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Introducing nanorods into a polymeric matrix can enhance the physical and mechanical properties of the resulting material. In this paper, we focus on understanding the dispersion and orientation patterns of nanorods in an unentangled polymer melt, particularly as a function of nanorod concentration, using Molecular Dynamics (MD) simulations. The system is comprised of flexible polymer chains and multi-thread nanorods that are equilibrated in the NPT ensemble. All interactions are purely repulsive except for those between polymers and rods. Results with attractive versus repulsive polymer-rod interactions are compared and contrasted. The concentration of rods has a direct impact on the phase behaviour of the system. At lower concentrations rods phase separate into nematic clusters, while at higher concentrations more isotropic and less structured rod configurations are observed. A detailed examination of the conformation of the polymer chains near the rod surface shows extension of the chains along the director of the rods (especially within clusters). The dispersion and orientation of the nanorods is a result of the competition between depletion entropic forces responsible for the formation of rod clusters, the enthalpic effects that improve mixing of rods and polymer, and entropic losses of polymers interpenetrating rod clusters., Comment: 16 pages, 15 figures