New Deterministic Mathematical Model for Estimating the Useful Energy Output of a Medium-Sized Solar Domestic Hot Water System

Abstract

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 m2 of gross collector area is 1303 kWh in the case of Madrid, 918.5 kWh for Budapest, and 768 kWh for Helsinki weather conditions.

Heat Transfer and Heat Recovery Systems

“…Żukowski and Jezierski used a mathematical approach to investigate the impact of various factors on the thermal performance of solar domestic hot water (SDHW) systems in different European climates [15]. They created three deterministic mathematical models using data from computer simulations of SDHW systems in Madrid, Budapest, and Helsinki.…”

The Use of Solar Collectors in Domestic Hot Water Systems in Central and Eastern European Countries: Simulation in TRNSYS

“…Zukowski and Jezierski [21] estimated the effect of five selected parameters (volume of heat storage tanks, total area of solar collectors, optical efficiency, daily consumption of domestic hot water, and heat loss coefficient) on the thermal power output of a solar domestic hot water system in three European cities, Madrid, Budapest, and Helsinki. Based on an existing installation operating under real conditions in Bialystok, they created and validated a model of the system, simulated its operation in TRNSYS software, and then developed three new deterministic mathematical models for determining the impact of the factors mentioned above on the annual useful energy output.…”

Peak Power of Heat Source for Domestic Hot Water Preparation (DHW) for Residential Estate in Poland as a Representative Case Study for the Climate of Central Europe

“…The decreased hot water usage caused the higher water consumption irregularity which influences the heating peak power of the heat source. In the literature, one can find articles presenting the results of research on the possibility of increasing the efficiency of domestic hot water preparation systems, such as [24], as well as analyzing the possibility of their integration with renewable energy sources [25], usage of phase change materials in solar domestic hot water systems [26,27] or verifying the influence of technical parameters of the hot water preparation system on its effectiveness [28]. The sheer volume of hot water consumption by building residents is also a subject of analysis.…”