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By using two generic polymer models, namely self-consistent field theory and bond-fluctuation Monte-Carlo simulations, we investigate numerically the properties of a polymer melt in a hexagonal array of nanotubes as a function of the polymer length, the interaction with the nanotubes and the compressibility or average density. The combined effect of the attractive interaction with the nanotube walls, the entropy decrease due to the impenetrability of the walls and the hexagonal arrangement of the nanotubes with varying gap size in between them leads to a wide array of possible density profiles and polymer configurations as a function of the model parameters. Even in the case of the Monte-Carlo simulations, where the contact interaction affects only the first layer of monomers, the effect of the wall can nevertheless be felt throughout the entire melt at intermediate temperatures.