A Simplified Model of a Solar Water Heating System with Phase Change Materials in the Storage Tank

The intermittent and variable nature of solar energy poses challenges for maintaining stable thermal performance in solar heating systems. One effective approach to mitigate this limitation is to store surplus thermal energy during periods of high solar irradiance and release it when solar input is insufficient. Phase change materials (PCMs) are particularly suitable for this purpose due to their ability to absorb and release large amounts of latent heat during phase transition. The aim of this work is to develop a mathematical model of a flow-through tank containing a phase change material in the form of a spherical packed bed. Including longitudinal dispersion in the model equations allows for a more accurate description of the heat transfer process in a tank containing PCM elements. Simulation calculations based on the model were carried out to demonstrate its potential applicability to practical problems. The influence of the following parameters on the process was investigated: tank volume, water flow rate, phase change temperature, process duration, dispersion coefficient during water flow, radius of the packed-bed elements, and cyclic variations of the inlet water temperature. A significant influence of the axial dispersion coefficient in the tank containing PCM on the outlet water temperature profile was demonstrated. It was found that the internal heat transfer coefficient within the packing elements containing PCM falls within the range of 58–145 W/(m2K).