Phase change materials are extensively studied for use in low-, mid-, and high-temperature applications due to their melting and solidification temperatures, latent heat, and thermophysical properties. This work aims to explore the energy stored, or released and their duration for the energy storage unit formed of a phase change material surrounding a tube within which a hot or cold, single or Two-Phase fluid flows, serving as a heat source or sink. The 3D axial transient thermal analysis of the energy storage unit is performed using the finite element method via a MATLAB-developed computer program. The effects of single- or Two-Phase fluid flow on temperature distribution, solidification, melting duration, and energy stored within phase change materials are investigated. The heat transfer coefficient and pressure drop for the single-phase and Two-Phase Flow are presented. A parametric study is performed on thermal energy storage and release, as well as the unit's melting duration. The involved parameters are tube diameters, inlet temperature, Reynolds number of the flowing fluid, and different Phase change materials. The results show that fluid inlet temperature has a significant impact on the stored energy and the melting duration. Increasing the Reynolds number from 1500 to 12000 reduces the melting duration of the unit using Calcium Chloride Hexahydrate by 66%, while increasing the stored energy by 194.12%. The unit with the larger tube diameter showed a faster thermal response than the unit with the smaller diameter under the same operating conditions. Increasing the quality of Two-Phase Flow increases the energy stored and shortens its duration.