# The Use of Capsuled Paraffin Wax in Low-Temperature Thermal Energy Storage Applications: An Experimental and Numerical Investigation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Phase Change Material (PCM)

#### 2.1. General Description of the PCM

#### 2.2. Analysis of the PCM’s Internal Structure

#### 2.2.1. Test Conditions and Testing Procedures

#### 2.2.2. SEM Analysing

## 3. Experimental Set-Up and Measuring Procedure

#### 3.1. General Description

^{3}/h, which was generated for the maximum electrical power of the fan engine, equal to 150 W.

#### 3.2. Tested Module

#### 3.3. Preparation of the Module to the Test

#### 3.4. Measurement and Control Systems

#### 3.5. Velocity Profiles at the Inlet and Outlet of the Measurement Section

## 4. Numerical Modeling of the Analyzed System with PCM

#### 4.1. Process Governing Equations

#### 4.2. Geometry, Boundary and Initial Conditions and Numerical Schemes

^{−6}; however, a maximum of 30 iterations per time-step was done. For energy, liquid fraction, and turbulence equations the under-relaxation of 0.5 was applied. For other equations, the default values were set. The calculations were conducted in a parallel mode on a cluster with the use of 16 Intel Xeon E5-2670 v3 2.3 GHz (Haswell) processors. The time of the calculations was approximately two weeks.

## 5. Results

#### 5.1. Experimental Results

#### 5.2. Numerical Results

## 6. Conclusions

- For analysed PCM, five distinct phases during the heating process can be observed (Figure 10). Two of these phases are a phenomenon, in which phase change processes can be singled out. The first transformation is characteristic for water in the temperature range from −4 °C to 0 °C and the second is identified for paraffin from 4 °C to 6 °C.
- Because of the use of forced convection, the time of the melting process can be reduced by even up to 87% (RTI) as compared to stagnation conditions, as shown in Table 6 and Table 7 and Figure 13. It is also worth emphasising that, when changing the outer diameter from the module from 22 to 28 mm, these changes are less noticeable than for the diameters of 18 to 22 mm.
- The mathematical model that is based on the enthalpy porosity method (Equations (1)–(4)) reproduces the conditions in the phase change material during the heating process with a maximum error of up to 20%. (Figure 14, Figure 15 and Figure 16 and Figure 19). It is very important that the proposed model should be implemented in the numerical code, together with variable thermophysical properties (Equations (5)–(7)).
- The SEM tests confirmed the homogeneous structure of the mixture and the lack of changes in the internal structure during phase transformations at characteristic temperatures (Figure 3).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CFD | Computational Fluid Dynamics |

FSOHP | Flower Shape Oscillating Heat Pipe |

FVM | Finite Volume Method |

LHTES | Latent Heat Thermal Energy Storage |

PCM | Phase Change Material |

PDE | Partial Differential Equation |

RTI | Relative Time Increase |

SEM | Scanning Electron Microscope |

TES | Thermal Energy Storage |

## References

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**Figure 3.**Analysis of the PCM internal structure, made for different temperatures and magnifications obtained while using the SEM.

**Figure 10.**Measured temperatures evolution for d = 28 mm PCM module and 0.92 m/s value of the velocity.

**Figure 11.**Derivation evolution of ${T}_{3}$ thermocouple for d = 28 mm PCM module and 0.92 m/s value of the velocity.

**Figure 12.**${T}_{3}$ thermocouple evolution for different diameter of PCM module and velocity: (

**a**) Case 0–0.0 m/s, (

**b**) Case I–0.92 m/s, (

**c**) Case II–2.27 m/s, and (

**d**) Case III–3.18 m/s.

**Figure 14.**Comparison of the experimental and numerical results for the inlet velocity of 0.92 m/s and different cylinder diameters.

**Figure 15.**Comparison of the experimental and numerical results for the inlet velocity of 2.27 m/s and different cylinder diameters.

**Figure 16.**Comparison of the experimental and numerical results for the inlet velocity of 3.18 m/s and different cylinder diameters.

**Figure 17.**Numerical results of temperature distribution in the middle vertical plane for the inlet velocity of 0.92 m/s and cylinder diameter of 15 mm and different times of the simulation.

**Figure 18.**Numerical results of temperature distribution in the middle horizontal plane for the inlet velocity of 0.92 m/s and cylinder diameter of 15 mm and different times of the simulation.

**Table 1.**The thermophysical properties of the Phase Change Material (PCM) used during the experiments [40].

Property | Unit | Minimum | Maximum |
---|---|---|---|

PCM content in the dispersion | % | 25 | 30 |

PCM content in dry capsule | % | 75 | 80 |

Dry content in the dispersion | % | 35 | 38 |

PCM melting range | °C | 4 | 6 |

Heat storage capacity (of slurry) | kJ/kg | 60 | 72 |

Heat storage capacity (of dried microcapsules) | kJ/kg | 180 | 192 |

pH | − | 7.0 | 9.0 |

Density | kg/m^{3} | 900 | 970 |

Dynamic viscosity (at 25 °C) | kg/(m s) | 0.1 | 0.5 |

Average particles size | μm | 10 | 30 |

Outer Diameter of Module | $\mathbf{mm}$ | 15 | 22 | 28 |
---|---|---|---|---|

PCM/module mass fraction | % | 25.23 | 31.53 | 37.82 |

Copper/module mass fraction | % | 74.77 | 68.47 | 62.18 |

Sensible heat of copper | $\mathrm{kJ}$ | 1.62 | 2.66 | 3.71 |

Sensible heat of PCM | $\mathrm{kJ}$ | 2.87 | 5.46 | 10.19 |

Latent heat of PCM | $\mathrm{kJ}$ | 2.46 | 4.68 | 8.74 |

PCM/module heat fraction | % | 76.69 | 79.22 | 83.63 |

Copper/module heat fraction | % | 23.31 | 20.78 | 16.37 |

Parameter | Unit | Case 0 | Case I | Case II | Case III |
---|---|---|---|---|---|

Power of the fan | W | 0 | 60 | 80 | 150 |

Mean velocity | m/s | 0.00 | 0.92 | 2.27 | 3.18 |

Maximum deviation from the average value | % | – | 7.36 | 7.15 | 5.19 |

Material | Density kg/m ^{3} | Specific Heat J/(kg K) | Thermal Conductivity W/(m K) | Dynamic Viscosity kg/(m s) | Melting Heat J/kg | Solidus Temperature °C | Liquidus Temperature °C |
---|---|---|---|---|---|---|---|

Paraffin wax | Equation (5) | 2500 | Equation (6) | Equation (7) | 72,000 | 4 | 6 |

Air | 1.125 | 1006.43 | 0.0242 | 1.7894 × 10^{−5} | - | - | - |

Plexi-glass | 1000 | 1000 | 0.2 | - | - | - | - |

Copper | 8978 | 381 | 387.6 | - | - | - | - |

Domain/Material | Location | Boundary | Unit | Value |
---|---|---|---|---|

Duct/plexi-glass | External walls | Wall-temperature | °C | 24 |

Internal walls | Interface | – | Coupled wall [47] | |

Air/air | Duct wet walls | Interface | – | Coupled wall [47] |

Upper base wet walls | Interface | – | Coupled wall [47] | |

Lower base wet walls | Interface | – | Coupled wall [47] | |

Cylinder base wet walls | Interface | – | Coupled wall [47] | |

Inlet | Inlet-velocity | m/s | 0.92,2.27,3.18 | |

Inlet-temperature | °C | 24 | ||

Outlet | Outlet-pressure | bar | 1 | |

Upper base/copper | External and internal walls | Interface | – | Coupled wall [47] |

Lower base/copper | External and internal walls | Interface | – | Coupled wall [47] |

Cylinder/copper | External and internal walls | Interface | – | Coupled wall [47] |

PCM module/paraffin wax | External walls | Interface | – | Coupled wall [47] |

Case | PCM 15 mm | PCM 22 mm | PCM 28 mm |
---|---|---|---|

Case 0 | 05 min 45 s | 18 min 55 s | 35 min 30 s |

Case I | 03 min 00 s | 11 min 00 s | 17 min 30 s |

Case II | 02 min 20 s | 07 min 15 s | 12 min 30 s |

Case III | 01 min 55 s | 05 min 15 s | 11 min 05 s |

Case | PCM 15 mm | PCM 22 mm | PCM 28 mm |
---|---|---|---|

Case 0 | 05 min 25 s | 24 min 05 | 36 min 5 s |

Case I | 02 min 25 s | 10 min 50 s | 13 min 50 s |

Case II | 02 min 00 s | 04 min 55 s | 07 min 00 s |

Case III | 00 min 50 s | 03 min 00 s | 04 min 40 s |

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**MDPI and ACS Style**

Ochman, A.; Chen, W.-Q.; Błasiak, P.; Pomorski, M.; Pietrowicz, S.
The Use of Capsuled Paraffin Wax in Low-Temperature Thermal Energy Storage Applications: An Experimental and Numerical Investigation. *Energies* **2021**, *14*, 538.
https://doi.org/10.3390/en14030538

**AMA Style**

Ochman A, Chen W-Q, Błasiak P, Pomorski M, Pietrowicz S.
The Use of Capsuled Paraffin Wax in Low-Temperature Thermal Energy Storage Applications: An Experimental and Numerical Investigation. *Energies*. 2021; 14(3):538.
https://doi.org/10.3390/en14030538

**Chicago/Turabian Style**

Ochman, Agnieszka, Wei-Qin Chen, Przemysław Błasiak, Michał Pomorski, and Sławomir Pietrowicz.
2021. "The Use of Capsuled Paraffin Wax in Low-Temperature Thermal Energy Storage Applications: An Experimental and Numerical Investigation" *Energies* 14, no. 3: 538.
https://doi.org/10.3390/en14030538