Immersion of fins in latent heat thermal energy storage (LHTES) systems has been used as an influential approach to remedy the poor thermal conductivity of phase-change materials (PCMs). This paper numerically investigates heat transfer and phase-change improvement by means of longitudinal fins in a double pipe thermal energy storage unit. The main aim of this study is to investigate the effect of fin orientation on the performance of the thermal storage unit. Six configurations of different fin numbers (2, 4, and 8 fins) and orientations (π/2, π/4, and π/8) are tested. For simulations, a two-dimensional mathematical model incorporating the enthalpy-porosity method and finite volume techniques are established and solved by ansys-fluent. The numerical predictions are successfully validated by comparison with experimental and numerical data from the literature. Heat transfer characteristics and melting process are analyzed through streamlines, isotherms, mean temperature, heat flux (HF), and heat transfer coefficient (HTC) as well as transient melting front position and liquid fractions. Results show that orientation of fins has a significant impact on the charging time for two cases (2 and 4 fins) whereas no significant reduction in charging time was obtained for the case of 8 fins. In case of utilizing 2 fins, a fin orientation of 0 deg (vertical fins) shortens the charging time by up to 2.5 folds compared with the horizontal fins (90 deg). These results could help designing efficient latent thermal energy storage units.