A wavy shape was used to enhance the thermal heat transfer in a shell-tube latent heat thermal energy storage (LHTES) unit. The thermal storage unit was filled with CuO-coconut oil nano-enhanced phase change material (NePCM). The enthalpy-porosity approach was employed to model the phase change heat transfer in the presence of natural convection effects in the molten NePCM. The finite element method was applied to integrate the governing equations for fluid motion and phase change heat transfer. The impact of wave amplitude and wave number of the heated tube, as well as the volume concertation of nanoparticles on the full-charging time of the LHTES unit, was addressed. The Taguchi optimization method was used to find an optimum design of the LHTES unit. The results showed that an increase in the volume fraction of nanoparticles reduces the charging time. Moreover, the waviness of the tube resists the natural convection flow circulation in the phase change domain and could increase the charging time.