# Impact of Filled Materials on the Heating Uniformity and Safety of Microwave Heating Solid Stack Materials

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Multiphysics Simulation

#### 2.1.1. Geometry

#### 2.1.2. Governing Equations

_{e}is the electric charge density. Equation (1) in the time harmonic field can be then written as the Helmholtz equation [38]

_{r}is the relative permeability, k

_{0}is the wave number in free space, ε

_{r}is the relative permittivity, ε

_{0}is the permittivity of vacuum, ω is the angular frequency, σ is the electrical conductivity and μ

_{0}is the permeability of vacuum.

_{e}of the processing materials can be gained from the computed electric field by the following equation [39,40]

_{p}is the material heat capacity under atmospheric pressure, T is the temperature, Q is the heat source and k is the thermal conductivity.

#### 2.1.3. Input Parameters and Boundary Conditions

#### 2.1.4. Mesh Size

#### 2.1.5. Simulation Process

#### 2.2. Experimental Setup

#### 2.2.1. Experiment System

#### 2.2.2. Experimental Procedures

_{e}, which is defined as

_{c}is the cut-off frequency of the BJ22 waveguide, f is the frequency of the microwave. The corresponding modification of the experimental length of the BJ22 waveguide is realized by the slide short. A simple test system, shown in Figure 5, is performed to adjust the position of the slide short. By combining the S

_{11}gained from the vector network analyzer (N5230A, Agilent Technologies Inc., Santa Clara, CA, USA), the position of the slide short is confirmed to match the simulation.

## 3. Results and Discussion

#### 3.1. Experiment Validation

#### 3.2. Effect of Introducing Fluid Materials with Different Dielectric Properties

^{3}in order to get a higher temperature rise, and the initial temperature is set as 20 degrees centigrade. The whole heating process lasts 120 s. In the computation results, the reflection parameters S

_{11}of the heating system, the average body temperature $\overline{T}$ of the solids, the coefficient of variation (COV) value of the solids’ final temperature and the maximum modulus value of the electric field |$\overrightarrow{\mathrm{E}}$|

_{max}in the whole processing materials are analyzed. The COV of temperature can be expressed by

_{11}, $\overline{T}$, COV and |$\overrightarrow{\mathrm{E}}$|

_{max}along with ε′ are shown in Figure 8. It is worthy to note that the reflection parameter is calculated by the rate of reflection power and incident power. Computation results of the system are firstly characterized by the reflection coefficient S

_{11}, namely the power absorbed by the processing materials. As shown in Figure 8a, the increasing of ε′ has obvious but nonlinear effects on the S

_{11}and will thus decide the corresponding $\overline{T}$ through its impact on the microwave feeding condition.

_{max}as it changes from 478,870 V/m to 19,982 V/m, which is reduced by about 24 times. Out of this range, the influence of the increasing ε′ stays weak. The differences could be further described by the mean square error as it is 191,152.0 V/m in the former range while it is 3109.9 V/m in the latter, which is reduced by about 60.5 times. Compared with normal heating solids with air surroundings, namely ε′ = 1, the introduction of fluid materials with proper ε′ shows a more convenient way to achieve uniform and safe microwave heating.

_{11}and thus bring more efficient heating. While the S

_{11}and $\overline{T}$ almost stay the same out of this range.

_{max}, as the increasing of ε″ from 0.1 to 0.9 has reduced the |$\overrightarrow{\mathrm{E}}$|

_{max}by about 34% to 55%. However, higher ε″ will cause worse heating uniformity as shown in Figure 9b.

_{max}in simulation models is always gained in the interface between the solids and the fluid materials. Combined with the cure trend shown Figure 8b and the relative permittivity of the solids shown in Table 1, it is deduced that the maximum modulus value of the electric field |$\overrightarrow{\mathrm{E}}$|

_{max}stays huge when the ε′ of fluid materials is much different with the one of solids. A comparison of the variation of |$\overrightarrow{\mathrm{E}}$|

_{max}on fluid materials’ ε′ with solids of different relative permittivity is performed in Figure 10 and the simulation results have agreed with our deduction.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Normalized power absorption (NPA) variation of heating computations with different mesh sizes.

**Figure 6.**Structure of the silicon carbide spheres: (

**a**) Experimental structure; (

**b**) simulation structure.

**Figure 7.**Temperature variation comparisons between the experiment and simulation: (

**a**) Temperature of point (5,0,0) with water as the fluid material; (

**b**) temperature of point (−5,0,0) with water as the fluid material; (

**c**) temperature of point (5,0,0) with glycerol as the fluid material; (

**d**) temperature of point (−5,0,0) with glycerol as the fluid material.

**Figure 8.**Influence of ε′ on the final parameters at time 120 s: (

**a**) Variations of the S

_{11}and the $\overline{T}$; (

**b**) variations of the coefficient of variation (COV) and $\overline{T}$; (

**c**) variations of the |$\overrightarrow{\mathrm{E}}$ |

_{max}.

**Figure 9.**Influence of ε″ on the final parameters with ε′ = 85 at time 120 s: (

**a**) Variations of the S

_{11}and the $\overline{T}$; (

**b**) variations of the COV and the |$\overrightarrow{\mathrm{E}}$|

_{max}.

$\mathbf{\epsilon}\prime \text{}$ | $\mathbf{tan}\mathbf{\delta}\text{}$ | μ_{r} | σ (S/m) | k (W/m·K) | ρ (kg/m^{3}) | C_{p} (J/kg·K) | |
---|---|---|---|---|---|---|---|

Air | 1 | 0 | 1 | 0 | 2.524 × 10^{−}^{2} | 1.205 | 1005 |

Silicon carbide | 12.3 | 0.12 | 1 | 0 | 450 | 3200 | 1600 |

Quartz | 4.2 | 0 | 1 | 1 × 10^{−14} | 10 | 2600 | 260 |

Water | 79.4 | 0.12 | 1 | 5.5 × 10^{−6} | 0.59 | 1000 | 4187 |

Glycerol | 6.33 | 0.18 | 1 | 6.4 × 10^{−8} | 0.27 | 1264 | 2735 |

${\mathbf{\epsilon}}^{\prime}$ | $\mathbf{tan}\mathbf{\delta}$ | ${\mathit{S}}_{11}(\mathbf{dB})$ | $\overline{\mathit{T}}(\xb0\mathbf{C})$ | $\mathbf{COV}$ | ${\left|\overrightarrow{\mathbf{E}}\right|}_{\mathit{m}\mathit{a}\mathit{x}}(\mathbf{V}/\mathbf{m})$ |
---|---|---|---|---|---|

15 | 0 | −3.5994 | 80.48 | 0.160856772 | 12,105 |

0.1 | −5.0345 | 93.66 | 0.145737029 | 10,183 | |

0.5 | −7.3592 | 107.61 | 0.202485855 | 4558.9 | |

0.9 | −7.6533 | 108.9 | 0.229677999 | 4136.1 | |

50 | 0 | −2.0435 | 60.28 | 0.154154613 | 7525.2 |

0.1 | −3.8066 | 82.65 | 0.122400265 | 6047.8 | |

0.5 | −5.9392 | 99.98 | 0.170629879 | 4484.6 | |

0.9 | −5.8709 | 99.54 | 0.193053244 | 4136.1 | |

85 | 0 | −2.8677 | 71.88 | 0.073144433 | 10,796 |

0.1 | −4.0862 | 85.44 | 0.088155288 | 8663.5 | |

0.5 | −5.0389 | 93.68 | 0.176975505 | 6465.7 | |

0.9 | −4.9559 | 93.03 | 0.198345404 | 5898 |

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**MDPI and ACS Style**

Wang, J.; Hong, T.; Xie, T.; Yang, F.; Hu, Y.; Zhu, H. Impact of Filled Materials on the Heating Uniformity and Safety of Microwave Heating Solid Stack Materials. *Processes* **2018**, *6*, 220.
https://doi.org/10.3390/pr6110220

**AMA Style**

Wang J, Hong T, Xie T, Yang F, Hu Y, Zhu H. Impact of Filled Materials on the Heating Uniformity and Safety of Microwave Heating Solid Stack Materials. *Processes*. 2018; 6(11):220.
https://doi.org/10.3390/pr6110220

**Chicago/Turabian Style**

Wang, Jing, Tao Hong, Tian Xie, Fan Yang, Yusong Hu, and Huacheng Zhu. 2018. "Impact of Filled Materials on the Heating Uniformity and Safety of Microwave Heating Solid Stack Materials" *Processes* 6, no. 11: 220.
https://doi.org/10.3390/pr6110220