In this paper, the cross-plane thermal conductance σ of multi-layer graphene nanobundles (MLGNBs) is investigated using the non-equilibrium Green's function method. For the normal MLGNBs, the σ has a positive dependence on the lateral area S due to more atoms involved in the heat transport in the larger S. However, the thermal conductance per unit area Λ is negative dependent on the S since high-frequency phonons contribute less to Λ with low transmission function and small number while the increased phonon branches are mainly located in the high-frequency range. Interestingly, as the S is larger than several square nanometers, the Λ converges to the macroscopic value, independently on the S. Then the staggered MLGNBs is investigated, the results show that increasing both staggering distance between neighboring graphene layers with each other and the graphene layer number in the central device can modulate the σ in a large scope due to the boundary scattering. Finally, in the MLGNBs junction, we found the variation of heat flux direction has an important effect on the σ while the layer number in the central device has weak effect on the cross-plane thermal transport Our results help understand the cross-plane thermal transport of MLGNBs and provide a model to investigate the thermal property of layered material nanobundles.
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