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Crystals 2021, 11, 951 5 of 14 2.4. Thoretical Background of TES System Evaluation In this section, we review the necessary equations and theoretical foundations to evaluate the thermal energy storage (TES) and the temperature of the feed water, which was calculated at the start using Equation (1): Tw,aw = Tw1 + Tw2 (1) 2 By linearly interpolating the literature data, the density and specific heat of the water were calculated using Equation (2): f (T) = f (T0) + f (T1) − f (T0) × (Tw,aw − T0) (2) T1 − T0 Equation (3) was used to calculate the heat flux transferred from the water to the PCM material throughout the storage loading process as well as the amount of heat according to the dependency: Q = ρw × Vw × Cw × (Tw,1 − Tw,2) (3) The heat accumulation during the charging and discharging of the paraffin bed were determined by Equation (4). Finally, we determined the theoretical heat using Equation (5): η = Q × 100% (4) t Qt =mPCM×CPCM,S×(Tm−T1)+mPCM×L+mPCM×CPCM,L×(T2−Tm) (5) For more information on the abbreviations and symbols for equations, see Appendix B. 3. Results and Discussion 3.1. TES System Evaluation Based on the obtained results, the heat transferred from the feed water to the PCM material (i.e., PW) when the heat storage was being charged and the heat received by the water from the phase modification material through the heat storage discharge were calculated. Therefore, the feedwater temperature was calculated at the beginning, according to Equation (1). In order to conduct further analysis of the test results, the density and specific heat of the supply water needed to be determined. However, these values change as a function of temperature, as shown in Table 2. Since the literature data only provide the thermophysical properties of water at selected temperatures, analysis of the obtained test results and the density and specific heat of the water were calculated by linearly interpolating the literature data using Equation (2). Table 2. The density and specific heat of water as a function of temperature. Temperature (◦C) 0.01 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 Density (kg/m3) 999.90 999.70 998.20 995.70 992.20 988.10 983.20 977.80 971.80 965.30 958.40 Specific Heat (J/kg. K) 4.212 4.191 4.183 4.174 4.174 4.174 4.179 4.187 4.195 4.208 4.220PDF Image | Paraffin Wax As a Phase Changing Material PCM
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