# Investigation on the Melting Performance of a Phase Change Material Based on a Shell-and-Tube Thermal Energy Storage Unit with a Rectangular Fin Configuration

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Experimental Setup

_{103}), fin temperatures (T

_{102}and T

_{104}), PCM temperature without fins (T

_{105}), inlet HTF temperature (T

_{101}) and outlet HTF temperature (T

_{106}). All thermocouples were calibrated in advance by means of comparison between standard and calibrated thermocouples using a temperature calibration furnace, and the measuring range and accuracy of these thermocouples were −20~100 °C and ±0.2 °C, respectively. The temperature calibration furnace used in this study was a high-precision, multi-functional temperature-measuring testing product, and its machine type and temperature range were SPMK313A and −33~155 °C, respectively. The calibration method could be listed as follows: (1) The tested thermocouples were evenly surrounded around the standard thermocouple and tied up together when their measuring ends were on the same vertical plane. (2) The thermocouples were placed in the temperature calibration furnace, a specific temperature value was set and the thermoelectric potentials of the tested and standard thermocouples were measured, respectively. (3) The deviations between the tested thermocouples and the indexing table at the specific temperature points were calculated using the thermoelectric potentials on the indexing table, the potential values of the specific temperature points in standard certification and the differential thermoelectric potentials at each scale point of the thermocouples. In addition, a data acquisition module was used to collect and record the measuring temperatures once every 3 s during the charging process.

#### 2.3. Experimental Procedure

#### 2.4. TES Characteristics Indexes

_{ch}) and the average charging rate (P

_{ch}) [29]. The total charging time was obtained by monitoring the PCM temperature and its changing rate, while the average charging rate was determined using the following equations.

_{ch}represented the total TES of the PCM unit during the charging process (J), c

_{p}was the HTF specific heat capacity (J/(kg·K)), q

_{HTF}was the HTF flow rate (kg/s), T

_{in}and T

_{out}were the inlet and outlet HTF temperatures (°C), respectively, and n was the number of time intervals.

#### 2.5. Uncertainty Analysis

## 3. Results

#### 3.1. Material Analysis

_{m}/T

_{s}) and phase change latent heat (ΔH

_{m}) of the paraffin wax were determined based on a DSC thermal analysis, as listed in Table 4. The melting temperature represents the initial phase change temperature of the paraffin wax during the charging process, and the solidification temperature represents the initial phase change temperature of the paraffin wax during the discharging process. The latent heat of the paraffin wax was obtained with the numerical integration of the area under the second peak in Figure 4a. However, the latent heat value obtained with the DSC thermal analysis was a little different from that provided in Table 1. The different methods used to determine the specific value of latent heat of paraffin wax may have caused this to happen. Therefore, the thermophysical properties of paraffin wax used in the following analysis were subjected to the results of the DSC thermal analysis.

#### 3.2. Melting Performance of the PCM Unit

_{103}) rose dramatically in the initial period, which was caused by the large temperature difference between the HTF and the PCM. As T

_{103}approached its melting temperature, its temperature rising rate gradually slowed down for a while. This was because the solid–liquid phase change of the paraffin wax absorbed the thermal energy of the HTF by using its latent heat. After the solid–liquid phase change of the paraffin wax was finished, T

_{103}continued to rise slowly as the temperature difference between the HTF and the PCM shrunk. It was observed that both T

_{102}and T

_{104}were higher than T

_{103}for the whole charging process, which meant the temperature gradient between the rectangular fins and the PCM existed. Comparing T

_{105}and T

_{103}, the time for the PCM between fins to melt was much shorter than for that without fins. The reason was that the fins employed expanded the heat transfer area significantly between the HTF and the PCM, which enhanced the charging rate greatly. Moreover, the PCM temperature was always lower than the HTF temperature during the entire charging process, which can be illustrated as follows. Firstly, the heat transfer rate between the HTF and the PCM decreased with the reduction in natural convection in the PCM unit when all the PCM was melted completely. Secondly, the thermal loss from the shell of the PCM unit to the ambient environment without insulation prevented the PCM temperature from increasing inevitably.

_{HTF}= 68 °C and q

_{HTF}= 7 L/min. At the beginning of the melting procedure (Figure 6a), the solid paraffin wax began to expand upward owing to the heat transfer between the HTF and the PCM and the density difference between the solid state and the liquid state of the paraffin wax, indicating that thermal conduction was the present dominant driving force of the melting procedure. As time elapsed (Figure 6b), natural convection took place in the liquid paraffin wax due to the increase in the liquid fraction of the paraffin wax. At this moment, the buoyancy force of the liquid paraffin wax grew strong enough to overcome the flow resistance caused by the viscous force. It was observed that the paraffin wax was firstly heated up and turned to the liquid state in the upper layer. Then, the liquid paraffin wax contacted with the solid paraffin wax along with the solid–liquid interface with the help of natural convection, which accelerated the melting rate further. As the liquid fraction of the paraffin wax in the PCM unit further increased (Figure 6c), the solid–liquid interface gradually moved to the lower layer, and liquid paraffin wax from the lower layer came up to the upper layer, which improved the melting rate significantly. From Figure 6d, most of the paraffin wax was melted in the PCM unit, except for some around the wall corner in the lower layer of the unit. The main reason was that the thermal loss from the shell of the PCM unit to the ambient environment slowed down the melting rate. No difference could be observed from Figure 6e,f, as the paraffin wax had fully melted at that moment.

_{103}reached a relatively steady temperature during the melting procedure, which was also the time when the temperature changing rate of T

_{103}was approaching zero and had a tendency to rise at the same time. For that purpose, the temperature changing rate of T

_{103}when T

_{HTF}= 68 °C and q

_{HTF}= 7 L/min was calculated and is described in Figure 7. Two thermal energy storage stages can be found in Figure 7: the phase change thermal energy storage stage (Stage 1) and the sensible thermal energy storage stage (Stage 2). In addition, the total charging time was considered to be the dividing line of these two stages. The total absorbed thermal energy storage and average charging rate were calculated using Equations (1) and (2), respectively. Table 5 shows the thermal energy storage characteristics of the PCM thermal energy storage unit when T

_{HTF}= 68 °C and q

_{HTF}= 7 L/min. It is worth noting that the charging time determined based on the measuring thermocouple of T

_{103}was relatively shorter than that obtained from the melting photographs in Figure 6, which was possibly owing to the temperature non-uniformity of the paraffin wax during the charging process.

## 4. Discussion

#### 4.1. Influence of Inlet HTF Temperature

#### 4.2. Influence of HTF Flow Rate

_{103}in the PCM unit with HTF flow rates of 4, 7 and 10 L/min. No significant changes in T

_{103}were examined during the charging procedure with HTF flow rates of 4, 7 and 10 L/min. Considering that a higher HTF flow rate requires more pumping power, a lower value of HTF flow rate was suggested for an energy efficient LTES unit.

## 5. Conclusions

- (1)
- The PCM unit with rectangular fins showed the potential for enhancing the melting performance when compared to that without fins. By visualization, the performance was dominated by thermal conduction in the initial state. As time elapsed, natural convection developed to accelerate the melting rate of the PCM.
- (2)
- The inlet HTF temperature had a great influence on the characteristics compared with the inlet HTF flow rate. The total charging time was reduced by 62.38% and the average charging rate was increased by 165.51% when the inlet HTF temperature was increased from 57 to 68 °C.
- (3)
- The higher value of the inlet HTF temperature and the lower value of the HTF flow rate were suggested to improve the energy storage efficiency and reduce the energy consumption of the LTES unit at the same time.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Abbreviation | |

DSC | differential scanning calorimeter |

HTF | heat transfer fluid |

LTES | latent thermal energy storage |

PCM | phase change material |

TES | thermal energy storage |

Symbols | |

cp | specific heat capacity (J·kg^{−1}·K^{−1}) |

Δf | uncertainty of experiment |

ΔH_{m} | latent heat of fusion (J·kg^{−1}) |

l | location of thermocouples (m) |

m | mass (kg) |

n | number of intervals |

P_{ch} | average charging rate (W) |

Q_{ch} | total heat storage (J) |

q | mass flow rate (kg·s^{−1}) |

T | temperature (°C) |

t_{ch} | total charging time (s) |

Subscript | |

ch | charging |

HTF | heat transfer fluid |

in | inlet |

m | melting |

out | outlet |

PCM | phase change material |

s | solidification |

101 | thermocouple 101 |

102 | thermocouple 102 |

103 | thermocouple 103 |

104 | thermocouple 104 |

105 | thermocouple 105 |

106 | thermocouple 106 |

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**Figure 5.**Transient temperature variation in each measuring point in the PCM unit during its charging period.

**Figure 6.**Melting procedure of paraffin wax during different stages of the charging process when T

_{HTF}= 68 °C and q

_{HTF}= 7 L/min. (

**a**) 5 min; (

**b**) 10 min; (

**c**) 15 min; (

**d**) 20 min; (

**e**) 25 min; (

**f**) 30 min.

**Figure 8.**Melting performance of paraffin wax during different stages of the charging procedure with inlet HTF temperatures of 57 and 68 °C. (

**a**) 10 min; (

**b**) 20 min; (

**c**) 30 min.

**Figure 9.**Melting performance of paraffin wax during different stages of the charging procedure with HTF flow rates of 4, 7 and 10 L/min. (

**a**) 10 min; (

**b**) 20 min; (

**c**) 30 min.

Property | Value | Unit |
---|---|---|

Phase change temperature | 48–50 | [°C] |

Specific heat capacity | 2.6 | [kJ/(kg·K)] |

Phase change latent heat | 210 | [kJ/kg] |

Density in solid (at 20 °C) | 0.88 | [kg/L] |

Density in liquid (at 80 °C) | 0.77 | [kg/L] |

Thermal conductivity | 0.2 | [W/(m·K)] |

Volume expansion | 12.5 | [%] |

Thermal expansion coefficient | 5.9 × 10^{−4} | [1/K] |

Parameter | Value | Unit |
---|---|---|

Shell width | 64 | [mm] |

Shell depth | 64 | [mm] |

Shell length | 210 | [mm] |

Shell thickness | 5 | [mm] |

Tube length | 250 | [mm] |

Inner diameter of tube | 13.8 | [mm] |

Tube thickness | 0.7 | [mm] |

Dimensions of fins | 50 × 50 | [mm] |

Fin thickness | 0.15 | [mm] |

Fin pitch | 5 | [mm] |

Number of fins | 36 | [-] |

PCM volume | 0.55 | [L] |

Component | Type | Parameter |
---|---|---|

Circulating pump | MP-20R | Voltage: 220 V; nominal power: 15 W; nominal capacity: 27 L/min; nominal lift: 3.1 m |

Rotameter | Liquid-LZM-15 | Measuring range: 2~18 L/min; accuracy: ±2% |

Thermocouples | T type | Measuring range: −20~100 °C; accuracy: ±0.2 °C |

Sample | T_{m} [°C] | T_{s} [°C] | ΔH_{m} [kJ/kg] |
---|---|---|---|

Paraffin wax | 48 | 52 | 202 |

Parameter | Value | Unit |
---|---|---|

P_{ch} | 241.69 | [W] |

Q_{ch} | 110.21 | [kJ] |

t_{ch} | 7.6 | [min] |

Parameter | Value | Unit | |
---|---|---|---|

T_{HTF} = 57 °C | T_{HTF} = 68 °C | ||

P_{ch} | 91.03 | 241.69 | [W] |

Q_{ch} | 110.33 | 110.21 | [kJ] |

t_{ch} | 20.2 | 7.6 | [min] |

Parameter | Value | Unit | ||
---|---|---|---|---|

q_{HTF} = 4 L/min | q_{HTF} = 7 L/min | q_{HTF} = 10 L/min | ||

P_{ch} | 194.47 | 241.69 | 242.98 | [W] |

Q_{ch} | 110.85 | 110.21 | 107.88 | [kJ] |

t_{ch} | 9.5 | 7.6 | 7.4 | [min] |

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## Share and Cite

**MDPI and ACS Style**

Yu, M.; Sun, X.; Su, W.; Li, D.; Shen, J.; Zhang, X.; Jiang, L.
Investigation on the Melting Performance of a Phase Change Material Based on a Shell-and-Tube Thermal Energy Storage Unit with a Rectangular Fin Configuration. *Energies* **2022**, *15*, 8200.
https://doi.org/10.3390/en15218200

**AMA Style**

Yu M, Sun X, Su W, Li D, Shen J, Zhang X, Jiang L.
Investigation on the Melting Performance of a Phase Change Material Based on a Shell-and-Tube Thermal Energy Storage Unit with a Rectangular Fin Configuration. *Energies*. 2022; 15(21):8200.
https://doi.org/10.3390/en15218200

**Chicago/Turabian Style**

Yu, Meng, Xiaowei Sun, Wenjuan Su, Defeng Li, Jun Shen, Xuejun Zhang, and Long Jiang.
2022. "Investigation on the Melting Performance of a Phase Change Material Based on a Shell-and-Tube Thermal Energy Storage Unit with a Rectangular Fin Configuration" *Energies* 15, no. 21: 8200.
https://doi.org/10.3390/en15218200