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Thermal conductivity is investigated for a cubic C (diamond). Boundary scattering, Umklapp processes, normal processes, and the presence of impurities are the mechanisms considered for heat flow resistance. Three symmetry directions , , , and three polarizations for each direction in the first Brillouin zone are considered for the material. The main purpose of this study is to analyze the effect of the curvature of phonon dispersion curves on the thermal conductivity, and develop an accurate model. The model incorporates the effects of impurity and impurity concentration, film thickness, and crystal orientation on thermal conductivity. The model is validated by comparing results with experimental data for diamond in the  direction. The model is then used for the other symmetry directions using the appropriate dispersion curves. The results show that the curvature of the dispersion curves dramatically affects the thermal conductivity. A sensitivity analysis is conducted to study the effect of boundary scattering as the film decreases in thickness and the effect of impurities.