Over the last decade, much research has been done to understand the role of nanoparticles in heat transfer fluids. While experimental results have shown "anomalous" thermal enhancements and non-linear behavior with respect to CNT loading percentage, little has been done to replicate this behavior from an analytical or computational standpoint. This study is aimed towards using molecular dynamics to augment our understanding of the physics at play in CNT-nanofluid systems. This research begins with a heat transfer study of individual CNTs in a vacuum environment. Temperature gradients are imposed or induced via various methods. Tersoff and AIREBO potentials are used for the carbon-carbon interactions in the CNTs. Various chirality CNTs are explored, along with several different lengths and temperatures. The simulations have shown clear dependencies upon CNT length, CNT chirality, and temperature. Subsequent studies simulate individual CNTs solvated in a simple fluidic box domain. A heat flux is applied to the domain, and various tools are employed to study the resulting heat transfer. The results from these simulations are contrasted against the earlier control simulations of the CNT-only domain. The degree by which the solvation dampens the effect of physical parameters is discussed. Effective thermal conductivity values are computed, however the piecewise nature of the temperature gradient makes Fourier's law insufficient in interpretting the heat transfer. Nevertheless, the computed effective thermal conductivities are applied to classical models and better agreement with experimental results is evident. Phonon spectra of solvated and unsolvated CNTs are compared. However, a unique method utilizing the Irving-Kirkwood relations reveals the spatially-localized heat flux mapping that fully illuminates the heat transfer pathways in the solid-fluid composite material. This method confirms why conventional models fail at predicting effective thermal conductivity. Specifically, it reveals the volume of influence that the CNT has on its surrounding fluid.