Phase change material (PCM) modeling of heat transfer in multi-plate heat exchangers (MPHEs) is a fundamental research topic aimed at improving the efficiency of warm management frameworks. The main focus of this work is the analytical and mathematical modeling of the heat transmission elements inside MPHEs in conjunction with PCMs, which are renowned for their high inert heat limit and ability to maintain relatively constant temperatures across phase transitions. These days, with fuel sources becoming more and more important, the ability to store energy in heat exchangers using Phase Change Materials (PCM) and release it when needed is crucial. This study aims to illustrate the home water heating system in which paraffin serves as a phase-changing substance and a solar energy storage medium. By assembling the managing conditions, establishing them as a one-layered, verifiable approach, and mathematically estimating the technique conditions, the behavior of a PCM plate was emphasized. Using this framework for solar home water heaters seems appropriate, as evidenced by the results of comparative investigations confirming the modeling’s accuracy for PCM’s overall softening and hardening.