The dynamic melting of CuO–coconut oil was addressed in a latent-heat thermal energy storage unit loaded with copper foam. In a new design, the thermal storage unit is made of a shell-tube-shaped chamber, in which a liquid flow of hot phase-change material (PCM) is allowed to enter the chamber from a port at the bottom and exit at the top. A fin is mounted in the chamber to forward the entrance PCM liquid toward the solid regions. The control equations were solved using the finite element method. The impact of foam porosity, inlet pressure, fin length, and the concentrations of CuO nanoparticles on the thermal charging time of the chamber was investigated. A fast-charging time of 15 min with a foam porosity of 0.95 was achieved. A porosity of 0.95 can provide a maximum thermal charging power of 15.1 kW/kg. The inlet pressure was a significant parameter, and increasing the inlet pressure from 0.5 kPa to 4 kPa reduced the melting time by 2.6 times. The presence of the fin is not advantageous, and even a long fin could extend the thermal charging time. Moreover, dispersed nanoparticles were not beneficial to dynamic melting and extended the thermal charging time.