# Experimental Investigation into the Effect of Fin Shapes on Heat Dissipation Performance of Phase Change Heat Sink

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}K

^{−1}, pure PCM cannot provide the necessary temperature adjustment capability during the long-term use of the seeker. Researchers are now focusing on how to enhance the phase change module’s thermal conductivity in order to boost its heat storage capacity [12,13].

## 2. Model Preparation

#### 2.1. Physical Model

^{3,}with a mass of 52 g. Their weights are shown in Figure 3b and Table 1 as 52.1 g, 52 g, 52 g, and 51.8 g, respectively.

#### 2.2. Theoretical Enthalpy Calculation

_{o}is the initial temperature, h

_{o}is the enthalpy of reference, C

_{p}is specific heat, L is the latent heat of PCM, and λ is the liquid fraction that varies between 0 and 1, which can be calculated by

_{l}and T

_{s}denote the liquidus and solidus temperatures. In this temperature range, PCM takes place, forming a mushy region [36].

## 3. Experimental

#### 3.1. Materials

^{−1}. The thermal conductivity of the paraffin wax (solid/liquid phase) is 0.2 Wm

^{−1}k

^{−1}, and volume expansion coefficient is 1.21 (liquid density 0.87 g/cm

^{3}, solid density1.05 g/cm

^{3}).

^{−1}K

^{−1}and density of 2719 kg/m

^{3}[11]. The contact surface of the chip and the phase change module was coated with a thermally conductive ester, with a thermal conductivity of 6 Wm

^{−1}K

^{−1}, to reduce the contact thermal resistance between them; it was purchased from Suzhou TianMai Thermal Technology Co., Ltd., Suzhou, China.

#### 3.2. Experimental Procedure

_{2}O

_{3}coated with electrode slurry, was used for a heat supply. We prepared three sizes of heating plates, 30 mm × 30 mm, 40 mm × 40 mm, and 50 mm × 50 mm, and the thickness was uniformly 2 mm.

## 4. Uncertainty Analysis

#### 4.1. Error of Input Power

#### 4.2. Error of Ambient Temperature

#### 4.3. Error of Processing and Filling

## 5. Results and Discussions

#### 5.1. Temperature Rise of Different Fin Structures

#### 5.2. Thermal Performance under Different Powers and Heater Areas

^{2}, 1.875 W/cm

^{2}, and 1.2 W/cm

^{2,}accordingly.

^{2}. After 300 s, the temperature change rates of the three heat sources all increased significantly for module 1. This demonstrates that the heat flux of 1.2 W/cm

^{2}is greater than the thermal diffusivity. Module 2 did not change all that much. This demonstrates that a 30 mm heat source exhibits good internal thermal diffusivity within 10 min.

^{2}exceeded its thermal diffusivity, so all three curves had inflection points. Module 2 did not change too significantly. This shows that for a heat source of 30 mm × 30 mm, a good internal thermal diffusion capacity within 10 min could elongate its temperature control time.

#### 5.3. Analysis of the Temperature Rise Curve

_{1}reached 78.6 °C the temperature rise rate slowed down, and when the heating time t

_{2}reached 300 s the temperature rise rate increased significantly. Decreasing the power to 20 W, T

_{1}dropped to 75.2 °C and t

_{2}became 350 s. When the heater size was increased to 50 mm, T

_{1}became 74.5 °C and the t

_{2}inflection point did not appear within 600 s. When changing the heat sink to a bar-shaped structure, T

_{1}rose to 83.4 °C and t

_{2}was delayed by about 400 s. This shows that, for the same fin structure, as the power decreased, the temperature T

_{1}decreased and the t

_{2}was prolonged. The sunflower structure had greater local thermal conductivity and worse overall thermal conductivity; therefore, when compared to Heater 2, T

_{1}of Heater 4 was raised and t

_{2}was extended. In conclusion, Heater 2’s temperature was lower than Heater 4’s.

## 6. Conclusions

- In the case of low power (10 W), the continuous fin structure in module 3 and module 4 had better performance. Under the power consumption of 10 W, the square-shaped fin structure in module 3 performed the best. Based on the temperature rise of module 1, the temperature rise of module 3 was about 10%~20% lower than that of module 2.
- Under the condition of 30 W power, the early stage in module 3 and module 4 had a better heat transfer effect. However, with the prolongation of heating time, the thickness and spacing of the fins played an important role; the linear fin structure in module 2 showed a more stable and lasting enhanced heat dissipation capability.
- For heat sources that work for a long time, the emphasis is on extending the heat to the surrounding area and extending the time of the second inflection point.
- For heat sources with high power consumption and a short working time, the focus is on strengthening the local thermal conductivity and reducing the temperature of the first inflection point.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Physical model of fins with different structures of (

**a**) a discrete columnar-shaped structure, (

**b**) a continuous bar-shaped structure, (

**c**) a continuous square-shaped structure, and (

**d**) a continuous sunflower-shaped structure.

**Figure 6.**Performance of each module under 10 W with heat source size S = (

**a**) 30 mm × 30 mm, (

**b**) 40 mm × 40 mm, and (

**c**) 50 mm × 50 mm.

**Figure 7.**Performance of each module under 30 W with heat source size S = (

**a**) 30 mm × 30 mm, (

**b**) 40 mm × 40 mm, and (

**c**) 50 mm × 50 mm.

**Figure 8.**Performance of each phase change module under 30 W with different heat source sizes: (

**a**) module 1, (

**b**) module 2, (

**c**) module 3, (

**d**) module 4.

Model | Shell Weight (g) | PCM Weight (g) | Total Weight (g) | ||||
---|---|---|---|---|---|---|---|

Theoretical | Practical | Deviation Ratio | Theoretical | Practical | Deviation Ratio | Practical | |

M1 | 189.75 | 194.8 | 2.67% | 52 | 52.1 | 0.19% | 246.9 |

M2 | 189.75 | 194 | 2.23% | 52 | 52 | 0% | 246 |

M3 | 189.75 | 195 | 2.77% | 52 | 52 | 0% | 247 |

M4 | 189.75 | 192.9 | 1.67% | 52 | 52.8 | 1.54% | 245.7 |

Material | k (Wm^{−1} K^{−1}) | ρ (kg m^{−3}) | C_{p} (Jkg^{−1} K^{−1}) |
---|---|---|---|

Al (T6-6063) | 202.4 | 2719 | 871 |

PCM | 0.2 | 867 (l) | 2000 |

Thermal ester | 6 | 1900 | 1200 |

Plate heater | 20 | 3600 | 750 |

Module Number | S (mm) | P (W) | I (A) | V (Volt) | dP | dp/p × 100% |
---|---|---|---|---|---|---|

Module 1 | 30 × 30 | 10 W | 1.66 | 5.98 | 0.07 | 0.70% |

20 W | 2.33 | 8.72 | −0.32 | −1.60% | ||

30 W | 2.81 | 10.68 | −0.01 | −0.03% | ||

40 × 40 | 10 W | 1.68 | 5.91 | 0.07 | 0.70% | |

20 W | 2.39 | 8.38 | −0.03 | −0.15% | ||

30 W | 2.75 | 10.8 | 0.3 | 1.00% | ||

50 × 50 | 10 W | 1.46 | 6.90 | −0.07 | −0.70% | |

20 W | 2.03 | 9.75 | 0.21 | 1.05% | ||

30 W | 2.50 | 12.00 | 0 | 0.00% | ||

Module 2 | 30 × 30 | 10 W | 1.65 | 5.97 | 0.15 | 1.50% |

20 W | 2.34 | 8.72 | −0.4 | −2.00% | ||

30 W | 2.74 | 10.79 | 0.44 | 1.47% | ||

40 × 40 | 10 W | 1.62 | 6.12 | 0.09 | 0.90% | |

20 W | 2.33 | 8.72 | −0.32 | −1.60% | ||

30 W | 2.92 | 10.3 | −0.08 | −0.27% | ||

50 × 50 | 10 W | 1.51 | 6.64 | −0.03 | −0.30% | |

20 W | 2.12 | 9.44 | −0.01 | −0.05% | ||

30 W | 2.58 | 11.61 | 0.05 | 0.17% | ||

Module 3 | 30 × 30 | 10 W | 1.69 | 5.94 | −0.04 | −0.40% |

20 W | 2.35 | 8.67 | −0.37 | −1.85% | ||

30 W | 2.82 | 10.63 | 0.02 | 0.07% | ||

40 × 40 | 10 W | 1.67 | 5.98 | 0.01 | 0.10% | |

20 W | 2.40 | 8.34 | −0.02 | −0.10% | ||

Module Number | S (mm) | P (W) | I (A) | V (Volt) | dP | dp/p × 100% |

Module 3 | 40 × 40 | 30 W | 2.79 | 10.8 | −0.13 | −0.43% |

50 × 50 | 10 W | 1.46 | 6.90 | −0.07 | −0.70% | |

20 W | 2.02 | 9.71 | 0.39 | 1.95% | ||

30 W | 2.63 | 11.4 | 0.02 | 0.07% | ||

Module 4 | 30 × 30 | 10 W | 1.63 | 6.14 | −0.01 | −0.10% |

20 W | 2.34 | 8.72 | −0.4 | −2.00% | ||

30 W | 2.74 | 10.81 | 0.38 | 1.27% | ||

40 × 40 | 10 W | 1.59 | 6.24 | 0.08 | 0.80% | |

20 W | 2.28 | 8.78 | −0.02 | −0.10% | ||

30 W | 2.98 | 10.6 | −0.40 | −1.32% | ||

50 × 50 | 10 W | 1.51 | 6.64 | −0.03 | −0.30% | |

20 W | 2.14 | 9.41 | −0.14 | −0.70% | ||

30 W | 2.47 | 12.12 | 0.06 | 0.20% |

**Table 4.**The temperature of different size heat sources under each cooling module working at 10 W power for 10 min.

Power | Size | Module | Initial Temperature | End Temperature | Temperature Rise | Temperature Contrast |
---|---|---|---|---|---|---|

10 W | 30 mm | M1 | 69.9 °C | 81.8 °C | 11.9 °C | 0% |

M2 | 70 °C | 78.4 °C | 8.4 °C | 29.4% | ||

M3 | 70 °C | 76.3 °C | 6.3 °C | 47.1% | ||

M4 | 70.1 °C | 77.9 °C | 7.8 °C | 34.5% | ||

40 mm | M1 | 70.1 °C | 80.3 °C | 10.2 °C | 0% | |

M2 | 70.1 °C | 76.7 °C | 6.6 °C | 34% | ||

M3 | 70 °C | 75.8 °C | 5.4 °C | 47.1% | ||

M4 | 70 °C | 75.4 °C | 5.8 °C | 43.1% | ||

50 mm | M1 | 70.2 °C | 77.2 °C | 7.0 °C | 0% | |

M2 | 70 °C | 75.3 °C | 5.3 °C | 24.3% | ||

M3 | 70.1 °C | 74 °C | 3.9 °C | 44.3% | ||

M4 | 70 °C | 74.6 °C | 4.6 °C | 34.3% |

**Table 5.**The temperature of different size heat sources under each cooling module working at 30 W power for 10 min.

Power | Size | Module | Initial Temperature | End Temperature | Temperature Rise | Temperature Contrast |
---|---|---|---|---|---|---|

30 W | 30 mm | M1 | 70 °C | 116.3 °C | 46.3 °C | 0% |

M2 | 70 °C | 96.8 °C | 26.8 °C | 42.1% | ||

M3 | 70.1 °C | 99.9 °C | 28.8 °C | 37.8% | ||

M4 | 70.1 °C | 103.4 °C | 33.4 °C | 27.9% | ||

40 mm | M1 | 70.1 °C | 108.3 °C | 38.2 °C | 0% | |

M2 | 70 °C | 87.3 °C | 17.3 °C | 54.7% | ||

M3 | 69.9 °C | 88.9 °C | 19 °C | 50.3% | ||

M4 | 69.9 °C | 89.1 °C | 19.2 °C | 49.7% | ||

50 mm | M1 | 70 °C | 95.7 °C | 25.7 °C | 0% | |

M2 | 70.1 °C | 83.6 °C | 13.5 °C | 47.5% | ||

M3 | 70 °C | 86.4 °C | 16.4 °C | 36.2% | ||

M4 | 69.8 °C | 85.6 °C | 15.8 °C | 38.5% |

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**MDPI and ACS Style**

Liu, X.; Zhu, K.; Wei, Y.; Chen, Z.; Ge, M.; Huang, Y. Experimental Investigation into the Effect of Fin Shapes on Heat Dissipation Performance of Phase Change Heat Sink. *Aerospace* **2022**, *9*, 664.
https://doi.org/10.3390/aerospace9110664

**AMA Style**

Liu X, Zhu K, Wei Y, Chen Z, Ge M, Huang Y. Experimental Investigation into the Effect of Fin Shapes on Heat Dissipation Performance of Phase Change Heat Sink. *Aerospace*. 2022; 9(11):664.
https://doi.org/10.3390/aerospace9110664

**Chicago/Turabian Style**

Liu, Xu, Keyong Zhu, Yijie Wei, Ziwei Chen, Mingming Ge, and Yong Huang. 2022. "Experimental Investigation into the Effect of Fin Shapes on Heat Dissipation Performance of Phase Change Heat Sink" *Aerospace* 9, no. 11: 664.
https://doi.org/10.3390/aerospace9110664