# Evaluation of the Performance of a Heat Pipe for Pre-Frozen Soil around a Solar Support by a Numerical Method

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Mathematical Model

- The water in soil pores is an incompressible fluid, and convective heat transfer is ignored.
- The soil is considered an isotropic porous medium with pores filled with water, and the volume change of water during phase transition is ignored.
- The soil particles are rigid, and the thermophysical properties are independent of temperature.
- The temperature of the heat pipe is constant.

#### 2.2. Governing Equations and Boundary Conditions

_{eff}stands for the integrated thermal conductivity of the soil. L indicates the latent heat. Meanwhile, the subscripts p, s, and l stand for the soil, and water in solid and liquid, respectively.

_{eff}represent the latent heat of the water and the average thermal conductivity. F is the liquid phase rate, characterizing the proportion of liquid components in the phase change process of water, which can be defined as [33]:

_{S}and T

_{L}are the melting temperature and freezing temperature of the water, respectively.

_{a}and T

_{0}stand for the ambient temperature and the temperature of an outer surface of the heat pipe, respectively. $d$ is the diameter of the heat pipe.${h}_{w}$ represents the comprehensive convective heat transfer coefficient between the ambient and ground surface.

#### 2.3. Solution and Validation of the Model

^{−6}. The buried depth of ground heat exchange pipes (GHEPs) was 1 m, while the temperature of the heat pipe was set to 250 K. The air temperature and combined convective heat transfer coefficient of the ground surface were 268 K and 23.2 W/(m·K), respectively. The parameters of the materials are shown in Table 1.

## 3. Results and Discussion

#### 3.1. Spatiotemporal Characteristics of Soil Freezing

#### 3.2. Effects of Soil Moisture Content on Freezing

#### 3.3. Effects of Soil Types on Freezing

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Digital images of solar collector mount (China Photovoltaic and Energy Storage Demonstration Experimental Platform, Daqing Base).

**Figure 5.**Typical freezing phenomenon characteristics: (

**a**) temperature; (

**b**) temperature distribution.

**Figure 6.**Variation of soil temperature and liquid fraction with radial distance: (

**a**) temperature; (

**b**) liquid fraction.

**Figure 7.**Soil temperature distribution of the calculation region for a month-long operation: (

**a**) after 1 day; (

**b**) after 1 week; (

**c**) after 2 weeks; (

**d**) after 1 month.

**Figure 8.**Variation of temperature and liquid fraction with soil porosity versus (

**a**) temperature; (

**b**) liquid fraction.

**Figure 9.**Variation of temperature and liquid fraction with soil types versus (

**a**) temperature; (

**b**) liquid fraction.

Materials | Density (kg/m ^{3}) | Specific Heat Capacity (J/kg·K) | Thermal Conductivity (W/m·K) | Thermal Diffusivity mm ^{2}/s | Latent Heat (J/kg·K) | ||
---|---|---|---|---|---|---|---|

Clay | 1500 | 1100 | 0.9 | 0.545 | - | ||

Sand | 1900 | 1260 | 1.8 | 0.752 | - | ||

Sandstone | 2500 | 1110 | 2.5 | 0.900 | - | ||

Soil | 1500 | 1000 | 2 | 1.333 | - | ||

Water | 1000 | Liquid | 4189 | Liquid | 0.56 | 0.131 | 333,400 |

Solid | 2093 | Solid | 2.24 | 0.143 |

**Table 2.**Material parameters in the referenced literature [34].

Materials | Density (kg/m ^{3}) | Specific Heat Capacity (J/kg·K) | Thermal Conductivity (W/m·K) | Thermal Diffusivity m ^{2}/day | Porosity |
---|---|---|---|---|---|

Dry sand | 2650 | 1100 | 0.29 | 0.0198 | 0.36 |

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**MDPI and ACS Style**

Li, D.; Yang, X.; Zhao, X.; Yang, R.; Meng, L.; Fu, S.
Evaluation of the Performance of a Heat Pipe for Pre-Frozen Soil around a Solar Support by a Numerical Method. *Processes* **2023**, *11*, 51.
https://doi.org/10.3390/pr11010051

**AMA Style**

Li D, Yang X, Zhao X, Yang R, Meng L, Fu S.
Evaluation of the Performance of a Heat Pipe for Pre-Frozen Soil around a Solar Support by a Numerical Method. *Processes*. 2023; 11(1):51.
https://doi.org/10.3390/pr11010051

**Chicago/Turabian Style**

Li, Dong, Xinpeng Yang, Xuefeng Zhao, Ruitong Yang, Lan Meng, and Shaojie Fu.
2023. "Evaluation of the Performance of a Heat Pipe for Pre-Frozen Soil around a Solar Support by a Numerical Method" *Processes* 11, no. 1: 51.
https://doi.org/10.3390/pr11010051