# Modelling and Characterization of Effective Thermal Conductivity of Single Hollow Glass Microsphere and Its Powder

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Hollow Glass Microspheres

_{2}and 20% CaO.

## 3. Experiment

#### 3.1. Introduction of the TPS Method

#### 3.2. Experimental Program

## 4. Computational Model and Results

#### 4.1. Three Different HGM Stacking Elements

#### 4.2. 3D Two-Step Hierarchical Computational Method

_{2}system is approximately given through the rule of mixture as 1.03 W/(mK) [37], which is close to that of glass [38]. The thermal conductivity of matrix material is assumed to be 0.93 W/(mK), unless specially stated. In the analysis, the fictitious matrix material is just introduced in the computational method to form new composite systems, thus the predicting results of the microsphere should theoretically be independent of the choice of matrix material. Additionally, it is assumed that each material phase is isotropic and homogeneous.

#### 4.2.1. The Composite System with Actual Filler

#### 4.2.2. The Composite System with Equivalent Filler

#### 4.2.3. Basic Heat Transfer in the Two Composite Systems

#### 4.2.4. Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**Principal experimental setup for the transient plane source (TPS) method and the sensor shape.

**Figure 6.**The TPS equipment for powder measurement (

**a**) Indicator; (

**b**) two sensors; (

**c**) cylindroid container.

**Figure 7.**Assumed configurations of HGMs in the powder: (

**a**) the periodic cubic close-packing and (

**b**) the periodic hexagonal close-packing.

**Figure 8.**The corresponding HGM stacking elements: (

**a**) the single HGM stacking element; (

**b**) the cubic HGM stacking element and (

**c**) the truncated octahedron HGM stacking element.

**Figure 9.**Schematic diagram of basic procedure of the present method for arbitrary stacking element.

**Figure 13.**Distributions of (

**a**) the temperature and (

**b**) the heat flow ${q}_{z}$ along the z direction in the three-phase composite unit cell with 20% microsphere volume fraction.

**Figure 14.**Variations of heat flux component ${q}_{z}$ along the z direction in the two-phase composite unit cell with 20% microsphere volume fraction.

**Figure 15.**Results from the two-phase and three-phase composite systems for different microsphere volume fractions.

Group | Heating Power (W) | Temperature Increase (K) | Thermal Conductivity (W/(mK)) |
---|---|---|---|

A | 0.061 | 282.78 | 0.0981 |

0.071 | 283.79 | 0.1005 | |

0.081 | 285.29 | 0.1014 | |

B | 0.061 | 283.25 | 0.0877 |

0.071 | 284.76 | 0.0969 | |

0.081 | 284.39 | 0.1054 | |

C | 0.061 | 281.81 | 0.1083 |

0.071 | 284.11 | 0.0943 | |

0.081 | 284.69 | 0.1115 | |

D | 0.061 | 282.73 | 0.0952 |

0.071 | 284.30 | 0.1013 | |

0.081 | 285.40 | 0.1025 |

Particle Size | Value |
---|---|

Average outer diameter D = $2R$ ($\mathsf{\mu}\mathrm{m}$) | 58.64 |

wall thickness t ($\mathsf{\mu}\mathrm{m}$) | 1.6 |

Thermal conductivity | |

Thermal conductivity of the gas ${k}_{g}$ (W/(mK)) | 0.023 [38] |

Thermal conductivity of the solid wall ${k}_{w}$ (W/(mK)) | 1.03 |

Thermal conductivity of the matrix ${k}_{c}$ (W/(mK)) | 0.93 |

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**MDPI and ACS Style**

Liu, B.; Wang, H.; Qin, Q.-H.
Modelling and Characterization of Effective Thermal Conductivity of Single Hollow Glass Microsphere and Its Powder. *Materials* **2018**, *11*, 133.
https://doi.org/10.3390/ma11010133

**AMA Style**

Liu B, Wang H, Qin Q-H.
Modelling and Characterization of Effective Thermal Conductivity of Single Hollow Glass Microsphere and Its Powder. *Materials*. 2018; 11(1):133.
https://doi.org/10.3390/ma11010133

**Chicago/Turabian Style**

Liu, Bing, Hui Wang, and Qing-Hua Qin.
2018. "Modelling and Characterization of Effective Thermal Conductivity of Single Hollow Glass Microsphere and Its Powder" *Materials* 11, no. 1: 133.
https://doi.org/10.3390/ma11010133