance is larger when the heat flux flows from the thick part to the thin part when the length of the structure is about 10 nm. The larger variation in the cross-section leads the larger difference in the thermal resistance with opposite heat flux. The mechanism of the rectification is discussed. If we take phonons as liquid particles and consider the case of a liquid flowing through a channel with step expansion in cross-section, the flow resistance is less with liquid flowing from the narrow part to the wide part than that in the case with contrary flow direction. In fact, the scattering of phonons at the step face reduces the mean free path of phonon when heat flux conducts from the narrow end to the wide end.

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