Melting in Shell-and-Tube and Shell-and-Coil Thermal Energy Storage: Analytical Correlation for Melting Fraction
Abstract
:1. Introduction
2. Materials and Methods
3. Visual Observations
4. Thermal Analysis
5. Modeling
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Symbols | density [kg/m3] | ||
surface area [m2] | liquid fraction [-] | ||
specific heat capacity [J/kg·K] | Abbreviations | ||
diameter [m] | ANN | artificial neural network | |
Fourier number [-] | CPV | concentrator photovoltaic | |
gravitational acceleration [m/s2] | DC | direct current | |
latent heat [J/kg] | DSC | differential scanning calorimeter | |
characteristic dimension [m] | HTF | heat-transfer fluid | |
length [m] | HVAC | heat, ventilation, and air conditioning | |
mass [kg] | LHTES | latent heat thermal energy storage | |
Nusselt number [-] | PCM | phase-change material | |
Prandtl number [-] | PV | photovoltaic panel | |
heat flux [W/m2] | PVT | photovoltaic thermal collector | |
Rayleigh number [-] | RES | renewable energy sources | |
modified Rayleigh number [-] | TES | thermal energy storage | |
Reynolds number [-] | Subscripts | ||
Stefan number [-] | avg | average | |
modified Stefan number [-] | eq | equivalent | |
t | time [s] | in | inlet |
temperature [°C] | m | melting | |
thermal diffusivity [m2/s] | out | outside | |
thermal expansion coefficient [1/K] | s | solidification | |
thermal conductivity [W/m·K] | t | total | |
dynamic viscosity [Pa·s] | V_avg | volume-averaged | |
kinematic viscosity [m2/s] | w | wall |
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Property | Value | Unit |
---|---|---|
0.329 | W/mK | |
1130 | Kg/m3 | |
146.7 | kJ/kg | |
2.07 | kJ/kg·K | |
25.5 | °C | |
0.02 | Pa·s | |
1.77 × 10−5 | m2/s | |
7.61 × 10−4 | 1/K | |
1.4 × 10−7 | m2/s | |
125.8 | - |
Year | Article | Correlation | Boundary Condition | PCM |
---|---|---|---|---|
1986 | [42] | gallium (pure) | ||
1993 | [18] | n-Octadecane (pure) | ||
1999 | [43] | PEG900 | ||
2001 | [19] | gallium (pure) n-Eicosane (pure) n-Tricontane (pure) | ||
2018 | [44] | Li2CO3–K2CO3 | ||
2019 | [45] | lauric acid (pure) | ||
2023 | [41] | RT35 |
Parameter | Units | Operating Range | Uncertainty | Error |
---|---|---|---|---|
°C | 10–60 | ±0.2 | - | |
V | 1 | ±2 × 10−3 | - | |
A | 5.13 | ±0.01 | - | |
W | 50 | ±0.02 | - | |
m | 0.46 | ±5 × 10−4 | - | |
m | 6 × 10−3 | ±4 × 10−6 [46] | - | |
A | m2 | 8.67 × 10−3 | 7.23 × 10−4 | ±8% |
W/m2 | 597 | ±4 | ±0.8% |
Studied Case | Parameter | Value |
---|---|---|
Tube | 0.105807 | |
75,908.44 | ||
16.5 | ||
Coil | 0.11286 | |
41,456.13 | ||
10.3125 | ||
Coil | 0.38078 | |
1111.5 | ||
10.3125 |
Studied Case | Threshold | A | B | C | E | F | |
---|---|---|---|---|---|---|---|
Tube | −9.115 | −3.508 | 0.6725 | 0.469 | 6.981 | 0.9953 | |
−0.09181 | 0.7105 | 0.05595 | 0.0117 | 2.098 | 0.5268 | ||
Coil | 0.2438 | 0.3932 | 0.08631 | 0.7176 | 0.9447 | 0.9989 | |
0.3567 | 0.47 | 0.1006 | 0.05653 | 0.8187 | 0.1148 | ||
Coil | 0.2753 | 0.5387 | 0.08948 | 0.5043 | 0.9987 | 0.9764 |
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Rogowski, M.; Fabrykiewicz, M.; Andrzejczyk, R. Melting in Shell-and-Tube and Shell-and-Coil Thermal Energy Storage: Analytical Correlation for Melting Fraction. Energies 2025, 18, 2923. https://doi.org/10.3390/en18112923
Rogowski M, Fabrykiewicz M, Andrzejczyk R. Melting in Shell-and-Tube and Shell-and-Coil Thermal Energy Storage: Analytical Correlation for Melting Fraction. Energies. 2025; 18(11):2923. https://doi.org/10.3390/en18112923
Chicago/Turabian StyleRogowski, Michał, Maciej Fabrykiewicz, and Rafał Andrzejczyk. 2025. "Melting in Shell-and-Tube and Shell-and-Coil Thermal Energy Storage: Analytical Correlation for Melting Fraction" Energies 18, no. 11: 2923. https://doi.org/10.3390/en18112923
APA StyleRogowski, M., Fabrykiewicz, M., & Andrzejczyk, R. (2025). Melting in Shell-and-Tube and Shell-and-Coil Thermal Energy Storage: Analytical Correlation for Melting Fraction. Energies, 18(11), 2923. https://doi.org/10.3390/en18112923