| Summary: | According to the authors of this paper, the mathematical point of view allows us to see what sometimes cannot be seen from the designer’s point of view. The aim of this study was to estimate the influence of the most important parameters (volume of heat storage tanks, daily consumption of domestic hot water, optical efficiency, heat loss coefficient, and total area of a solar collector) on the thermal power output of solar domestic hot water (SDHW) system in European climatic conditions. Three deterministic mathematical models of these relationships for Madrid, Budapest, and Helsinki were created. The database for the development of these models was carried out using computer simulations made in the TRNSYS software environment. The SDHW system located at the Bialystok University of Technology (Poland) was the source of the measurement results used to validate the simulation model. The mathematical optimization procedure showed that the maximum annual useful energy output that can be obtained from 1 m<sup>2</sup> of gross collector area is 1303 kWh in the case of Madrid, 918.5 kWh for Budapest, and 768 kWh for Helsinki weather conditions.
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