In this research, a multi-tube heat exchanger filled with phase change material (PCM) is constructed and investigated experimentally to evaluate its capability to serve as a heat storage unit in solar domestic water heating (SDWH) systems. Several operational conditions comprising the PCM initial temperature and the water discharge flowrates are included in the test as external factors to evaluate the performance of the proposed shell-and-tube latent-heat storage unit (STLHS) as a part of a SDWH system. The STLHS unit is assessed according to several quantitative, qualitative, and economic key performance indicators extracted from the Egyptian plumbing code (EPC). Firstly, the quantitative results show that the proposed STLHS unit increased the water temperature by a range of 7–12 °C and maintained a constant hot water supply for extended periods, 2–3 h. Secondly, from the qualitative point of view, the achieved heating levels are insufficient to fulfill the domestic needs according to the benchmark water temperature established by the EPC. Thirdly, evaluating the STLHS unit on an economic basis shows that the annual fuel saving increases by increasing the unit initial temperature, where the annual fuel consumption savings reach 130 m3 of natural gas. Finally, the acquired techno-economic performance measurements emphasize that the proposed unit has a notable possibility for several design modifications to achieve more improvements in its performance.