Compact Microwave Continuous-Flow Heater

Abstract

Microwave continuous-flow heating has been proven to reduce the time of chemical reaction, increase the conversion rate, and improve product purity effectively. However, there are still problems such as relatively low heating efficiency, unideal heating homogeneity, and poor compactness, which brings further drawbacks like difficulty in fabrication and integration. In this study, a compact microwave continuous-flow heater based on six fractal antennas is proposed to address the problems above. First, a multi-physics simulation model is built, while heating efficiency and the volumetric coefficient of variance (COV) are improved through adjusting the geometric structure of this heater and the phase assignment of each radiator. Second, an experiment is conducted to verify the simulation model, which is consistent with the simulation. Third, a method of fast varying phases to achieve greater heating efficiency and heating homogeneity is adopted. The results show that the single-phase radiator improved efficiency by 31.1%, and COV was significantly optimized, reaching 64%. Furthermore, 0–100% ethanol–water solutions are processed by the heater, demonstrating its strong adaptability of vastly changing relative permittivity of liquid load. Moreover, an advance of this microwave continuous-flow heater is observed, compared with conventional multi-mode resonant cavity. Last, the performance of this microwave continuous-flow heater as the chemical reactor for biodiesel production is simulated. This design enables massive chemical production in fields like food industry and biodiesel production, with enhanced compactness, heating efficiency, and heating homogeneity.

1. Introduction

Microwave continuous-flow heating has been widely used as a fast, efficient, and clean heating method in many fields, such as food sterilization, material synthesis, and chemical engineering [1,2,3,4,5]. Extensive studies have proven that continuous-flow heating facilitates process intensification and continuous processes [6,7], allowing for more efficient and consistent production [8,9,10,11]. Therefore, it has great significance for large-scale chemical production. Although it has been proven to have many advantages, there are still many limitations in the design of continuous-flow systems. Among them, most continuous-flow heating systems have large, resonant cavities that are not compact enough and are difficult to fabricate [12,13]. In addition, microwave heating efficiency deserves attention, which can be reduced by energy loss due to the mismatch between the microwave heater and the source [14]. Discussions of microwave heating efficiency are often restricted to a specific load [15,16]. However, once the temperature of the liquid increases, or once contents change during the chemical reaction, the impedance of the liquid load will greatly change, causing a large variation in heating efficiency [17]. Meanwhile, the uneven distribution of the electric field in the cavity not only affects the uniformity of heating but also causes thermal runaway [18,19]. Moreover, the limited microwave penetration depth makes it difficult for the inner sections of liquid to be heated to meet the requirements of large-scale chemical production [20,21,22]. These problems have greatly restrained the application and development of microwave continuous-flow heating in the chemical area.

There has been significant effort trying to address these problems. For example, M. Gable et al. designed a continuous-flow microwave-heating system of 15 pentagonally arranged magnetrons for the conditioning and cooking of canola oil extraction [23]. Although oil yield increases and oil quality are not significantly different from the conventional steam-heating process, the equipment is bulky, and the microwave heating is combined with hot air heating, so the contribution of microwave heating to efficiency and uniformity cannot be determined precisely. Similarly, a novel and compact multi-mode microwave cavity was proposed by O. Karatas et al. for flash pasteurization of beer [24]. Proper time-temperature combination has been settled through COMSOL simulation, but efficiency and heating uniformity are not covered. S. Phromphithak et al. applied a multi-mode cavity for the chemical reactor to synthesize methyl esters from palm oil catalysed by choline hydroxide [25]. A series of experiments were conducted to determine the best reaction condition, the device is relatively compact, and the formula of microwave heating efficiency is provided, but efficiency is not calculated and heating uniformity is not discussed. H. Yang et al. proposed a continuous-flow microwave heater of a rectangular resonant cavity mounted by an array of 12 rectangular waveguides, which are delicately adjusted by stub tuners as equivalent capacitors for the pasteurization of milk [13]. Although simulation is performed to optimize the geometrical structure and efficiency is more than 70%, this microwave heater is too bulky and difficult to integrate with other systems, and heating uniformity is not mentioned. Although these researchers have addressed some of the problems, a more compact, efficient, and uniformly heating continuous-flow microwave heating device is still desired.

This essay describes a novel continuous-flow microwave heater involving a patch fractal antenna. Optimization of dimensional details and phase setting is conducted through multi-physics simulation, and its performance of heating solid and fluid water is displayed. Heating performance within a large dynamic range of dielectric constants of liquids is simulated with 0–100% (v/v) of ethanol–water solutions, “(v/v)” is used here to clearly indicate the volume ratio relationship between ethanol and water in a mixed solution, and the method of fast varying phases is adopted to increase temperature homogeneity. These simulated results are compared with multi-mode resonant cavities and verified by experiments, and the performance of this continuous-flow microwave heater as a chemical reactor of biodiesel production is also simulated.

We proposed the design of a microwave-heating device based on six fractal antennas, which is the most critical innovation in this paper. The core design objectives of our device are to enhance efficiency and achieve miniaturization. Compared to traditional multi-mode resonant cavities, the design of fractal antennas and their paired linear arrangement result in a more uniform electromagnetic field distribution, thereby improving heating uniformity. This also prevents the issue of energy focusing when using a cylindrical material structure. Additionally, we have continuously optimized the antenna structure design and phase adjustment, significantly improving the utilization efficiency of electromagnetic energy and addressing common issues in traditional microwave heating systems, such as localized overheating and uneven heating. Our research is supported by simulation results and experimental validation, which enhance the credibility and practicality of the design. Most importantly, this paper focuses on compact design, which ensures efficient heating without occupying excessive space, meeting the modern industry’s demands for equipment miniaturization and integration. To provide readers with a clear understanding of the novelty of this device, we have compared it with traditional multi-mode resonant cavity heaters, demonstrating the significant performance improvements of this design, particularly in terms of microwave heating efficiency and uniformity. This makes the device particularly effective in chemical and biological reactions that require precise temperature controls. During the validation process, it became evident that the design also shows good adaptability to changes in the dielectric constant of liquids, making it a high-potential application for complex industrial applications.

2. Methodology

2.1. Configuration of Microwave Continuous-Flow Heater

Configuration of this microwave continuous-flow heater was constructed utilizing the commercial finite element software, COMSOL Multiphysics (COMSOL Inc., Stockholm, Sweden), seen in Figure 1 The model primarily comprises six fractal antennas on a cylindrical metal shell, which are coaxially fed separately, and a quartz tube, with liquid intended for heating inside. Each of the three radiators are equally arranged within the model as a cohesive unit. After the configuration of the physical layout, the performance of the device is optimized from the aspects of antenna size, space arrangement, and phase of the input port. The six antennas used in the device are the new antennas proposed by our research group teacher Yang Yang in [26].

2.2. Governing Equations and Input Parameters

Hereinafter, we quote some classical fundamental equations of electromagnetism and heat conduction. Among them, Maxwell’s equations are referred to in Classical Electrodynamics (J.D. Jackson) and Electromagnetic Fields and Waves (R.E. Collin). The reference book for heat transfer equations is Incropera and DeWitt. The calculation of S-parameters (such as S11, S21, etc.) mentioned in the article is based on the basic electromagnetic theory, and the reference book is the theory of S-parameters in microwave engineering (David M. Pozar). The COV calculation method provides the basic knowledge of citation statistics, and the reference book is Applied Statistics (Montgomery and Runger). The formula for calculating efficiency is derived from Fundamentals of Thermodynamics and Statistical Mechanics (Fermi).

2.2.1. Electromagnetic Wave

Electromagnetic field is computationally determined solving Equation (1), which is deduced from time-harmonic Maxwell Equation. Where ${\mu }_r$ is the relative permeability, $\nabla$ represents the gradient operator, $\mathit{E}$ represents the electric field strength, ${\epsilon }_r$ represents the relative permittivity, $\sigma$ represents the conductivity, $\omega$ represents the angular frequency, and ${\epsilon }_0$ represents the permittivity in vacuum, while $k_0$ represents the number of waves in free space.

$${\displaystyle \frac{1}{{\mu }_r}}\nabla \times \nabla \times \mathit{E}-k_0^2\left({\epsilon }_r-{\displaystyle \frac{j\sigma }{\omega {\epsilon }_0}}\right)\mathit{E}=0$$

(1)

Electromagnetic dissipation density can then be calculated by Equation (2), where ${\mathit{\epsilon }}_{\mathit{r}}^{″}$ denotes imaginary part of relative permittivity. $\mathit{r}$ represents displacement from the reference point and $t$ represents time.

$$P_d\left(\mathit{r},t\right)={\displaystyle \frac{1}{2}}\omega {\epsilon }_0{\epsilon }_r^{″}{\left|\mathit{E}\right|}^2$$

(2)

Boundary condition of perfect electric condition is set on the surface of the system, where $\mathit{n}$ represents the normal vector at the interface

$$\mathit{n}\times \mathit{E}=0$$

(3)

2.2.2. Heat Transfer

Heat is generated by electromagnetic dissipation, and its transfer follows the Fourier equation:

$$-k{\nabla }^{2}T+\rho C_p{\displaystyle \frac{\partial T}{\partial t}}=Q_e$$

(4)

where $k$ represents thermal conductivity $\left(\mathrm{W}/\left(\mathrm{mK}\right)\right)$, $T$ indicates temperature $\left(\mathrm{K}\right)$, $\rho$ means density $\left(\mathrm{kg}/{\mathrm{m}}^3\right)$, $C_p$ symbolizes constant pressure heat capacity $\left(\mathrm{J}/\left(\mathrm{kg}.\mathrm{K}\right)\right)$, and $Q_e$ refers to heat source $\left(\mathrm{W}\right)$. Initial temperature is set as 293.15 K.

2.2.3. Laminar Flow

In this study, we assumed that the solution is an incompressible Newtonian fluid, and the fluid flow in the tube was regarded as laminar flow with a Reynolds number of less than 500 [27]. The mass conservation equation (continuity equation) and Navier–Stokes equation were applied to describe the flow of the well-mixed solution in detail [28].

$$\rho ·{\displaystyle \frac{\partial u}{\partial t}}+\rho \left(u·\nabla \right)u=\nabla ·\left[-pI+\mu \left(\nabla u+{\left(\nabla u\right)}^T\right)\right]+F$$

(5)

$$\nabla ·u=0$$

(6)

where $\rho$ is the fluid density (kg/${\mathrm{m}}^3$), $\mu$ is the fluid dynamic viscosity (Pa⋅S), u is the velocity vector (m/s), $I$ is a dimensionless identity matrix, p is the hydrodynamic pressure (Pa), and F is the body force vector (N/${\mathrm{m}}^3$). For the inner walls of the tube, there was no-slip condition, and the pressure was atmospheric pressure. The outlet was controlled by back-flow suppression and pressure.

2.2.4. Esterification Reaction

It was assumed that the esterification reaction of methanol and oleic acid is a reversible one that follows second-order kinetics. The kinetics of the esterification reaction can be described as follows [29]:

$$-{\displaystyle \frac{d\left(C_{RCOOH}^0-C_{H_{2}O}\right)}{dt}}=k_1\left(C_{RCOOH}^0-C_{H_{2}O}\right)\left(C_{CH3OH}^0-C_{H_{2}O}\right)-k_{-1}{C}_{H_{2}O}^2$$

(7)

where $C_{RCOOH}^0$ and $C_{CH3OH}^0$ are the concentrations of oleic acid and methanol in the well-mixed solution before the reaction, respectively, and $C_{H_{2}O}$ is the concentration of water. The conservation of each species was governed by the following equation [30]:

$$\rho ·{\displaystyle \frac{\partial {\omega }_m}{\partial t}}+\nabla ·j_m+\rho \left(u·\nabla \right){\omega }_m=R_m$$

(8)

$$N_m=j_m+\rho u{\omega }_m$$

(9)

where $R_m$ was expressed by Equations (11) and (12) in the COMSOL calculations, $\rho$ is the electrical resistivity or specific resistance of the fluid, ${\omega }_m$ is the curl of the magnetic vector potential, usually related to the magnetic field strength, and $\nabla ·j_m$ is the divergence of magnetic flux density,

$$R_m=v_m{M}_m\left(r_{M{V}_{.m}}^{for}-r_{M{V}_{.m}}^{rev}\right)$$

(10)

$$r_{M{V}_{.m}}^{for}=k_1{\displaystyle \prod }_n{\left({\displaystyle \frac{\rho {\omega }_n}{M_n}}\right)}^{-v_{m.n}}$$

(11)

$$r_{M{V}_{.m}}^{rev}=k_{-1}{\displaystyle \prod }_l{\left({\displaystyle \frac{\rho {\omega }_l}{M_l}}\right)}^{v_{m.l}}$$

(12)

In this reaction, the stoichiometric coefficients of oleic acid and methanol are −1, while those of methyl oleate and water are 1. Moreover, $k_1$ and $k_{-1}$, which satisfy the Arrhenius equation, are the forward- and reverse-reaction-rate constants, respectively [31]:

$$k_1=A_1\exp (-E_a^f/R_{1}T)$$

(13)

$$k_{-1}=A_{-1}\exp (-E_a^r/R_{1}T)$$

(14)

where $A_1$ and $A_{-1}$ are the frequency factors of the forward and reverse reactions, respectively, and $E_a^f$ and $E_a^r$ are the activation energies (see

Table 1. Material parameter [33,34,35].

Stats	Materials	Value
Real part of the relative dielectric constant (${\epsilon }^{\prime }$)	quartz	4.2
	PTFE	2.1
	Water	$88.15-0.414\left(T-273.15\right)+1.31\times {10}^{-3}(T$ $-273.15{)}^2-4.6\times {10}^{-6}{(T-273.15)}^3$
	Alcohol	$0.429\left(T-273.15\right)-2.37$
Imaginary part of the relative dielectric constant (${\epsilon }^{″}$)	quartz	0
	PTFE	0
	Water	$28.297-0.907\left(T-273.15\right)+1.21\times {10}^{-2}(T$ $-273.15{)}^2-5.712\times {10}^{-5}{(T-273.15)}^3$
	Alcohol	$$\begin{gathered} 0.0022{(T-273.15)}^2+0.2284\left(T-273.15\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+2.1528 \end{gathered}$$
Thermal conductivity ($\mathrm{W}/\left(\mathrm{mK}\right)$)	quartz	1.4
	PTFE	0.24
	Water	$$\begin{gathered} -0.87+0.0089T-1.58\times 10-5T^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+7.98\times {10}^{-9}{T}^3 \end{gathered}$$
	Alcohol	$0.26-3.06\times {10}^{-4}T$
	copper	400
Constant pressure heat capacity ($\mathrm{J}/\left(\mathrm{kgK}\right)$)	quartz	730
	PTFE	1050
	Water	$$\begin{gathered} \text{12,010.15}-80.4T+0.31T^2-5.38-4T^3 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+3.63\times {10}^{-7}{T}^4 \end{gathered}$$
	Alcohol	$-384.39+9.6T$
	Copper	385
Density (${\mathrm{kg}/\mathrm{m}}^3$)	quartz	2210
	PTFE	2200
	Water	$$\begin{gathered} 0.0000103\times T^3-0.0134\times T^2+4.97\times T \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+432.26 \end{gathered}$$
	Alcohol	$1038.80-0.85T$
	Copper	8960
Dynamic viscosity ($\mathrm{Pa}\cdot \mathrm{s}$)	Water	$1.38-0.02T+1.35\times {10}^{-4}{T}^2-4.65\times {10}^{-7}{T}^3$ $+8.9\times {10}^{-10}{T}^4-9.08\times {10}^{-13}{T}^5$ $+3.85\times {10}^{-16}{T}^6$
	Alcohol	$0.18-0.0019T+7.92\times {10}^{-6}{T}^2$ $-1.44\times {10}^{-8}{T}^3+9.76\times {10}^{-12}{T}^4$

for the specific values) [32]. Further, R is the molar gas constant. For the chemical reaction field, the walls of the tube are “no flux” for the reaction solutions, and the outlet is the “outflow”, which means that no solution will flow back.

2.2.5. Input Parameters

Empirically, the composition of the solution will change dynamically with temperature, while other physical properties such as thermal conductivity, dynamic viscosity, specific heat capacity, and density will also change with temperature, and it is particularly important to discuss the close relationship between these properties. Table 1 details the main material parameters involved in order to better analyse and model the behaviour of the solution during microwave heating.

The permittivity relative to the volume ratio of ethanol is provided in

Table 2. Relative dielectric constants of ethanol–aqueous solution.

Ethanol Percentage by Volume (%)	Relative Dielectric Constant
100	8.48–7.64j
90	14.41–11.55j
80	18.74–12.87j
70	31.49–15.24j
60	38.45–15.45j
50	45.75–15.52j
40	55.16–15.74j
30	60.72–14.09j
20	65.52–12.59j
10	75.99–11.51j
0	83.77–10.05j

[17], and the ratio of the thermophysical properties of mixtures of ethanol and water is set based on their mass fraction [36]. When the ethanol volume ratio is 0%, it means that the test sample is deionized water, which is obtained by removing ionic impurities from tap water. This deionized water is commonly used in laboratory and industrial applications to ensure the accuracy of the desired experimental results. j in the table below refers to imaginary units.

2.3. Experimental Setup

2.3.1. Efficiency Measurement

Similarly, tests were conducted using the vector network analyzer shown in Figure 2 to evaluate the microwave energy efficiency of the microwave continuous-flow heater. When measuring the corresponding port of the microwave continuous-flow heater, the other ports are matched with 50 ohm matching pieces. In addition, the measurement of port mutual coupling is very important. For two-port measurements, the S21 parameter can be used to evaluate the microwave energy input from Port 1 and output from Port 2. Therefore, the input energy is equal to the energy absorbed by the load plus the energy coupled by the ports. We chose a 0–100% ethanol–aqueous solution to verify its port reflection coefficient. We chose ethanol–water solutions with concentrations ranging from 0% to 100% primarily based on their wide range of dielectric constants (from 8.48–7.64j to 83.77–10.05j). This large dynamic range helps us better explore the relationship between the efficiency of the device and the dielectric constant of the load.

For the calculation of efficiency, the following three formulas are predominantly employed. Firstly, Formula (15) serves as the formula for computing efficiency, where $P_{ab}$ represents the power absorbed by the heating item, and $P_{in}$ refers to the input power, with the input power being a known quantity. According to Formula (16), the absorbed power of the article can be calculated by combining the reflection coefficient. In this system, $P_{out}$ indicates the absorbed power of the item, $P_{ref}$ represents the reflected power, and $\Gamma$ stands for the reflection coefficient. The numerical value of the reflection coefficient can be determined by the $S_{11}$ parameter, and the efficiency can be calculated after the absorption power of the item is obtained through Formula (17).

$$\mathit{E}\mathit{f}\mathit{f}\mathit{i}\mathit{c}\mathit{i}\mathit{e}\mathit{n}\mathit{c}\mathit{y}={\displaystyle \frac{{\mathit{P}}_{\mathit{a}\mathit{b}}}{{\mathit{P}}_{\mathit{i}\mathit{n}}}}$$

(15)

$${\mathit{P}}_{\mathit{o}\mathit{u}\mathit{t}}={\mathit{P}}_{\mathit{i}\mathit{n}}-{\mathit{P}}_{\mathit{r}\mathit{e}\mathit{f}}={\mathit{P}}_{\mathit{i}\mathit{n}}\left(\mathbf{1}-{\left|\Gamma \right|}^{\mathbf{2}}\right)$$

(16)

$${\mathit{P}}_{\mathit{o}\mathit{u}\mathit{t}}={\mathit{P}}_{\mathit{i}\mathit{n}}\left(\mathbf{1}-{\left|{\mathit{S}}_{\mathbf{11}}\right|}^{\mathbf{2}}\right)$$

(17)

2.3.2. Continuous-Flow Temperature Measurement

We established an experimental system as shown in Figure 3, in which a six-port solid-state microwave source (WSPS 2450-160-6 Watersene Sichuan Province, China, Chengdu) was used to provide 100 W of po17o press the ethanol–aqueous solution into a continuous-flow heater and provide a steady flow rate. The six coaxial ports are connected to the microwave solid-state source outlet by coaxial cable. At the outlet, a thermometer (TM-902C Type K) is used to measure the temperature in the center area of the outlet flow. When the temperature begins to rise, the temperature is timed and heated for 60 s. The experiment was repeated five times, and the average results were taken.

3. Optimization of the Microwave Continuous-Flow Heater

This section explores the effects of radiator height, radius, antenna distribution, and phase on heating performance, followed by a discussion of the model’s robustness. In this model, the frequency of the electromagnetic wave was set to 2.45 GHz and the input power of each port was set to 100 W. In the context of a stationary liquid undergoing heating, this simulation focuses on assessing the uniformity and efficiency of the process. Efficiency is determined by calculating the volume fraction of electromagnetic power loss density within the targeted liquid area. To evaluate uniformity, the analysis utilizes the covariance of temperature across the heated field. We used the calculation method of COV reported by Zhu et al. in 2018 [37]:

$$\begin{array}{c}COV=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{\left(T_i-T_a\right)}^2}{n}}}/\left(T_a-T_0\right)\end{array}$$

(18)

In this expression, the temperature of the i-th measuring point, designated as $T_i$, is represented. $T_a$ represents the mean temperature; that is, the average of the temperatures at all measuring points. $T_0$ represents the initial temperature, which is the temperature at the onset of the experiment or heating process. $n$ denotes the number of temperature measuring points; that is, the total quantity of different measuring points selected in the experiment.

3.1. The Influence of Different Factors on the Heating Performance of the Device

3.1.1. Effect of Height and Radius of Radiator on Heating Performance

The design of the continuous-flow radiator structure discussed in this part includes shell height and radius. The height ranged from 250 mm to 350 mm, with a step size of 10 mm, and the radius ranged from 41 mm to 43 mm, with a step size of 0.5 mm. The effect of the height and radius of the radiator on heating performance is shown in Figure 4 and Figure 5. Observations indicate that efficiency shows an initial increase followed by a decrease with increasing height, reaching its peak value at approximately 300 mm. Simultaneously, the efficiency exhibits a significant decline as the radius decreases. The volumetric coefficient of variation (COV) demonstrates high sensitivity to changes in height, with a lower value observed for heights exceeding 300 mm. However, it exhibits low sensitivity to variations in radius. Since efficiency is the primary concern in real production, it is crucial to prioritize it. Hence, it is reasonable to target a height–radius combination that achieves an efficiency greater than 94.5%. Meanwhile, the combination with the lowest COV is selected, provided that the efficiency requirement is met. Consequently, for subsequent calculations, the model’s height was fixed at 300 mm, and the radius was set to 41 mm. It is notable that the paper uses a frequency of 2.45 GHz to obtain a wavelength of 122 mm. The diameter of the cavity is 82 mm, and the nature of the load is considered during the study to guarantee that the electromagnetic field distribution during the heating process can achieve optimal results. In this paper, the main research object is the water and ethanol solution. The dielectric coefficient of alcohol is 24 and that of water is 81, respectively, which are substituted into the formula for calculation. It is calculated that the wavelength in water is 1.36 cm. The 8.2 cm cavity is about six times the wavelength of water. This means that the cavity can hold multiple wavelength cycles, which can form an effective standing wave field, and in ethanol, the wavelength is 2.48 cm. The 8.2 cm cavity diameter is about 3.3 times the wavelength of ethanol. This means that the cavity can accommodate multiple wavelength cycles, which can also form an effective standing wave field. Where $\mathsf{\lambda }$ is the wavelength, ${\mathsf{\lambda }}_{\mathbf{0}}$ is the wavelength in the vacuum, and ${\mathit{\epsilon }}_{\mathit{r}}$ is the relative dielectric constant.

$$\mathsf{\lambda }={\displaystyle \frac{{\mathsf{\lambda }}_{\mathbf{0}}}{\sqrt{{\mathit{\epsilon }}_{\mathit{r}}}}}$$

(19)

3.1.2. Effect of Antenna Distribution on the Heating Performance

The design of the continuous-flow radiator structure discussed in this part includes the crucial consideration of antenna distribution. Assuming that the two rows of antennas are symmetrically distributed, the height of the lower row of antennas from the bottom surface is denoted as D. The value of D is adjusted through simulation to facilitate changes in the antenna distribution. The parameter D was systematically varied across a range of 40 mm to 125 mm, with an increment of 5 mm, as depicted in Figure 6. Figure 7 illustrates the impact of antenna distribution on the heating performance of the radiator. The observed data reveal distinct efficiency patterns characterized by two peaks, wherein the peak associated with the smaller D exhibits a comparatively lower volumetric COV. Considering the need to strike a balance between ensuring optimal efficiency and minimizing the COV, a value of 70 mm was determined as the optimal choice for D. In addition, it should be noted that the motivation for choosing six antennas is mainly to consider that the six antennas can be arranged in 2 × 3 groups, and since the feed power of each antenna can be set at about 100–200 w, the total feed power is between 600–1200 w, considering that the power of commonly used household heating equipment, such as microwave ovens, is about 500–900 w. The power provided by six antennas can meet most of the use cases, although 12 antennas can conduct the 2 × 2 × 3 packet arrangement, but the power provided by it exceeds the actual need and will increase the system complexity and design cost. More significantly, after discussing the impact of six antennas on efficiency, many of his conclusions can be directly mirrored in 12 antennas arranged in the same manner (that is, four groups of three antennas on the same horizontal plane are distributed, equivalent to replicating the original six antennas).

3.1.3. The Influence of Phase of Each Port on Heating Performance

The design of the continuous-flow radiator structure discussed in this part includes the phase of each port. To simplify the analysis, the phase values of antennas within the same column were configured to be identical. The specific phase values assigned to each column can be observed in Figure 8. The following strategy is employed for adjusting the phase settings. Initially, DA1 is assigned a phase value of 0°, while an initial value is assigned to DA2 and DA1 based on previous experience. Subsequently, the value of DA2 is held constant as DA3 is varied, and the heating indicator is assessed to determine the optimal value of DA3. Finally, with DA3 fixed, DA2 is adjusted to determine its optimal value, thus completing the phase-adjustment process. The optimization outcomes for DA3 and DA2 are presented in Figure 9. It is evident that there exists an inverse relationship between efficiency and the volumetric COV associated with their respective phases. Accordingly, the values of DA3 = 220° and DA2 = 110° are selected as the optimal choices due to their simultaneous achievement of high efficiency and low COV.

3.2. Experimental Verification of Simulation Model

In order to verify the correctness of the model, we measure the reflection coefficient of the port through experiments and compare it with the efficiency of the simulation. The relative permittivity produced by different volume ratios of ethanol and water varies over a wide range (10–80), as shown in

Table 3. Port interconnection.

Ethanol Percentage Mutual Coupling S Parameter	S21 (dB)	S31 (dB)	S41 (dB)	S51 (dB)	S61 (dB)
0%	−15.855	−15.850	−22.568	−26.223	−26.186
10%	−18.690	−18.710	−22.931	−24.252	−24.240
20%	−18.566	−18.580	−21.538	−28.128	−28.124
30%	−17.582	−17.586	−22.120	−32.377	−32.376
40%	−17.373	−17.374	−23.018	−33.751	−33.738
50%	−18.165	−18.168	−24.956	−31.460	−31.447
60%	−18.879	−18.886	−25.727	−32.037	−32.030
70%	−18.616	−18.620	−26.790	−35.333	−35.330
80%	−19.242	−19.243	−30.975	−37.941	−37.938
90%	−19.677	−19.680	−32.850	−40.128	−40.128
100%	−19.282	−19.281	−37.804	−50.1064	−50.115

. Therefore, we chose a 0–100% ethanol–aqueous solution to verify its port reflection coefficient. Different concentrations were configured, the solution was filled inside the container through the peristaltic pump, and the water outlet was observed. When the water outlet was filled with water and no bubbles rose out, the S11 at the port at that time was recorded. In the experiment, the port reflected power at different percentages of ethanol–aqueous solution, which was measured using a vector network analyser, from which the heating efficiency was inferred. The simulated multi-port S parameters are shown in the following table, indicating that the power input from Port 1 to other ports is very small and can be ignored.

Figure 10 shows the efficiency values obtained by the simulation and experiment. It can be seen that the experiment is basically consistent with the simulation, and the efficiency is stable and greater than 90%. However, at high ethanol content, the error is larger, reaching 6%. The reason for the error may be that the dielectric constant of simulated ethanol is different from the actual one. The residual water solution on the cup wall will bring errors to the newly added well-proportioned ethanol–water solution. However, the overall efficiency is consistent, which verifies the correctness of the model [38].

For the continuous-flow heating verification of the microwave continuous-flow heater model, the single-phase heating method is used to conduct the experiment. Three different percentages of ethanol–aqueous solutions were selected for the experiment. The experimental results are shown in Figure 11, which shows the temperature in the centre of the outlet section obtained by experiment and simulation. The experimental results are in good agreement with the simulation results, thus confirming the effectiveness of the proposed microwave continuous-flow heater model. As can be seen, the simulation temperature is slightly higher than the measured temperature, which may be due to the loss of energy in the experiment or the loss of the transmission line. However, the time for the three states to reach stability is in good agreement with the experiment. The stability temperature of the 100% ethanol solution simulation is higher than that of the experiment, with an error of 2 °C. This may be due to the fact that more microwave energy is concentrated at the edge of the cylinder during the heating process, resulting in lower internal heat-exchange energy. Another reason may be the inconsistent flow of peristaltic pumps due to voltage instability. In general, the continuous-flow simulation of the microwave continuous-flow heater is in good agreement with the experimental results, which verifies the correctness of the model and lays a foundation for the discussion in the following sections.

4. Results and Discussion

4.1. Robustness Evaluation of the Model

In the context of production processing, the presence of machining errors and assembly errors necessitates a thorough evaluation of their influence on the model. This section focuses on the analysis of four key aspects: quartz wall thickness $d_g$, antenna thickness $d_a$, antenna length $l_a$, and antenna rotation angle $\mathit{D}\mathit{A}\mathbf{4}$. A comprehensive illustration of these factors is presented in Figure 12, providing a detailed visual representation. Firstly, the inner diameter of the quartz wall was intentionally modified to introduce fluctuations around the standard value, enabling an assessment of the resulting changes in heating-performance indicators. Additionally, the thickness and length of each of the six heated antennas were systematically varied. Furthermore, simulations were conducted to replicate scenarios where the antennas were assembled with rotational deviations. Specifically, simulations were performed for both Antenna 1 rotating independently and Antennas 1, 2, and 4 rotating collectively. The standard dimensions and detailed simulation settings are provided in

Table 4. Robustness baseline values and simulation settings.

	Quartz Wall Thickness (mm)	Antenna Thickness (mm)	Antenna Length (mm)	Single Antenna Rotation (degree)	Three Antenna Rotation (degree)
Standard value	4	1	13.2	0	0
Minimum value	2.0	0.5	11.7	−45	−45
Maximum value	5.5	2.5	14.7	45	45
Step length	0.5	0.5	0.5	5	5

. Figure 13 provides insightful observations regarding the impact of production processing factors on heating performance. Notably, the results indicate that the effect on heating performance is largely insignificant, with the exception of a slight fluctuation resulting from variations in quartz wall thickness. The maximum errors in efficiency and volumetric COV attributed to quartz wall thickness are measured at 2.48% and 5.82%, respectively. Based on these findings, it can be concluded that the present model exhibits commendable robustness. Among them, the diverse colors in the figure correspond to a series of sample points generated by the impact of various independent variables on the horizontal axis on efficiency and COV.

As can be observed from Figure 13, there exists a certain degree of fluctuation in efficiency as the thickness of quartz and the antenna changes, particularly at low thicknesses, where a significant decline in efficiency is witnessed (the yellow dot near the left reflects this). This phenomenon implies that when the thickness of the quartz or the antenna is small, the transfer of microwave energy might be affected, leading to a reduction in system efficiency. Simultaneously, the variation in antenna length also has an impact on the efficiency. However, the fluctuation of efficiency is relatively minor compared to the thickness. It demonstrates that adjusting the antenna length within a reasonable range has a less significant effect on efficiency than the thickness. In Figure 13 on the right, COV varies with the increase in the thickness of quartz and the antenna. The changes in COV correspond to those in efficiency, and lower thicknesses result in larger fluctuations in COV, suggesting that heating uniformity might be decreased under such circumstances. The effect of antenna length on COV is also present, but again, it is not as prominent as that of the thickness. This indicates that the heating uniformity of the system can remain relatively stable under different antenna lengths. It can be noticed from Figure 13 that the changes in efficiency and COV of most data points are within the margin of error (near the baseline), suggesting that the overall performance of the system is relatively stable at different settings of thickness and length. While some specific combinations of thickness or length may cause a minor decrease in efficiency or a slight increase in COV, these changes are still within a reasonable margin of error and do not notably affect the overall performance of the system.

4.2. Comparison with Conventional Heaters

Traditional microwave-heating methods predominantly rely on multimode resonant cavity heating. This section primarily focuses on the comparative analysis of the heating performance achieved by the designed multi-port radiator and the conventional multimode resonant cavity. When the liquid remains stationary, the degree of uniformity in the electric field distribution directly influences the uniformity of the corresponding temperature field distribution. However, when the liquid is in motion, the flow properties additionally contribute to the uniformity of the temperature field. To comprehensively investigate the influence of the electromagnetic field on temperature uniformity, separate discussions are conducted for both the stationary and flowing states of the liquid. Furthermore, in the process of comparison, an optimized heating technique is presented, wherein uniform heating is achieved through the continuous and rapid alteration of the phase of the ports. Initially, a set of 20 phase combinations was meticulously chosen to ensure uniformly distributed electric field distributions. Subsequently, the power dissipation density at every point within the liquid to be heated was computed for each of these combinations. The average power dissipation density was then determined by calculating the mean value from the 20 computed values at each individual point. This resultant average power dissipation density was subsequently incorporated into the simulation setup as the designated heat source. Finally, the simulation was executed to replicate the impact of rapid phase variation at each port, thereby examining its effects comprehensively.

4.3. State in Liquid

4.3.1. Static Liquid State

Assuming a heating duration of 60 s and a total input power of 600 W, a comparative analysis is conducted to assess the heating performance of three distinct heating methods. Figure 14 displays the temperature distribution across a cross-sectional view. Notably, the radiator exhibits superior uniformity in heating compared to the multimode resonant cavity approach. Furthermore, the heating technique employing continuous phase variation achieves a more homogeneous temperature distribution in regions beyond the centrally heated area when compared to single-phase heating, albeit with only marginal overall changes. The decreasing trend observed in the maximum temperature values of the three heating methods indicates a progressive alleviation of localized heating phenomena and an enhancement in heating uniformity.

Following simulation calculations,

Table 5. Results of efficiency and volumetric COV for the simulation of three heating methods.

	Multimode Resonant Cavity Heating	Single Phase Heating	Continuous Phase Change Heating
Efficiency	0.68479	0.99564	0.99408
COV	1.39004	0.50121	0.48962

presents the efficiency and volume of COV. It is evident that the radiator showcases notable enhancements in both efficiency and COV as compared to the multimode resonant cavity method. It is noteworthy that the marginal decrease in efficiency observed in the continuous-phase-changing method may be attributed to the fact that the phase combinations utilized in the single-phase mode are specifically optimized to achieve maximum efficiency. Nevertheless, the efficiency of the 20 selected phase combinations, while still effective, is slightly lower than the optimal value. Consequently, when these values are averaged, a slight reduction in overall efficiency may arise as a result. Additionally, the COV for continuous-phase variation demonstrates a further reduction when compared to single-phase heating, thus implying further improvements in the heating model.

It should also be noted that the traditional cavity herein is not an existing cavity, and the waveguide model it employs is BJ26, as depicted in Figure 14a. Its magnetron feed power amounts to 600 W, and the feeding mode is via the waveguide. Figure 14b,c features the novel devices designed by us, which adopt the antenna-feeding approach and are coaxially fed by six 100 W antennas, with the total input power still being 600 W. The traditional cavity is a rectangular one, which can be observed from the lower cross-section of Figure 14a, being similar in size to the circular tube cavity utilized in this paper (similarly, the cross-sections of Figure 14b,c are observed). The diameter of the cylindrical tube cavity employed in this paper is 82 mm, and the side length of the traditional cavity is 82 mm. There exist certain differences in volume between the two, but the overall size is similar.

4.3.2. Liquid Flow State

In the presence of the fluid field within the radiator, the assessment of uniformity is primarily based on the COV measured at the outlet surface. The simulation setup employed remains consistent with the static liquid scenario, while Figure 15 showcases the temperature distribution of the radiator when the liquid is in motion. Remarkably, as the liquid traverses from the inlet to the outlet, a gradual heating process ensues, resulting in a progressive reduction in COV. Notably, the minimum COV value is observed at the outlet surface. These findings indicate that the combined influence of a uniform electric field and fluid flow contributes to further enhancing the uniformity of the radiator. In a similar vein, a fluid field was introduced into both the multimode resonant cavity and the radiator employing continuous-phase variation. Subsequently, the temperature distribution on the outlet surface was observed after a continuous duration of 60 s, as illustrated in Figure 16. Firstly, it is imperative to highlight that, in general, the radiator exhibits higher temperatures in comparison to the multimode resonant cavity, thereby indicating a more pronounced heating effect. Secondly, upon meticulous examination of the temperature distribution within the multimode resonant cavity, a notable concentration of elevated temperatures is observed on the side that is in closer proximity to the waveguide. Furthermore, as the distance from the waveguide surface increases, a discernible decrease in temperature, characterized by a staircase-like pattern, becomes apparent, thus implying the presence of localized heating phenomena. In contrast, the radiator provides a comprehensive heating pattern, with higher temperatures at the circumference and centre, and a gradual transition from the edges to the centre in terms of temperature distribution. Additionally, the heating method utilizing the continuous-phase variation achieves a more uniform transition when compared to the single-phase approach. The efficiency and outlet COV results for the three heating methods were computed through simulations and are presented in

Table 6. Results of efficiency and outlet COV for the simulation of three heating methods.

	Multimode Resonant Cavity Heating	Single-Phase Heating	Continuous-Phase-Change Heating
Efficiency	0.68329	0.99463	0.99276
Outlet COV	0.30262	0.23116	0.22275

. Analogous to the scenario involving stationary liquid, the radiator demonstrates notably superior performance in terms of efficiency when compared to the multimode resonant cavity. Moreover, the COV exhibits a gradual decrease, signifying a consistent enhancement in heating uniformity.

4.4. Analysis of Heating Performance with a Wide Range of Dielectric Constant Variations

This section addresses the issue of load mismatch arising from substantial variations in the dielectric properties of the liquid targeted for heating and investigates its impact on the performance of the radiator. Specifically, the heating performance of the radiator is assessed utilizing continuous-phase shifting and compared to that of a multimode resonant cavity operating under identical conditions.

The evaluation encompasses key metrics such as efficiency and COV at the outlet surface. The findings and corresponding data are comprehensively presented in Figure 17. Regarding efficiency, the radiator exhibits a notable advantage by consistently maintaining a value exceeding 93.5% across all alcohol concentrations. Conversely, the heating efficiency of the multimode resonant cavity proves to be unstable, with a minimum value approaching 68%. Although the efficiency of the multimode resonant cavity gradually improves with increasing alcohol concentration, it consistently remains lower than that of the radiator. Turning to the analysis of the COV results, a general trend emerges wherein the phenomenon of localized heating becomes more apparent as the alcohol concentration rises. In Figure 18, a clear phenomenon can be observed where, as the concentration increases, the central region becomes more difficult to heat, while the temperature rise at the edges becomes higher. Notably, the radiator outperforms the multimode resonant cavity across most concentration ranges in terms of COV performance.

4.5. Chemical Reaction

In the study of the esterification reaction process in the device, we selected three different port flow rates to explore their influence on the reaction and analysed the influence of port flow rates on the reaction from the temperature distribution, the absorption efficiency of the device, and the velocity field of the device. First, we explored the temperature field corresponding to different port speeds and selected the result of heating for 90 s, as shown in Figure 19 below. It can be found that with the increase of port speed, the temperature field distribution at the outlet of the device becomes more uniform, and the average temperature decreases, which accords with empirical cognition.

The following three diagrams (Figure 20, Figure 21 and Figure 22) will show the temperature field distribution of the flow rate at each port at different times. Since the total duration is 90 s, we chose 30 s as an interval to observe the change of the temperature field with time in a total of four times.

The above three sets of experiments show that the temperature field will change more and more evenly with time, and the temperature distribution will be more average. The following chart (Figure 23) will directly show the temperature variation trend of the three kinds of feed port flow rates with time. At the same time, the starting temperature of the three groups of charts is 293.15 K, which ensures the same initial value and can have a better and clearer understanding of the trend change at different speeds.

By comparing the above three groups of charts, we can find that the trend of temperature change over time is generally the same at different port flow rates. Of course, only the situation at low flow rates is discussed here. At the same time, the chart also shows that, in the first 20 s, the temperature changes greatly, and then the trend becomes slow growth. This is also consistent with the above temperature distribution at the exit. Next, we make a brief discussion on the COV trend corresponding to different port speeds at the same time. The moment we choose here is 90 s after heating, as shown in

Table 7. The relationship between port speed and COV (t = 90 s).

Comparison Item	First Experiment	Second Experiment	Third Experiment
Port speed (m/s)	0.01 m/s	0.02 m/s	0.03 m/s
Outlet COV	0.550	0.577	0.661

below.

It is not difficult to find from the figure above that when other parameters are fixed, the value of COV also decreases as the port speed decreases. From this, we can conclude that COV is sensitive not only to changes in device size but also to changes in port speed, which cannot be ignored. Next, we will study the overall efficiency of the device according to the size of the overall electromagnetic loss power of the device. Compare the change of efficiency over time under different hidden speeds and the association between efficiency and different port speeds at the same time. The detailed graphs are as follows. It is worth noting that since the device has six feed ports, and each port feeds 100 W of power, we can see that the overall power of the device is 600 W. After calculating the electromagnetic power loss density through COMSOL, we divide the value by 600 W to obtain the efficiency value.

By observing the three curves presented in Figure 24, it is not difficult to find that, within 90 s of heating, the overall efficiency of the device is maintained at more than 90%, and as the heating time becomes longer, the heating efficiency gradually decreases slowly. However, in general, the efficiency is higher, and too much energy loss is avoided.

As seen from the

Table 8. The relationship between port speed and efficiency (t = 90 s).

Comparison Item	First Experiment	Second Experiment	Third Experiment
Port speed (m/s)	0.01 m/s	0.02 m/s	0.03 m/s
Efficiency	0.901	0.916	0.919

, when the device is at the same time as the acceleration of the port speed, the device efficiency also has a slight increase. Finally, we conduct a brief analysis of the velocity fields corresponding to different port speeds to ensure the same time. Here, 90 s is selected, and the results are shown in Figure 25 below.

It is not difficult to find that the distribution of the velocity field is consistent at different speeds, but the size of the velocity field changes dramatically and shows a nonlinear monotonic trend.

It is worthy of mention that we also investigate the distribution of electric fields. The subsequent Figure 26 presents the distribution of the electric field in the esterification reaction. It can be observed that the distribution of the electric field intensity in Figure 26 is relatively uniform along the length of the reactor. Although there are certain local areas of high intensity in the middle part (red), the variation of the electric field intensity in the majority of areas is gentle. This relatively uniform distribution of electric fields is conducive to achieving homogeneous heating; that is, the reactants in the reactor can be heated evenly throughout the volume.

5. Conclusions

This article introduces a compact microwave continuous-flow heater based on radiators, which can effectively improve the uniformity and efficiency of cylindrical load microwave heating. Firstly, this chapter establishes a multi-physics field-simulation model for cylindrical load microwave heating. Then, robustness analysis was conducted on the proposed microwave continuous-flow heater, analysing the effects of container height and radius, antenna thickness and length, and rotation angle on heating efficiency and uniformity. This robustness analysis effectively predicts the impact of machining errors or installation errors. Secondly, perform-phase modulation on multiple radiators and obtain the optimal single-phase heating effect by analysing different phases for heating. On this basis, a heating method with continuous phase change was developed to further improve the heating effect. Then, an analysis was conducted on the steady-state liquid, and the two methods were compared with the multimode cavity-heating method. The efficiency of the two-phase modulation methods was 99.56% and 99.4%, respectively, both higher than 68.4% of the multimode cavity-heating method. In terms of uniformity, the two-phase modulation methods are 0.5 and 0.489, respectively, while the multimode cavity heating method is 1.39. This indicates that the proposed compact microwave continuous-flow heater can effectively improve efficiency and uniformity for steady-state cylindrical loads. Finally, the continuous flow liquid was analysed and experimental verification was conducted. The results showed that the continuous flow of liquid would further optimize the uniformity of heating. Surprisingly, the two-phase modulation methods increased efficiency and uniformity by 31% compared to the multimode cavity-heating method, and the COV was optimized by 23%, both of which showed significant improvements. In addition, we analysed the ethanol–water solution with a volume percentage of 0–100% ethanol and verified the heating effect of the heater on samples with a wide dielectric range. The results indicate that the compact microwave continuous-flow heater can improve the uniformity of microwave heating within a certain range of dielectric samples. The proposed method helps to promote the industrial application of microwave energy, improve heating uniformity, and improve product quality.

As shown in

Table 9. Device-improvement comparison table.

Comparison Item	Traditional Multimode Resonant Cavity Design	Design in the Article	Improvements and Contributions
Antenna Design	Multimode resonant cavity with conventional antennas	Fractal antennas, paired linear arrangement	Improved electromagnetic field distribution, enhanced heating uniformity
Phase Control	No precise phase control	Precise phase adjustment	Optimized electromagnetic energy utilization, increased heating efficiency
Heating Efficiency	Relatively low efficiency, insufficient energy utilization	31.1% increase in heating efficiency	Significantly improved energy utilization, reduced energy waste
Heating Uniformity	Issues with uneven heating	64% improvement in uniformity through optimized COV (Coefficient of Variation)	Reduced hotspots or cold spots, enhanced product quality
Adaptability	Poor adaptability, sensitive to changes in liquid dielectric constant	Adapts to various dielectric constants of liquids, such as 0–100% ethanol–water mixtures	Stable performance under different conditions, broader application range
Cavity Size and Structure	Large, complex, difficult to integrate	82 mm diameter, compact design	Easier integration into existing industrial systems, smaller footprint
Multiphysics Simulation and Experimental Verification	Mainly relies on experimental verification, insufficient simulation	Combined multiphysics simulation with experimental verification	Improved design accuracy and reliability
Application Scenarios	Mainly used for food heating or other large-scale applications	Miniaturized, continuous-flow heating, suitable for chemical reactions, laboratory use	Important applications in fine chemicals, pharmaceuticals, bioengineering

, in order to enable readers to more intuitively understand the advanced nature of the device in this paper, the following table lists the comparison between the device designed in this paper and the traditional multi-mode resonator and presents the comparison conclusions in the column of improvement and contribution.

In the end, we look forward to the future development scenario of the system. The system devised in this paper exhibits excellent modularity and can be extended to a larger heating cavity with relative ease by increasing the number of antennas or adjusting the arrangement of antennas. This modular characteristic endows the design with the potential to be scaled up to an industrial scale to a certain extent. Simultaneously, multi-physics simulation is employed to optimize the antenna structure and heating uniformity. The simulation approach can be readily extended to larger-scale designs to accommodate industrial applications with diverse sizes and power requirements. This offers robust technical support for the expansion of the design. Of course, the system does possess certain limitations that make scaling up the design less straightforward, such as the difficulty in maintaining heating uniformity in larger industrial applications. As the size of the heating chamber expands, the distribution of the electromagnetic field becomes more intricate, and the risk of local overheating or underheating escalates. This demands more complex antenna design and phase control, and even the development of new antenna array structures to guarantee uniform heating. At the same time, scaling up to a larger scale implies that higher input power needs to be managed to ensure the attainment of the desired heating effect. This imposes higher requirements on power-supply design, heat dissipation management, and the overall stability of the system. Especially during high-power operations, ensuring the heat dissipation of various components of the system, such as cables, antennas, and cavities, is a significant challenge and may require more complex cooling systems or thermal management schemes. When the system is applied in practical industrial scenarios, it is typically demanded that the equipment can operate stably under various harsh environmental conditions, such as high temperature, high humidity, and dust. Therefore, the design needs to be adapted to ensure long-term reliable operation in these environments. It is also crucial to consider that industrial equipment often needs to fulfill more stringent safety and regulatory requirements, which also introduces additional design complexity.

In future research endeavors, we will concentrate on further optimizing heating homogeneity and efficiency. We aim to incorporate adaptive phase-control technology to dynamically regulate the phase of the antennas based on real-time temperature distribution measurements, thereby further enhancing heating uniformity. This will be accomplished via a closed-loop control system, guaranteeing that the system sustains optimal performance under diverse load circumstances. Additionally, we propose to explore the utilization of multiple modes, especially in larger-scale applications, to further enhance the distribution of the electromagnetic field and circumvent issues related to uneven heating. This multi-modal design can be combined with various types of antenna arrays to attain a more intricate and uniform field distribution. We will persist in expanding the application scenarios and enhancing the system’s durability and stability through precise modeling and simulation. More significantly, we will further integrate and contrast this technology with existing approaches, such as traditional heating methods (e.g., electric heating, infrared heating), to precisely identify its advantages and limitations, and to more accurately position this technology within appropriate application scenarios. Finally, we plan to undertake industrial application research and testing, conducting trials in actual industrial settings to verify the system’s performance in real-world environments. These trials may encompass applications in domains such as food processing, chemical production, pharmaceuticals, and material synthesis.