In this study, the influences of inlet temperature and velocity of the heat transfer fluid and the capsule material on the performance of a latent heat thermal energy storage unit is numerically investigated. The enhanced thermal conductivity approach is implemented into the ANSYS-FLUENT software to consider the natural-convection-dominated melting process within the capsules. The accuracy of the procedure is checked by comparing the current findings for inward melting against the numerical results from the literature. The comparative results reveal that the proposed approach is successfully incorporated, and the maximum deviation is obtained to be less than 10%. Results of the parametric analyses are represented regarding the first and second laws of the thermodynamics. The time-wise variations of the melting front, the mean temperature of the phase change material, and the rate of entropy generation are evaluated. Increasing the inlet temperature and velocity of air significantly reduces the time for complete melting. The total time for melting is reduced by half when the inlet temperature of air is increased from T-m+10 to T-m+20 and the entropy generation rate increases more than four times. Besides, increasing the air inlet velocity from 0.5 m/s to 3.0 m/s doubles the entropy generation.