# Numerical Study of a New Solar Vacuum Tube Integrating with Phase Change Material

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

## 3. Macroscopic Governing Equations

#### 3.1. Macroscopic Governing Equations

- (I)
- A mushy zone exists during the melting of paraffin. Therefore, three phase zones exist during the melting of paraffin, which are; solid zone, liquid zone, and mushy zone.
- (II)
- The physical properties of paraffin in the solid phase and the liquid phase are constant. The physical properties of paraffin in the mushy state change linearly with the temperature.
- (III)
- The liquid paraffin is a Newtonian fluid.

_{f}is the density of the PCM liquid and $\overrightarrow{v}$ is the velocity of the liquid PCM.

_{mushy}is a constant of the mushy zone, which is in the range of 10

^{−4}–10

^{−7}. S

_{b}is the buoyancy term, which is expressed as:

_{ref}is the reference temperature.

_{ref}is the heat enthalpy of the PCM at T

_{ref}and L is the latent heat of the PCM for the solid-liquid phase change. The value of the liquid phase rate, β, during the phase change varies between [0, 1], defined as follows:

_{solid}and T

_{liquid}. T

_{solid}and T

_{liquid}are the low and high limit levels of the mushy zone temperature, respectively. In this paper, T

_{ref}= T

_{solid}.

#### 3.2. Boundary Conditions

_{u}, absorbed by the collection tube is imported into FLUENT by the UDF method. The calculation of Q

_{u}can be found in Appendix A. The temperature boundary condition of the upper surface is set as User-defined-flux.

#### 3.3. Parameter Settings

## 4. Results and Discussion

#### 4.1. Solid-liquid Phase Change Characteristics

#### 4.1.1. Dynamic Change of Average Temperature and Liquid Fraction

_{a}) and the liquid fraction (β) of the paraffin in the vacuum collection tube are shown in Figure 3. The paraffin experiences a process from solid phase to solid-liquid two-phase to liquid phase. As shown in Figure 3, the overall average temperature of the paraffin increases from 300 K to 392 K in one day, the paraffin temperature increases due to heating from solar energy.

#### 4.1.2. Temperature Distribution of Paraffin

#### 4.1.3. Evolution of Phase Change Interface of Paraffin

#### 4.2. Optimization Analysis of Fin Structure Parameters in Vacuum Tube

^{2}. The initial temperature of the paraffin is 325 K, and the heat loss of the vacuum collector to the surrounding environment is neglected. The simulation results are shown in Figure 8.

## 5. Conclusions

- (1)
- As the paraffin gets heat through the daytime, the paraffin experiences a process from solid phase to solid-liquid two phase to liquid phase. Meanwhile, paraffin temperature increases during the daytime. In solid-liquid two phase, paraffin temperature increases slowly as latent heat storage plays an important role during phase change.
- (2)
- The metal fin has a great effect on the phase change heat transfer process of paraffin in SVTs. The closer the paraffin is to the fins, the more uniform the paraffin temperature is and the sooner the paraffin melts.
- (3)
- The metal fin structure and arrangement are major factors that affect the paraffin melting time. The melting time of paraffin decreases with the increase of fin thickness and the decrease of fin spacing. With constant fin volume, it is better to choose a smaller fin thickness and smaller fin spacing.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

ρ_{f} | Density of the PCM liquid [kg.m^{−3}] |

g | Gravitational acceleration [m.s^{−2}] |

$\overrightarrow{v}$ | Velocity of liquid PCM [m.s^{−1}] |

t | Time [s] |

k | Heat conductivity [W.m^{−1}.K^{−1}] |

μ | Dynamic viscosity [kg.m^{−1}.s^{−1}] |

S | Source term in the momentum equation [kg.m^{−2}.s^{−2}.K] |

β | Ratio of the liquid phase to the whole PCM [kg.kg^{−1}] |

ε | Small calculation constant to avoid the denominator to be zero [-] |

A_{mushy} | Constant of mushy zone [-] |

S_{b} | Buoyancy term [kg.m^{−2}.s^{−2}.K] |

α | Volume expansion coefficient of phase change material [-] |

T_{ref} | Reference temperature [K] |

H | Enthalpy of PCM [kJ.kg^{−1}] |

h_{ref} | Heat enthalpy of PCM at T_{ref} [kJ.kg^{−1}] |

T_{solid} | Low limit level of the mushy zone temperature [K] |

T_{liquid} | High limit level of the mushy zone temperature [K] |

T | PCM temperature [K] |

## Appendix A

_{u}is the useful energy obtained by the collector tube, W, Q

_{L}is the heat loss of the collector tube to the surroundings in the same period, W. Q

_{0}is the solar radiation energy absorbed by collector tubes in the same period, W, which can be written as follows:

_{e}is the effective area that can collect solar energy, m

^{2}, I

_{θ}is the solar radiation intensity on the inclined surface of the collector, W/m

^{2}, and (τγ)

_{e}is the product of effective transmissivity and absorptivity of the heat absorbing surface.

_{L}, can be calculated by the following formula:

_{a}is the area of the SVT, T

_{p}is the surface temperature of the SVT, T

_{a}is the ambient temperature, and U

_{L}is the total heat loss coefficient.

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**Figure 1.**Schematic of a phase change energy storage solar vacuum tube. (

**a**) Axial cross–section (

**b**) A-A cross-section.

**Figure 5.**Temperature distribution of paraffin at different sections: (

**a**) At 10:00 am, (

**b**) at 12:00 am, (

**c**) at 13:00 am, (

**d**) at 15:00 am.

Items | Paraffin | |
---|---|---|

Melting point (K) | 328–334 | |

Latent heat (kJ·kg^{−1}) | 158.2 | |

Density(kg·m^{−3}) | Solid phase | 837.7 |

Liquid phase | 772.2 | |

Specific heat(J·kg^{−1}·K^{−1}) | Solid phase | 3200 |

Liquid phase | 2800 | |

Heat conductivity(W·m^{−1}·K^{−1}) | Solid phase | 0.35 |

Liquid phase | 0.15 |

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## Share and Cite

**MDPI and ACS Style**

Shi, J.; Xue, H.; Chen, Z.; Sun, L.
Numerical Study of a New Solar Vacuum Tube Integrating with Phase Change Material. *Sustainability* **2019**, *11*, 6960.
https://doi.org/10.3390/su11246960

**AMA Style**

Shi J, Xue H, Chen Z, Sun L.
Numerical Study of a New Solar Vacuum Tube Integrating with Phase Change Material. *Sustainability*. 2019; 11(24):6960.
https://doi.org/10.3390/su11246960

**Chicago/Turabian Style**

Shi, Juan, Hua Xue, Zhenqian Chen, and Li Sun.
2019. "Numerical Study of a New Solar Vacuum Tube Integrating with Phase Change Material" *Sustainability* 11, no. 24: 6960.
https://doi.org/10.3390/su11246960