A High-Efficiency Single-Mode Traveling Wave Reactor for Continuous Flow Processing

Abstract

This paper proposes a high-efficiency single-mode traveling wave reactor based on a rectangular waveguide and its design method for continuous flow processing. The reactor has a large-capacity reaction chamber (1000 mm × 742.8 mm × 120 mm) that can provide high-energy-efficiency and approximately uniform microwave heating. The microwave heating uniformity is improved by maintaining single-mode microwave transmission and eliminating higher-order modes in such a multi-mode reaction chamber. The high energy efficiency of microwave heating is achieved by adopting impedance matching techniques. The incident microwave in the reactor can remain in a traveling wave state, and the power reflection can be minimized. Several numerical simulations based on multi-physics modeling are conducted to investigate the heating uniformity, the energy efficiency and the flexibility under different operation conditions. The results show the microwave energy efficiency can be higher than 99%, and meanwhile, the coefficient of temperature variation can be lower than 0.4. Furthermore, when the reactor is operated under different flow velocities and with different heating materials, both the energy efficiency and the heating uniformity can also meet the above requirements. The proposed reactor can be used in the applications such as oil processing, wastewater tackling, chemical synthesis, beverage sterilization and other microwave-assisted continuous flow processes that require high heating uniformity, high energy efficiency and good adaptability.

1. Introduction

A continuous-flow microwave reactor is a device that utilizes microwave energy to heat and process continuously flowing chemical solutions; it combines the technologies of microwave heating and continuous flow reactors. Therefore, it shares the advantages of fast and selective heating, non-contact and penetrating processing, high controllability and safety, atom economy, eco-friendly reaction, and so on [1,2]. Because of these benefits, the continuous flow microwave reactor has been widely applied to organic synthesis [3,4], nanoparticle synthesis [5,6,7], heterogeneous catalysis and biofuel production [8], and so on [9,10,11].

With the rapid development of the microwave chemical industry, microwave heating is becoming a popular tool [12]. It is increasingly important to propose different microwave chemical reactors for various demands. Many devices for microwave-assisted chemical reactions have been developed during the past several decades. Generally, they can be classified into multi-mode reactors [13,14] and single-mode reactors [15,16,17,18,19]. However, when high-power microwaves are applied to the processed material, hot spots (large temperature gradient at the specific location) and thermal runaway (the uncontrollable temperature rise due to strong dielectric loss) often occur [20] In some cases, it can lead to the damage of a material or even cause an explosion. In addition to heating uniformity, high energy efficiency with minimum microwave reflection is a common demand for most industrial applications. Moreover, the microwave reactor in real industrial production is frequently expected to be capable of processing different materials under different operation conditions. Therefore, for most microwave reactors, heating uniformity, energy efficiency and adaptability under different operation conditions are of great importance [21,22]. Sarabi, F.E. et al. designed a new traveling wave reactor to heat the catalyst based on a coaxial waveguide structure, achieving high heating uniformity and high energy efficiency [9]. Furthermore, they investigated a reverse traveling reactor in which the microwave radiation was periodically switched from its two ports, and the heating uniformity was further improved [10]. However, the coaxial cable greatly limited its power capacity and large-power applications. Nishioka M. et al. investigated a single-mode microwave reactor for the rapid heating of flowing liquids (including water, ethylene glycol and ethanol) at pressures up to 10 MPa [6]. This reactor is based on a TM₀₁-mode cylindrical resonant cavity that gives it a high heating uniformity. However, its microwave energy efficiency has not been discussed. Mitani T. et al. designed a wideband microwave reactor with a coaxial waveguide structure, achieving high energy efficiency [16]. Their experimental results indicated that the microwave reflection of the reactor could be less than 2% in a certain microwave frequency range. Although high energy efficiency has been achieved, the heating uniformity still remains challenging and unsolved. Our team proposed a capacity-enhanced single-mode reactor for microwave chemistry research [23]. In this reactor, the input microwaves propagated only in TE₁₀ mode and other higher-order modes were successfully restrained, ensuring high heating uniformity. However, its microwave energy efficiency was not high.

Regarding the problems mentioned above, this paper proposes a continuous flow microwave reactor with high microwave energy efficiency, considerably uniform heating performance and good adaptability in processing different chemical reactions. Several multi-physics simulations are conducted to numerically investigate the performance of the reactor under different operation conditions. Among them, improving the uniformity of microwave heating in the reactor can effectively inhibit the occurrence of hot spots and thermal runaway, which can avoid material damage and even explosions. High energy efficiency with a minimum microwave reflection and good adaptability under different operation conditions can endow the proposed reactor with more advantages in industrial applications.

2. Reactor Design and Numerical Simulation

2.1. Geometrical Model and Computational Domain

Figure 1 shows the geometrical structure and the dimensions of the primary part of our proposed microwave continuous flow reactor. The upmost rectangular box is the reaction chamber, into which the reaction solution flows from the front cross section, having a size of $120\mathrm{mm}\times 724.8\mathrm{mm}$. There is a glass plate on the bottom of the reaction chamber, which separates it from a width-increased rectangular waveguide. The width-increased rectangular waveguide is connected with the reaction chamber aslant at an optimized angle of 21.1°. The microwave is generated by a magnetron source and transmitted in a standard WR-975 rectangular waveguide whose cross section has the size of $247.6\mathrm{mm}\times 123.8\mathrm{mm}$. A tapered waveguide is applied to connect the width-increased waveguide and the standard waveguide for the purpose of impedance matching and single-mode maintenance. This technique has been illustrated in detail in our previous work [23].

2.2. Mathematical Model and Boundary Conditions

The propagation, reflection and dissipation of the microwave in the reactor can be obtained by solving the Helmholtz wave equation in the frequency domain as follows:

$$\nabla \times {\mathsf{\mu }}_{\mathrm{r}}^{-1}\left(\nabla \times \overrightarrow{\mathrm{E}}\right)-{\mathrm{k}}_0^2\left({\mathsf{\epsilon }}_{\mathrm{r}}-\frac{\mathrm{j}\mathsf{\sigma }}{{\mathsf{\omega }}_{\mathrm{m}}{\mathsf{\epsilon }}_0}\right)\overrightarrow{\mathrm{E}}=0$$

(1)

$\overrightarrow{\mathrm{E}}$ is the vector of the microwave electric field and ${\mathsf{\omega }}_{\mathrm{m}}$ is its angular frequency ($\mathsf{\omega }=2\mathsf{\pi }\times 2.45\times {10}^9\mathrm{rad}/\mathrm{s}$ in the present case). ${\mathsf{\epsilon }}_{\mathrm{r}}$, ${\mathsf{\mu }}_{\mathrm{r}}$ and $\mathsf{\sigma }$ are the relative permittivity, the relative permeability and the conductivity of the dielectric material in the reactor, respectively. ${\mathrm{k}}_0$ and ${\mathsf{\epsilon }}_0$ are the wavenumber of the microwave in free space and the permittivity of vacuum, respectively. The microwave excitation on the input port of the reactor can be described by the boundary conditions as follows:

$$\overrightarrow{{\mathrm{E}}_0}=\{\begin{array}{c}{\mathrm{E}}_{\mathrm{x}}=0\\ {\mathrm{E}}_{\mathrm{y}}=0\\ {\mathrm{E}}_{\mathrm{z}}=\cos \frac{\mathsf{\pi }\mathrm{x}}{\mathrm{a}}\end{array}$$

(2)

$\overrightarrow{{\mathrm{E}}_0}$ is the normalized amplitude of the microwave electric field on the input port. $\mathrm{a}$ is the width of the cross section of the standard WR-975 waveguide $\left(\mathrm{a}=247.6\mathrm{mm}\right)$. Other boundaries are treated as perfect electric conductors (PEC boundary: $\overrightarrow{\mathrm{n}}\times \overrightarrow{\mathrm{E}}=0$).

The temperature distribution of the processing material is described by the transient heat transfer equation as follows:

$${\mathsf{\rho }\mathrm{C}}_{\mathrm{p}}\frac{\partial \mathrm{T}}{\partial \mathrm{t}}·\nabla \mathrm{T}+{\mathsf{\rho }\mathrm{C}}_{\mathrm{p}}\overrightarrow{\mathrm{u}}·\nabla \mathrm{T}+\nabla ·\left(-{\mathrm{k}}_{\mathrm{t}}\nabla \mathrm{T}\right)={\mathrm{Q}}_{\mathrm{e}}$$

(3)

$\mathrm{T}$ is the temperature (unit: K) of the processing material, $\mathsf{\rho }$ is the density (unit: $\mathrm{kg}/{\mathrm{m}}^3$), ${\mathrm{C}}_{\mathrm{p}}$ is the specific heat capacity at constant pressure (unit: $\mathrm{J}/\left(\mathrm{kg}·\mathrm{K}\right)$), ${\mathrm{k}}_{\mathrm{t}}$ is the thermal conductivity (unit: $\mathrm{W}/\mathrm{m}·\mathrm{K}$) and ${\mathrm{Q}}_{\mathrm{e}}$ (unit: $\mathrm{W}/{\mathrm{m}}^3$) is the heat source from the microwave dissipation that can be obtained by the following equation:

$${\mathrm{Q}}_{\mathrm{e}}=\frac{1}{2}\mathrm{Re}\left(\overrightarrow{\mathrm{D}}·\overrightarrow{{\mathrm{E}}^{*}}\right)$$

(4)

$\overrightarrow{\mathrm{D}}$ is the electric displacement vector of the microwave in the processing material and $\ast$ denotes the complex conjugate. $\overrightarrow{\mathrm{u}}$ is the velocity of the fluid flow in the reaction chamber, which can be obtained by solving the fluid flow equations in steady state. Based on the estimation of the Reynolds number, the fluid flow in the present study can be treated as an incompressible turbulent flow. Therefore, the fluid flow in the reactor chamber can be described by the well-known k-ω model as follows:

$$\mathsf{\rho }(\overrightarrow{\mathrm{u}}·\nabla )\overrightarrow{\mathrm{u}}=\nabla ·\left[-\mathrm{P}\overrightarrow{\mathrm{I}}+\left(\mathsf{\mu }+{\mathsf{\mu }}_{\mathrm{T}}\right)\left(\nabla \overrightarrow{\mathrm{u}}+{\left(\nabla \overrightarrow{\mathrm{u}}\right)}^{\mathrm{T}}\right)\right]$$

(5)

$$\mathsf{\rho }\nabla ·\overrightarrow{\mathrm{u}}=0$$

(6)

$$\mathsf{\rho }\left(\overrightarrow{\mathrm{u}}·\nabla \right)\mathrm{k}=\nabla ·\left[\left(\mathsf{\mu }+{\mathsf{\mu }}_{\mathrm{T}}{\mathsf{\sigma }}_{\mathrm{T}}^{*}\right)\nabla \mathrm{k}\right]+{\mathrm{P}}_{\mathrm{k}}-{\mathsf{\beta }}_0^{*}\mathsf{\rho }\mathsf{\omega }\mathrm{k}$$

(7)

$$\mathsf{\rho }\left(\overrightarrow{\mathrm{u}}·\nabla \right)\mathsf{\omega }=\nabla ·\left[\left(\mathsf{\mu }+{\mathsf{\mu }}_{\mathrm{T}}{\mathsf{\sigma }}_{\mathsf{\omega }}\right)\nabla \mathsf{\omega }\right]+\mathsf{\alpha }\frac{\mathsf{\omega }}{\mathrm{k}}-{\mathsf{\rho }\mathsf{\beta }}_0{\mathsf{\omega }}^2$$

(8)

Equation (5) is the Navier–Stokes equation, and Equation (6) is the mass conservation constraint. P is pressure, $\mathsf{\mu }$ is the dynamic viscosity, ${\mathsf{\mu }}_{\mathrm{T}}$ is the turbulent viscosity, $\overrightarrow{\mathrm{I}}$ is the unit tensor and T denotes the transpose matrix. The k-ω model has two additional Equations (7) and (8) that account for the turbulent kinetic energy $\mathrm{k}$ and the specific dissipation $\mathsf{\omega }$. The values of the parameters in Equations (7) and (8) are based on the Wilcox revised k-ω model and preset in COMSOL [24]. The boundary on the inlet of the reaction chamber for the fluid equations is described by a Dirichlet condition that imposes a constant normal inflow velocity on it. Consequently, a constant room temperature (293.15 K) is also installed on the inlet for the heat transfer equation.

2.3. Initial Values, Preset Parameters and Numerical Implementation

For the design of most microwave reactors, the interactions between the microwaves and the processing materials must be taken into account because they have a significant influence on the heating uniformity and energy efficiency. Only in this way, the simulated results can be reliable and reflect the real performance of the reactor. Furthermore, the adaptability of the microwave reactor in processing various kinds of materials is also vital to its industrial applications.

Based on the above analysis, the modeling processing materials in this study include the representative Debye medium, water, and other materials with different permittivity. Water is chosen as a typical modeling object because it has a temperature-dependent permittivity. Therefore, modeling the microwave heating of water can give representative insights into the interactions between microwaves and heating materials. Electromagnetic simulations with a wide range of permittivity were conducted to demonstrate the adaptability of the proposed reactor in processing different materials. The relative complex permittivity of water $\mathsf{\epsilon }\left({\mathsf{\omega }}_{\mathrm{m}},\mathrm{T}\right)$ can be described by the Debye model [25] as follows:

$$\mathsf{\epsilon }\left({\mathsf{\omega }}_{\mathrm{m}},\mathrm{T}\right)={\mathsf{\epsilon }}_{\infty }+\frac{{\mathsf{\epsilon }}_{\mathrm{s}}-{\mathsf{\epsilon }}_{\infty }}{1+{\mathrm{j}\mathsf{\omega }}_{\mathrm{m}}\mathsf{\tau }}$$

(9)

In the above equation, ${\mathsf{\epsilon }}_{\mathrm{s}}$ is the static relative permittivity that varies with the temperature T, ${\mathsf{\epsilon }}_{\infty }$ is the infinite frequency relative permittivity and $\mathsf{\tau }$ is the relaxation time. Their values can be found in the references [25]. Other parameters of the heat transfer and fluid dynamics of water used in the simulations are given in

Table 1. Preset parameters in the numerical simulations.

	Parameter	Symbol	Value	Source
	Electromagnetics
	Microwave frequency	$\mathrm{f}$	915 MHz	Given
Water	Ratio of specific heat	$\mathsf{\gamma }$	1
	Electrical conductivity	$\mathsf{\sigma }$	0 S/m
	Thermal conductivity	$\mathrm{k}$	0.55 W/(m·K)
	Mass density	$\mathsf{\rho }$	1000 kg/m3
	Heat capacity at constant pressure	${\mathrm{C}}_{\mathrm{p}}$	4200 J/(kg·K)
	Dynamic viscosity	$\mathsf{\mu }$	$1\times {10}^{-3}\mathrm{Pa}\cdot \mathrm{s}$

.

The initial value of the temperature was set to 293.15 K, and the input microwave power was 20 KW. The mathematical model and its numerical calculations were implemented in COMSOL Multiphysics, a commercial computational suite based on the finite element method. The total number of mesh elements was 269,688, and it took about 1 h and 12 min to complete a calculation. A computer with an I7-10700 CPU and 64 GB RAM was employed to do the numerical simulations. The detailed calculation procedure is shown in Figure 2.

3. Results and Analysis

3.1. Validity of Single-Mode Traveling Wave Heating

The proposed reactor was constructed based on the standard rectangular WR-975 waveguide. The TE₁₀ mode is the dominant electromagnetic mode of the rectangular waveguide, which has the minimum half-wave variations of the microwave electric field distribution. Therefore, it has the best uniform heating effect compared with other higher-order modes. Moreover, the TE₁₀ mode has the longest cutoff wavelength, good stability, a wide frequency band and low transmission loss. Accordingly, maintaining only the TE₁₀ mode is preferred when designing the reactor.

Another impact restricting large-scale applications of microwave reactors in industrial production is the volume capacity of the reacting solution. Therefore, the geometrical size of the reaction chamber was enlarged to contain a larger volume of materials for processing at one time. However, enlarging the rectangular resonant chamber generally means allowing higher-order electromagnetic modes to exist. The larger the reacting chamber is, the more the higher-order modes exist and the lower the heating uniformity can be. In this study, we followed our previous work using a proper tapered rectangular waveguide to connect the standard rectangular waveguide WR-975 with the size-enlarged reacting chamber. This technique has been demonstrated as being able to restrain higher-order modes and to maintain only the TE₁₀ mode when the geometrical size of the waveguide is enlarged [23].

Figure 3a shows the distribution of microwave electric field in the reactor when heating water at an input power of 20 KW. It can be observed that the microwave electric field has only one half-wave variation along the x-direction, and it is uniform in the z-direction even in the tapered waveguide. Such distribution characteristics can prove that the microwave in the reactor indeed propagates in a single mode, TE₁₀, without stimulating other higher-order modes. This can be achieved by optimizing the length of the tapered waveguide to a proper value based on full-wave numerical simulations.

In addition to the single-mode characteristics, our proposed reactor has another advantage that the microwave can transmit in the reactor with a little reflection approximately in a traveling wave state. The width-increased rectangular waveguide is connected aslant with reacting chamber at an optimized angle of 21.1°. In this way, the incoming microwave can change its transmission direction along with the reacting material in the glass pane and be absorbed gradually in the propagation. Thus, the reacting chamber with the processing material and the glass pane becomes an impedance-matched load. Such a technique of adding a lossy wedge at the end of a rectangular waveguide as an impedance-matched termination is extensively used and easily found in microwave engineering [26].

Figure 3b shows the microwave electric field distribution at the middle plane of the device. It can be seen that the amplitude of the microwave electric field decreases gradually with the increase of microwave propagation distance, and no apparent standing-wave variations can be observed. This field distribution characteristic can prove that the microwave propagates in a traveling wave state with a little microwave reflection.

In addition to the qualitative analysis of the field distribution characteristics, the values of the reflection coefficient $\mathsf{\Gamma }$ and the relevant voltage standing wave ratio (VSWR) can quantitatively describe the state of microwave propagation. The VSWR is defined as the maximum voltage to the minimum voltage in a standing wave pattern in a microwave transmission structure. It is a function of the reflection coefficient as given in Equation (10), and its value is in the range of $1\le \mathrm{VSWR}<\infty$.

$$\mathrm{VSWR}=\frac{1+\left|\mathsf{\Gamma }\right|}{1-\left|\mathsf{\Gamma }\right|}$$

(10)

The smaller the VSWR is, the better the load is matched to the rectangular waveguide, and the lower the microwave reflection is. When VSWR equals 1, no microwave power is reflected ($\left|\mathsf{\Gamma }\right|=0$), and the microwave propagates in an ideal traveling wave state.

As shown in Figure 4, the VSWR varies between 1.13 and 1.15 during the whole heating process and tends to a constant value of 1.135 after 40 s. The variation tendency agrees with the physical mechanism of microwave heating on water flow. At the beginning, the water absorbs microwave energy, its temperature rises, the microwave absorbing capability goes up, less microwave power is reflected and the VSWR declines. As time goes by, the fluid flow carries the absorbed energy away, forcing the heating and cooling to reach a balance. Figure 4 shows that the balance is reached approximately at 40 s. After that, the temperature distribution of the water flow and its equivalent dielectric permittivity remain constant. This is why the VSWR tends to remain at 1.135 after 40 s.

According to the above analysis, it can be inferred that the microwave chemical continuous flow reactor proposed in this paper can maintain $\mathrm{VSWR}\approx 1$ and $\left|\mathsf{\Gamma }\right|\approx 0$ throughout the whole heating process. It indicates that the reactor has a very limited reflected microwave power and proves again that the microwave in the reactor indeed propagates in a traveling wave state.

3.2. Heating Uniformity

Figure 5 presents the distribution of the temperature field in the reactor with and without a continuous flow at an inflow velocity of 0.05 m/s. It can be observed that the temperature distribution becomes more uniform when continuous flow exists. To quantify the heating uniformity, the coefficient of temperature variation was applied based on the temperature data obtained in simulations. The coefficient of variation (COV) is the standard deviation divided by the mean, which can be used as an indicator of heating uniformity. The COV of temperature can be expressed by [27]:

$$\mathrm{COV}=\frac{\sqrt{\frac{1}{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{T}}_{\mathrm{i}}-\overline{\mathrm{T}}\right)}^2}}{\overline{\mathrm{T}}-{\mathrm{T}}_0}$$

(11)

where $\mathrm{N}$ is the total number of temperature points, ${\mathrm{T}}_{\mathrm{i}}$ is the temperature at a point, $\overline{\mathrm{T}}$ is the averaged temperature and ${\mathrm{T}}_0$ is the initial temperature. The smaller the COV value of the temperature distribution is, the more uniform the microwave heating is. Comparing the COV values estimated based on the data in Figure 5, it demonstrates that continuous flow further improves the uniformity of microwave heating.

The above results demonstrate that the proposed reactor greatly improves the uniformity of microwave heating by utilizing continuous flow processing, maintaining single-mode microwave transmission and eliminating high-order modes.

3.3. Energy Efficiency under Different Operation Conditions

In most industrial applications, microwave energy efficiency is always one of the critical parameters. The analysis above has demonstrated that the microwave in the reactor can propagate in a traveling wave state with a little reflection, which indicates high efficiency of microwave power utilization. Since water is the only absorbing material in the reactor, the dissipated microwave energy can be only absorbed by it. However, an industrial microwave flow reactor is generally expected to have high adaptability under different operation conditions. Therefore, several numerical simulations were conducted to investigate the influence of different inflow velocities and different processing materials on energy efficiency.

For the one-port reactor in our case, the scattering parameter S₁₁ that indicates the microwave power reflection can also be applied to describe the energy efficiency. It is more commonly used in microwave engineering and directly linked with the power utilization and reflection, compared with the voltage reflection coefficient $\mathsf{\Gamma }$. Their relation can be expressed as follows [26]:

$$\left|{\mathrm{S}}_{11}\left(\mathrm{dB}\right)\right|=-20{\log }_{10}\left|\mathsf{\Gamma }\right|$$

(12)

Figure 6 shows the variation of ${\mathrm{S}}_{11} \left(\mathrm{dB}\right)$ at different inflow velocities. The results show that S₁₁ increases with the velocity of the water flow and gradually reaches a constant value lower than −23.5 dB. When the velocity of water flow goes up, more energy is brought out from the reactor, forcing the temperature to decrease to the preset room temperature 293.15 K. According to the Debye equation, the microwave absorbing capability of water decreases with the temperature decline [25]. Therefore, the S₁₁ (dB) increases with the velocity of the water flow up to a constant value as shown in Figure 6. This change coincides with the physical mechanism, which in turn proves the validity of the results. Furthermore, Figure 6 proves that the value of S₁₁ (dB) remains lower than −23.5 dB when the inflow velocity varies. This result indicates that the efficiency of microwave utilization can remain higher than 99%.

To figure out the adaptability of the reactor when the processing material changes, a set of calculations was conducted with different values of dielectric coefficient. The real part changed from 30 to 80, and the imaginary part changed from 10 to 60. It covered a wide range of materials in microwave flow processing, such as brine solution, HNO₃ solution, deionized water, wastewater, and so on.

Figure 7 is a three-dimensional scatter plot of S₁₁ (dB) with the change of the relative complex permittivity. Although the processing material and its dielectric coefficient changed, the S₁₁ (dB) remained lower than −22 dB. It means that less than 1% of the input microwave power was reflected, and the microwave energy efficiency was higher than 99%. It demonstrates the proposed microwave continuous flow reactor can maintain high efficiency of microwave energy utilization when processing different materials.

4. Conclusions

In this paper, a microwave reactor that has high energy efficiency, good heating uniformity and adaptability under different operational conditions is proposed for continuous flow processing. Several multi-physics simulations that considered microwave propagation and dissipation, fluid flow and heat transfer were conducted to investigate the performance of the reactor. The main conclusions can be summarized as follows.

(1)

The processing material can absorb 99% of the input microwave power, which demonstrates that the proposed reactor has high efficiency of energy utilization.

(2)

The coefficient of temperature variation can remain lower than 0.4, which indicates that the uniformity of the microwave heating in the proposed reactor is considerably high.

(3)

With a proper tapered waveguide connection, the input microwave can propagate only in TE₁₀ mode without stimulating other higher-order modes in the size-enlarged multi-mode waveguide and the reaction chamber. This single-mode characteristic can help to improve the heating uniformity.

(4)

By treating the processing material as a part of the waveguide structure and adopting the impedance matching technique, the input microwave in the reactor can remain in a traveling wave state during the whole heating process.

(5)

When the processing material and the inflow velocity change, the high energy efficiency and the heating uniformity can be also maintained, which demonstrates that the proposed reactor has good adaptability under different operational conditions.

The above advantages enable the reactor to have great potential in large-scale industrial applications. However, it is worth noting that the microwave heating in the width of the reaction chamber direction (x-direction as shown in Figure 5) still remained uneven, because of the standing wave distribution in this direction. Therefore, further improvements can be achieved, and they will be our future work.