State of the art of the fundamental aspects in the concept of microwave-assisted heating systems

International Communications in Heat and Mass Transfer 156 (2024) 107594 Available online 23 May 2024 0735-1933/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). State of the art of the fundamental aspects in the concept of microwave-assisted heating systems Crist´ obal Valverde * , Margarita-Manuela Rodríguez-García , Esther Rojas , Rocío Bay´ on CIEMAT-Plataforma Solar de Almería, Carretera de Sen´ es, km 4, 04200, Tabernas, Almería, Spain ARTICLE INFO Keywords: Microwave heating Industrial applications Design parameters Numerical simulation ABSTRACT As the processing of materials using clean energy becomes increasingly important, indirect conventional heating is being replaced by microwave-assisted heating. This method transforms energy directly into heat, providing rapid heating with instantaneous start-up, improved control and homogeneity of temperature distribution, and enabling a compact design. Therefore, the impact of microwaves in industry is growing in recent years. The complexity of incorporating microwaves into any industrial process resides in the need for a customised design. This is emphasised in the case of continuous flow microwave heating systems where the electromagnetic distribution and its transformation into heat, as well as the dynamics of the fluid to be heated under different operating conditions, are solved. For this purpose, and apart from the dielectric and magnetic properties of the material to be heated, which define how it behaves in relation to electric and magnetic fields when exposed to microwaves, there are several factors influencing the design of the process: the microwave generator and the transmission line, the geometry of the applicator where the electromagnetic field is distributed, the material container of the sample or the temperature measurement techniques to control the process. Additionally, numerical simulation is an essential tool for designing and predicting the suitability of any microwave system. This is the case of composite materials processing, where the application of numerical simulation tools arises from the need to achieve advanced materials more efficiently. In this paper, these fundamental aspects for the design of a microwave-assisted heating system are reviewed, presenting examples of various applications where this microwave technology is integrated. 1. Introduction Microwaves are electromagnetic waves in the frequency band between 300 GHz and 300 MHz, i.e., with wavelengths in the range of 1 to 1000 mm [1]. Although they do not constitute ionising radiation, these waves can interact directly with the matter at the molecular level, varying its electric and magnetic fields, resulting in the heating of the sample [2]. In the last decades, the use of microwaves for heating applications has exploded as resource efficiency and sustainable processing become more important, as it allows the use of renewable energy throughout the process. Noteworthy is the use of solar and wind energy to power microwaves in chemical reactors [3]. This is an increasingly cheaper alternative to conventional fossil-fuelled chemical reactor heating [4]. The main advantages of this method, as opposed to conventional heating, are that the energy is converted directly into heat inside the sample, rather than transferring that heat to the sample [5–10]. Moreover, heating rates of up to 400 K/min can be achieved [11], as well as no direct contact between the heat source and the material to be heated, greater control with instantaneous stops and starts, and reduction of equipment size and heat waste [12,13]. Several frequencies – 13.56 MHz ±6.68 kHz, 27.12 MHz ±16.0 kHz, 40.68 MHz ±20.0 kHz, 433.92 MHz ±87 MHz, 915 MHz ±25 MHz, 2450 MHz ±50 MHz, 5800 MHz ±75 MHz, 24,125 MHz ±125 MHz – are set for industrial, scientific and medical (ISM) use [14], however, it is 2450 MHz frequency magnetrons that are used for most applications. These magnetrons provide more efficient electromagnetic energy-to-heat conversions due to the higher performance factor of up to 86% efficiency in modern designs. Magnetrons with 915 MHz compared to the 2.45 GHz frequency can heat larger samples as they offer a higher depth of penetration (Dp) [15,16]. Marinel, et al. [17] developed a 915 MHz single mode cavity system for sintering large samples of low-loss dielectric alumina. The process is based on controlled hybrid heating with two SiC susceptor plates, placed parallel to the electric field to * Corresponding author. E-mail address: [email protected] (C. Valverde). Contents lists available at ScienceDirect International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt https://doi.org/10.1016/j.icheatmasstransfer.2024.107594 International Communications in Heat and Mass Transfer 156 (2024) 107594 2 avoid plasma and thermal instabilities, and within a thermal insulation material. Following this idea, Rosa, et al. [18] highlighted some research opportunities in the field of carbon combustion synthesis, specifically, synthesising nanostructured composites, exploring less conventional frequencies, e.g. 5800 MHz, corresponding to higher and lower penetration depths. At the same time, new ways of producing microwaves are emerging, using solid-state (semiconductor) technology, which offer controllable radiation to the product load, achieving more uniform heating compared to magnetrons [19,20]. 1.1. Brief state of the art of microwave-assisted heating applications This technology offers great possibilities in different sectors [21]. More and more applications for microwave heating are emerging as more and more research is done on how microwaves interact with different materials, their physical mechanisms, and how they can be used for heating [22,23]. This method depends on the dielectric properties of the material to be processed, which measure the response of the material to an electric field, while its magnetic properties affect the capacity of the material to store and convert the energy of the magnetic field into heat [24]. Concerning the sample to be heated, the mass/ volume to be treated, whether the sample is heterogeneous, initial, intermediate and end products, as well as its shape and location in the cavity, also have an influence [25]. In terms of equipment, the variables to have an impact on heating are the geometry, its dimensions, the microwave source and the energy transfer system, the selection of the material for the cavity and also the holder of the sample treated [19,25–29]. Microwave technology is used in different applications, which can be classified according to the required temperatures [13]. Table 1 presents a classification of microwave heating applications into three main groups according to temperature, based on the work of Mishra et al. [13]. To understand the impact of microwave heating on industry, the number of publications has been quantified using the Web of Science (WOS) online database. Fig. 1 shows the number of scientific publications on industrial microwave heating, their time evolution over the last 15 years, and the total number compared to other technologies. These are obtained by keywords in the WOS core collection. These keywords are “industrial process”, “heating”, “microwaves”, “flow” and “numerical simulation”. It can be seen that the number of articles has increased considerably over the last 7 years, reaching a record high of 85 articles in 2021 compared to 16 articles in 2009. The total amount represents almost 10% of all articles researching heating processes in industry. Among the total number of articles based on microwave heating processes, only 2% are articles where numerical simulation is the basis of the research conducted. In addition, microwave heating processes can be performed for static materials inside a cavity or in movement, i.e. a liquid or gas flowing through a carrier tube. In the last 15 years, the number of papers on heating of moving fluids with microwaves represents 8% of the total number of papers on industrial heating. 1.1.1. Examples of continuous flow microwave heating systems for different industries Continuous flow microwave heating is a very promising method for industries such as food and chemical engineering. It is a multiphysics approach, in which, unlike static microwave heating, not only electromagnetic distribution and its transformation into heat is involved, but also the fluid dynamics. To improve process efficiency, uniformity and adaptability under different operating conditions, there are new variables to investigate, such as flow rate, carrier tube geometry, number of tubes, use of spiral tubes, their location and orientation. Despite the many advantages of microwave heating, it is difficult to find scientific publications related to systems operating at moderate and high temperature, especially if the material to be heated is a moving fluid. That is not the case at lower temperatures. There are several works for the food industry. Topcam et al. [49] investigated the optimization of the cavity geometry and process design on an industrial scale in continuous flow processes for temperatures up to 60 ◦C. The aim is to avoid inhomogeneity in heating due to the limited Dp in the medium by microwaves. The systems used were cylindrical single mode cavity with only one magnetron of 915 MHz frequency, and multimode rectangular cavity with 8 magnetrons of 2450 MHz placed on the walls, close to the pipe. With another orientation in the second system, the results showed non-uniformities due to local temperature increases. The effect of the number of tubes inside the cavity and their orientation, the applied power and the fluid velocity were studied by multiphysics simulation using COMSOL Multiphysics software, the liquid sample being a whole liquid egg. It was shown that the elliptical cavity results in a more uniform temperature distribution. At the same time, it was shown that larger cavity dimensions for processing a larger sample volume, as we will see in section 2.1.2, are valid for continuous flows. In the same area of liquid heating for the food industry, Tuta et al. [50] worked with a unique single mode cavity and helical tube design, which tested different fluids at different flow rates by numerical simulation and subsequent experimental validation. Zhu et al. [22] also worked with numerical simulation to understand the effects of dielectric properties, in this case working with food liquids (apple sauce, skim milk, and tomato sauce) by varying different parameters such as location or dimension of the applicator inside the cavity with different diameters. More specifically, microwaves are proposed as an alternative to conventional heating for the aseptic processing of low-acid vegetable purees. Kumar et al. [51] studied in the scale-up of a pilot prototype to industrial scale, with extended run times of 8 h, avoiding process-related problems such as inhomogeneity in temperature distribution. The process scale-up of green pea puree and carrot puree resulted a success in a 60 kW microwave system and static mixers installed at the exit to homogenise the temperature distribution. The following figure, Fig. 2, shows some of these unique low-temperature continuous flow microwave designs for the food industry. There are also publications on continuous processes at low temperatures in the synthesis of chemical compounds. Baker-Fales et al. [39] focus on a microwave-assisted continuous flow-scale reactor for liquidphase chemical processing. In this work, a microwave-assisted scale reactor for the production of 5-hydroxymethylfurfural (HMF) from fructose dehydration was studied, with specific application to the production of 5-hydroxymethylfurfural (HMF). The microwave source was a variable frequency solid-state generator (900 W, 2.45 GHz as reference frequency) connected to a configurable Malachite H-field cavity via a WR340 waveguide. The device included a 3-stub tuner and a sliding short circuit. This scaled-up reactor demonstrated an HMF yield of around 55% and 8 times the productivity of a conventional system, while maintaining high energy efficiency and a CO2 emission reduction of >60%. In addition, the experiments were validated using a computational fluid dynamics (CFD) model. Other uses where scaling of Table 1 Classification of microwave materials processing according to temperature range and application [13]. Range of temperatures Relevant applications Refs. Low Temperature Processing (T <500 ◦C) Polymer, Polymer-matrix Composites (PMCs), Rubber [30–38] Chemical, Medical [39–48] Cooking, Drying [22,49–60] Moderate Temperature Processing (500 ◦C <T < 1000 ◦C) Ceramics, Glass [11,61–63] Low melting point metal-based materials [64–66] Synthesis of Carbon Nano Tubes (CNTs) or other nanocomposites [18,67–69] High Temperature Processing (T >1000 ◦C) High density ceramics, Ceramic-matrix Composites (CMCs) [17,70–73] High melting point metallic materials, Metallic-matrix Composites (MMCs) [74–79] Nano materials [72,73,80–84] C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 3 microwave systems is addressed include organic [40] or zeolite synthesis [41]. Research was also conducted on the use of the microwave cavity itself as a reactor, whose metal walls were adapted to continuous chemical reactions at high pressures of up to 7 MPa at temperatures of 200 ◦C [42]. The design was optimised and simulated with multiphysics simulation software by coupling wave propagation to heat transfer, and wave reflections were minimised, with the microwave energy being entirely absorbed by the reaction medium. In the same microwave reactor line, Saggadi et al. [43] developed a microwave device for chemical reactions with a single mode applicator that allows a uniform electromagnetic field. This setup resulted valid for the continuous chemical synthesis of quinoline from glycerol at temperatures up to 200 ◦C and high pressures up to 19 bar, with an important advantage being the long residence times or relatively high mass flow rates over 1 kg/h due to its large reactor volume. Comparing this pilot microwave reactor with conventional heating, the reaction time and energy consumption are shorter (32 min and 11,014 kJ/mol, compared to 112 min and 452,200 kJ/mol), and the quinoline yield is about 41% and 37% in the case of conventional heating. The following figure, Fig. 3, shows examples of these microwave reactors. Among the most relevant recent high-temperature microwave publications are those addressing the pyrolysis process. Chao et al. [85] analysed microwave-assisted heating in the preparation of cerium oxide micro-nano particles, obtaining a better finish than conventional Fig. 1. (a) Time trend in the number of publications on microwave-based industrial heating, (b) total number of these publications out of the number of publications on industrial heating in the last 15 years, (b.1) articles whose research is on numerical simulations, (b.2) articles dealing with microwave heating of moving fluids. Fig. 2. (a) Cylindrical and elliptical cavity simulations with a single 915 MHz magnetron, and rectangular cavity with 8 magnetrons and tube with wave geometry [49], (b) unique single mode cavity and helical tube design [50], and (c) 60 kW microwave system for the aseptic processing of low-acid vegetable purees [51]. C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 4 methods, in an efficient way. These conventional methods are based on contact heat transfer in fixed bed reactors, fluidised bed reactors or electric furnaces [86]. This microwave system used a Venturi reactor inside the microwave oven where microwaves were radiated by three equidistantly distributed magnetrons connected to this cavity with three BJ26 rectangular waveguides. In addition, numerical simulation was used to couple the various physics involved and determine the effects of microwave power, reactor location and waveguide arrangement. These factors modified the heating pattern, and it was observed that the degree of crystallinity and purity of cerium oxide improved with increasing microwave power. The following figure, Fig. 4, represents the diagram and model of the equipment used. Anis et al. [87] also studied the application of microwave-assisted pyrolysis in the production of liquid biofuel from oil. In this work, a 900 W microwave reactor with 300 g of commercial particulate charcoal was fed with used cooking oil or fresh cooking oil at various feed rates ranging from 0.051 kg/h to 0.306 kg/h and temperatures 450 ◦C – 550 ◦C. The reactor used nitrogen gas to remove oxygen within the reactor, ensuring the pyrolysis condition. Microwave irradiation for pyrolysis and distillation processes proved to be effective in the conversion of used cooking oil into liquid biofuels, especially green diesel. Microwaves and radiofrequency (RF) radiation have been widely studied and applied for the treatment of raw oil [88]. Rosin et al. [89] worked on decreasing the viscosity properties of oil by means of microwaves in a thermal process and reduction of energy consumption. The reactor is a laboratory-scale continuous cavity designed with a microwave window, simulated and validated in experimental tests, to operate at pressures up to 3 MPa, ensuring several key functions such as flow conditions, safety and energy transfer. In the synthesis of organic compounds, polymers, inorganic materials and nanomaterials, microwaves stand out from the conventional method with higher performance and precision in the preparation of desired catalytic and organic materials, controlling parameters such as temperature, pressure and temperature gradient [30]. In the same field, Morschh¨ auser et al. [90] described a continuous flow microwave system based on a shortcircuited waveguide as a reactor capable of operating at 310 ◦C and 6 MPa, using corundum as a transparent container material. This reactor was able to process chemical transformations with power outputs of 0.6–6 kW and flow rates of 3.5–6 l/h. There are more microwave designs in chemical reactors operating at high temperatures for chemical synthesis [44,45], waste gas treatment [46] or hydrothermal liquefaction of biomass [47], and others. Many of these processes require the presence of a solid catalyst within the reactor, which is exposed directly to microwaves in an efficient process that reduces the operating temperature in some cases to 1200 ◦C as waste gas treatment, since reaching the combustion temperature of the catalyst intensifies the process. The following figure, Fig. 5, presents two of the microwave applicators applied for the treatment of raw oil. 1.1.2. Comparison of microwave heating over conventional heating in specific applications As discussed in the examples of the different applications, most of them have advantages over conventional heating. The main advantages common to most cases are time and energy savings, as well as uniformity in temperature distribution which can lead to products with better properties. The table below, Table 2, presents the comparison of microwave-assisted and conventional heating in terms of time and energy consumption, as well as other advantages in some application examples. The aim of this review article is to present how the fundamental aspects to consider in the design of a microwave system have been applied to specific industrial applications, highlighting the technological solutions implemented. This paper is organized as follows: within section 2 where the fundamental aspects of microwave system design are analysed, the first subsection (2.1) deals with the main hardware of microwave systems: microwave generators (2.1.1), transmission lines (2.1.2) and cavities (2.1.3). The latter is divided into two further subdivisions: single mode cavities (2.1.3.1) and multimode cavities (2.1.3.2). The second (2.2) explains how matter interacts with microwaves, the mechanisms involved in heating, and their classification. A short section (2.2.1) is dedicated to aspects to be considered in microwave-transparent materials to contain the samples. The third subsection (2.3) presents the techniques used for microwave heating, from direct radiation on the material to hybrid or selective heating for more specific applications. The subsection 2.4 describes the technology used in microwave systems for temperature measurement. Numerical simulation tools are presented in section 2.5, and finally the section 3 and section 4 summarises the main conclusions and introduces new research opportunities. While reading the paper, some concepts appear that are analysed in detail in the following sections. 2. Fundamental aspects of microwave system design In order for microwaves to be absorbed by matter and transformed Fig. 3. (a) Microwave-assisted reactor with specific application to HMF production [39], and (b) diagram of continuous mode microwave pilot reactor for synthesis of quinoline from glycerol [43]. Fig. 4. Diagram and model of the microwave system developed to prepare cerium oxide micro-nano particles [85]. C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 5 into heat, several factors influence the process and therefore ‘tailormade’ design is required for each industrial application. Dabrowska et al. [84] described different self-designed microwave reactors for the synthesis of nanomaterials and other applications at laboratory and industrial scale. In the same line, Mishra et al. [13] identified the keys in the design of microwave-assisted systems for processing advanced materials such as the design of a suitable susceptor around the target material for a higher diffusion rate or a special tooling for the control of the microwave process. The following diagram, Fig. 6, summarises the main points to be addressed in the design of a microwave system, common to all applications, and which are discussed in detail with specific examples in the following sub-sections. 2.1. Microwave generators, transmission lines and applicators Although each process requires its own design for effective operation, they all share the same main components: a microwave generator, the power transmission and the applicator/cavity containing the sample to be treated [25]. 2.1.1. Microwave power generation As mentioned in Section 1, the sources of microwave for industrial applications are magnetrons and solid-state generators. In the case of magnetrons, their maximum power rating and electrical efficiency depend on the geometry of the magnetron and the quality and manufacturing precision of the components. Assuming good magnetron quality, an electrical efficiency of 70% can be achieved for 2.45 GHz magnetrons, while up to 90% can be reached for 915 MHz magnetrons. The lifetime of a magnetron expressed in total number of microwave hours is >8000 h [25]. Solid-state technology provides precise frequency control [4] and output power up to 300 W at 2.45 GHz and 700 W at 915 MHz [3]. However, compared to magnetrons, for the same power level, the cost is more than two to four times higher due to the complexity of the RF circuitry and materials, mainly the sophisticated low loss printed circuit board (PCB) substrates. In contrast, solid-state generators can operate uninterruptedly for 15 years without performance degradation [5]. Zhou, et al. [60] provided fundamental guidance on designing and modelling microwave heating systems based on solid-state generators. They used a domestic microwave oven to compare the frequency spectra (i.e. peak frequency and bandwidth) of the magnetron and the solid-state generator. While magnetron microwave spectra vary depending on the sample to be heated and its position, the ability of solid-state generators to control the operating frequency precisely makes this source of microwaves a key element in the development of the next generation of microwaves. The methodology for measuring the spectral quality of the solid-state generator relied on a spectrum analyser to measure microwave leakage from the oven. The antenna measured signals five times per second at two positions, 5 cm away from the microwave oven, to assess the influence of position. For three representative food loads and a maximum of 300 snapshots of frequency spectra during 60 s of microwave heating, it was shown that the measured peak frequencies exactly matched the set frequencies, independent of the food loads and their positions. In the same work, a simulation model was developed with COMSOL software that supports the results obtained by the solid-state generator with more stable and predictable heating patterns. 2.1.2. Microwave transmission lines In a microwave system, the radiated energy travels from the source to the cavity through a waveguide or coaxial cable, which are the most common transmission lines. A waveguide is a rectangular, circular or rigged hollow structure made of metal such as copper, aluminium or other metal with high thermal and electrical conductivity. The rectangular type is the most common as it supports the propagation of transverse electric (TE) and transverse magnetic (TM) modes. Its dimensions are standardised. At 2.45 GHz the waveguides used are WR284 (72.130 mm ×36.065 mm), WR340 (86.360 mm ×43.180 mm) and WR430 (247.500 mm ×123.750 mm), and at 915 MHz WR975 (247.500 mm × 123.750 mm) [25]. Ellison et al. [48] developed a microwave pyrolysis system for the thermochemical conversion of biomass into chemicals and biofuels (bio-oil and syngas), where the waveguide was used as a single mode cavity. This system implemented continuous phase shifting by means of a sliding short circuit to mitigate standing wave effects and achieve better heating uniformity. The figure below, Fig. 7, shows the experimental set up. Coaxial cable, consisting of a cylindrical conductor commonly made of copper, an air-like dielectric and a conductive screen, is capable of propagating a transverse electromagnetic (TEM) wave. The maximum power supported increases with size and the electromagnetic waves propagate at a frequency always below the maximum cut-off frequency. The power losses along the cable depend on the diameter and length required to connect the source to the cavity and are therefore important design parameters to consider in the TEM power absorbed by the sample. In addition to the transmission line itself, it is important to design the microwave transport system to ensure that the sample absorbs all the microwave power from the generator. Any design must control the reflected power, as high levels of reflected power can create arcing and damage the generator. A waveguide or coaxial circulator is a three-port device intended to create isolation between transmitted and received signals. To absorb the reflected power, a separate “dummy” load is connected to the circulator. Ideally, this circulator should not attenuate the power. 2.1.3. Microwave applicators/cavities Microwave applicators are structures, mostly metallic, that confine the microwave energy within the space where the sample to be processed is placed. The distribution of these microwaves inside the chamber are governed by Maxwell’s equations [98]. ∇ × E=j μω H(1) Fig. 5. (a) Simulation of the laboratory-scale reactor used by Rosin et al. [89], and (b) scheme of the continuous microwave synthesis designed by Morschh¨ auser et al. [90]. C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 6 ∇ × E= − j ωε 0 ε *E(2) ∇ • ( ε E) = 0 (3) ∇ • H=0 (4) where E is the time-harmonic electric field (V m−1), H is the magnetic field (A m−1), ε * is the complex permittivity of the material (F m−1), ε is permittivity, ε 0 is permittivity in air, μ is magnetic permeability of microwaves (H m−1) and ω is the angular frequency. By calculating the electromagnetic field pattern, with the system’s boundary conditions, the sample can be positioned in an area of maximum electromagnetic field strength, ensuring rapid processing [26,99,100]. These microwave applicators are classified into two groups according to their size: single mode or multimode cavities. The following figure, Fig. 8, shows how the electric field is distributed in both types of cavities. 2.1.3.1. Single mode microwave applicators. These applicators are closed structures of size comparable to the microwave wavelength in which only one electromagnetic mode is excited. Its design is based on Maxwell’s equations so that the wave mode resonates at the excitation frequency. In this case, the distribution of the electromagnetic field can be accurately predicted, allowing the sample to be placed where the field is at its maximum strength for faster and more homogeneous heating. However, its dimensions have the disadvantage of a smaller volume of material that can be heated. The amount of material can be increased with cavities designed to operate at lower frequencies (e.g. 915 MHz instead of 2450 MHz) [101]. Furthermore, the dielectric properties of the material, which are responsible for the absorption of electromagnetic energy, vary as the material heats up. This influences the resonant frequency and therefore requires a tuning system to adjust or tune the resonant cavity. This is the case for Lewis et al. [102] who implemented an EH tuner to a single mode cavity. With stepper motors, this control system has the ability to continuously change the position of plungers within the waveguide to obtain a lower inverse power reading. These plungers function as variable short circuits and therefore, it is possible to change the cavity dimension. Oliveira and Silva [103] developed a waveguide section delimited by a short-circuit plunger and an iris, inside which a thin ceramic cylinder is inserted. This model, with iris opening and short-circuit position, provided accurate results, thus solving the thermoelectromagnetic problem of heating ceramic samples. Among the applications where this type of microwave applicator is used include the processing of phase change materials (PCMs). This physical phenomena has been investigated numerically by developing models in one dimension [104], and two dimensions [105] in a cylindrical cavity. Ratanadecho et al. [52,53] makes use of a rectangular waveguide powered by a 1000 W magnetron to predict the temperature reached and melting front in multilayer packed beds of glass beads and water or ice, by applying a single transversal electric (TE 10 ) mode and frequency of 2.45 GHz. The developed model, its results for different layer positions, agreed with the experimental results. This rectangular waveguide microwave system was also used for the drying of multilayer porous materials. [54]. Depending on the pore size and moisture content of porous materials, their electromagnetic distribution within the waveguide varies, which affects the wave penetration and thus their absorbed power. The developed model predicts the microwave behaviour observed in the experiments, which improves the understanding of the microwave drying process. In this specific case, the smaller the pore size, the faster the drying speed due to higher capillary pressure. In cases such as the heating of granular materials with low thermal conductivity, microwaves are advantageous over any other method. These cases may be necessary to evaporate liquid contents. Examples are the remediation of organic contaminants from soils or rock fragments, and the extraction of organics from oil sands, oil shales and biomass. When the target compound is organic, the water contained in the sample acts as a receiver, allowing heat transfer to the organic contaminants. Robinson et al. [106,107], using single mode cavity, demonstrated the great potential of microwaves in the case of oil recovery from contaminated drill cuttings. Harutyunyan et al. [69] worked on the purification of singlewalled CNTs, making use of tuned single mode cavity microwaves inducing the TE 103 wave mode with power of 1.5 kW and 2.45 GHz. This Table 2 Comparison of time and energy savings and other significant advantages of microwave heating over conventional heating in some applications. Examples of applications MW vs Conventional heating Refs. Time consuming Energy consumption Other aspects Chemical reactions with microwave (continuous chemical synthesis of quinoline from glycerol) 32 min compared to 112 min 11.014 kJ/mol compared to 452.200 kJ/mol Quinoline yield is about 41% with microwaves and 37% in the case of conventional heating [43] Microwave treatment of raw oil N/A N/A Viscosity reduction by the conventional heating method is reversible, requiring heating equipment installed along the pipeline at a higher cost. [91] Microwave synthesis of micro-nano particles Up to 10 s compared to about 2 h for the conventional method N/A In the case of ZrO 2 particles, better dispersity of the particles via microwave heating whose size was <40 nm compared to conventional heating that exceeded 60 nm [92] Microwave melting of metals MW - Conventional 2 to 6 kW compared with induction heating which required 10 to 150 kW [74] Tin 5 min - 11 min Lead 6 min - 14 min Aluminium 9 min - 29 min Hybrid heating with microwaves (powder compacts of metal-based materials) 0.08–0.33 times compared to conventional sintering N/A Improved tensile properties due to less exposure to high temperatures. [93] Microwave sintering with ceramics 10 min compared to 1 h N/A Density of 99.9% with microwaves compared to 98.0% with conventional sintering. Also superior Vickers hardness (16.0 GPa) compared to conventional sintering (13.4 GPa) [94] Drying of ceramics (silica sludge) 15 min compared to 450 min N/A [95] Microwave curing of carbon fibre reinforced polymer (CFRP) composite through resonance structures 156 s or 30 s (microwave power level of 6 or 12 kW) compared to 1120 s Reduction of 99.2%, i.e., 0.26 kWh or 0.1 kWh to 18.4 kWh with the autoclave The flexural strength and the interlaminar shear strength (ILSS) resulted slightly higher, 4.28% and 6.33% respectively [37] PMCs with microwave (carbon fibre epoxy composite) 50% cure cycle time reduction N/A Shear strength 9% higher Lower void content (< 2%) [96] Hydrogen production with microwaves (catalytic dry reforming of methane) N/A 4.6 kWh/m3 of H 2 with MW compared with 9.47 kWh/mol conventionally 11% (over 10Ni/AC) and 8% (over Ni/MgO/AC) higher efficiency [97] C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 7 Fig. 6. Diagram of the main issues to be addressed in the design of a microwave system. Fig. 7. Experimental set up of a microwave pyrolysis system based on a single mode waveguide [48]. C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 8 local heating (up to 500 ◦C) weakens or removes the protective carbon layer, allowing acid treatment and removal of metal catalyst residues. Microwaves with such cavities have been successfully applied in other applications such as sintering of metallic and ceramic materials [61], or continuous flow processing applications [108,109]. Catal´ a-Civera et al. [110] designed a microwave-based system for the measurement of dielectric properties of materials up to temperatures of approximately 1000 ◦C. This system uses a cylindrical cavity with two electromagnetic sources and a cross-coupled filter to isolate the two wave modes, TE 111 with resonant frequency (~ 2.432 GHz) for sample heating, and transverse mode (TM 010 ) at the same frequency for measurement. The following figure, Fig. 9, shows a schematic of the equipment designed [111] The sample permittivity is calculated using an improved cavity perturbation method (CPM) based on the change of the resonance in the cavity when a material is introduced. There are other techniques to measure the permittivity of materials classified as resonant or nonresonant [112], as well as resonant cavities [113], open resonators [114], and dielectric resonators [115]. The improved CPM method ensures an overall accuracy of ±1.3%. In turn, a proportional – integral – derivative (PID) control algorithm adjusts the heating rate by adjusting the bandwidth of the sources, in this case, with solid-state technology. P´ erez-Campos et al. [116] used this dynamic permittivity measurement with dual-mode cylindrical cavity and frequency near to 2.45 GHz to characterize ground tire rubber (GTR). The results showed the high dependence of temperature, heating rate (power) and energy delivered with the GTR dielectric properties. Thus the samples experienced abrupt changes in their dielectric parameters at 160 ◦C and 190 ◦C, and after cooling the samples the permittivity values were different due to devulcanization. 2.1.3.2. Multimode microwave applicators. These are applicators with a size larger than the microwave wavelength, with multiple zones of electric field strength maxima and minima, where the multiple wave modes present within the cavity interfere. Their design, unlike the previous ones, is often based on experience [26]. In this type of applicator, hot spots form in the peak areas. By increasing their dimensions, this number of hot spots increases, which affects the uniformity of heating. To avoid this undesired effect, the most widely used solution is the installation of mode stirrers inside the cavity [117,118]. In order to avoid large microwave leakage, Monzo-Cabrera, et al. [119] designed a high-power coaxial filter for microwave ovens. This filter, with two-port coaxial cavities coupled via coaxial lines, allowed the introduction of metallic stirrers with attenuations up to 70 dB obtained by numerical simulation and experimentally. This type of applicator has been used for various industrial applications. For example, there are many works available in metallurgy with microwaves in multimode cavities. Of interest are those aimed at improving the mechanical properties of magnesium from synthesis with copper nanoparticles (NPs) [80], alumina [81], silicon carbide [82], or yttrium oxide [83] as a reinforcement. Although magnesium is an abundant element on Earth, very light, with high hardness, easily machinable and has a lower cost, its use in industry is still limited compared to aluminium, because of its low elasticity and resistance to high temperatures, as well as being highly corrosive due to its low electrical potential. The melting temperature of magnesium is 650 ◦C. In all these cases, rapid microwave sintering was advantageous as a step prior to hot extrusion to synthesise near-dense magnesium compounds. The results revealed an improvement in their hardness, yield strength, ultimate fracture toughness, or increased ductility as the amount of NP reinforcement increased. Chandrasekaran et al. [74] studied the melting of lead, tin, aluminium and copper using silicon carbide as an absorber in a hybrid heating process. Different power levels from 520 W (40%) to 1300 W (100%) were used for an operating frequency of 2.45 GHz, and temperature range up to 1083 ◦C. Compared to conventional 2500 W muffle furnace melting, microwaves require less time and energy. Microwaves have also been used for the synthesis of CMCs. The interest in Fig. 8. Examples of a) single mode applicator with coaxial probe. Plan and profile view of the electric field distribution; b) multimode applicator fed with a magnetron and with mode stirrers or stirrers. Section view of the electric field distribution (software: CST Studio Suite). C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 9 ceramic nanocomposites is due to the advantages they offer in hightemperature applications such as high hardness, high elastic modulus, strength and ductility, as well as low chemical wear, among others. Multimode cavity microwaves have been used in cases such as the sintering of zirconia-hardened alumina nanocomposites, a process with temperatures up to 1300 ◦C. Microwaves resulted in an improvement of the nanocomposite microstructure as the alumina particle size decreased, increasing the zirconium content and thus a higher densification of these nanocomposites compared to the use of an electric furnace by means of the conduction mechanism [72,73]. Another process with ceramics, in this case with a domestic microwave oven, is in the drying of silica sludge [55]. This new method reduces their volume and mass, reducing the process cost. In polymer processing, Porto et al. [31] investigated with a domestic microwave oven, and benzoyl peroxide as a catalyst, the polymerisation process of various monomers (vinyl acetate, styrene, methyl methacrylate and acrylonitrile), which resulted in an efficient method. 2.2. Behaviour of matter with microwaves Any material can be described electromagnetically by its relative dielectric permittivity, ε r = ε ’ - j ε ”, composed of the dielectric constant ( ε ’) which determines the spatial distribution of microwaves within matter, and the loss factor ( ε ”) primarily responsible for the conversion of microwaves into thermal energy in nonmagnetic materials [120].For magnetic materials, the permeability ( μ ’) and magnetic loss ( μ ”) determines the ability to store and convert the magnetic energy to heat [24]. These parameters are dependent on the operating frequency and temperature reached by the material. The power penetration depth, (Dp) is the distance from the surface of the sample at which the power decreases by a factor 1/e, and this is dependent, not only on the dielectric and magnetic properties ( ε ’, ε ”, μ ’, μ ”), but also on the volume of the object, its density which affects these properties [116,117], and the incident wavelength (λo) [97,118]. where tan δ e = ε ”/ ε ’ and tan δ μ = ε ”/ ε ’ are the loss tangents. Magnetite (Fe 3 O 4 ) and some iron oxide based ceramics are materials which interact with electric and magnetic fields. In the case of the materials interacting only with the electric field the expression for the Dp reduces to: Dp =λ0 2 π  2 ε ʹ (1+ (tanδe)2) √−1 √(6) The electromagnetic power absorbed by a material, P, depends on the microwave radiation penetrating the material by: P=2 π f ε 0 ε ʹʹE2rms +2 π f μ 0 μ ʹʹH2rms (7) where μ 0 is the magnetic permeability of air (H m−1) and μ ʹʹ is the magnetic loss factor, negligible in non-magnetic materials. Erms and Hrms are the root mean square of the electric and magnetic fields, respectively. The factors 2 π fE2rms and 2 π fH2rms are dependent only on the applicator and the emitted power. To obtain the energy absorbed by the material, Ayappa [121] obtained a critical thickness in slabs, which showed that valid power profiles are obtained using Lambert’s Law, considering an exponential decay of the energy absorption. Therefore, this approximation is used for the calculation of power in samples with sufficiently thick section: P=P0e(− 2 α y)=P0e(− 2y)/δ=P0e−y/Dp (8) where P0 is the incident power (W) at the surface of the sample, y is the distance inside the material and α is the attenuation factor (dB m−1) which is the inverse of the characteristic penetration depth (δ), i.e. the distance at which the field strength decreases by the same factor as the power penetration depth [98,122]. Note that Dp is half of δ. Therefore, not all materials interact in the same way with microwaves. As the electromagnetic waves penetrate into the material, the electric and magnetic field intensity vary [13]. In addition, as the material increases its temperature, these intensities are updated, making it difficult to measure the power absorbed. The time evolution and spatial distribution of the temperature can be calculated by applying the following energy balance [122]: ρ Cp ∂ T ∂ t=2 π f ε 0 ε ʹʹE2rms +2 π f μ 0 μ ʹʹH2rms +kT∇2T(9) where ρ is the density of the material (kg/m3), Cp is its specific heat (W), T is the temperature distribution (◦C), t is the time (s), kT is the thermal conductivity (W/moC). Fig. 9. Scheme of testing device for dielectric properties, using a cylinder cavity and dual mode [111]. Dp =λ0 2 π (2 ε ʹ μ ʹ) 1 / 2 [(1+ (tanδe)2(tanδ μ )2+(tanδ μ )2(tanδe)2) 1 / 2 +tanδetanδ μ −1]−1 / 2 (5) C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 16 [21] A. Martin, A. Navarrete, Microwave-assisted process intensification techniques, Curr. Opin. Green Sustain. Chem. 11 (Jun 2018) 70–75, https://doi.org/10.1016/ j.cogsc.2018.04.019. [22] J. Zhu, A.V. Kuznetsov, K.P. Sandeep, Mathematical modeling of continuous flow microwave heating of liquids (effects of dielectric properties and design parameters), Int. J. Therm. Sci. 46 (4) (2007) 328–341, https://doi.org/10.1016/ j.ijthermalsci.2006.06.005. [23] S. Curet, F. Begnini, O. Rouaud, L. Boillereaux, Modeling Microwave Heating during Batch Processing of Liquid Sample in a Single Mode Cavity, 2015. [24] M. Bhattacharya, T. Basak, A review on the susceptor assisted microwave processing of materials, Energy 97 (Feb 2016) 306–338, https://doi.org/ 10.1016/j.energy.2015.11.034. [25] M. Radoiu, A. Mello, Technical advances, barriers, and solutions in microwaveassisted technology for industrial processing, Chem. Eng. Res. Design 181 (May 2022) 331–342, https://doi.org/10.1016/j.cherd.2022.03.029. [26] E.T. Thostenson, T.-W. Chou, Microwave processing: fundamentals and applications, Compos. A: Appl. Sci. Manuf. 30 (9) (1999) 1055–1071, https://doi. org/10.1016/S1359-835X(99)00020-2. [27] M. Regier, H. Schubert, Introducing Microwave Processing of Food: Principles and Technologies, 2005, pp. 3–21. [28] A. Datta, Fundamentals of heat and moisture transport for Microwaveable food product and process development, Handbook Microwave Technol. Food Appl. (2001) 115–172, 01. [29] S.T. Dinani, M. Hasic, M. Auer, U. Kulozik, Assessment of uniformity of microwave-based heating profiles generated by solid-state and magnetron systems using various shapes of test samples, Food Bioprod. Process. 124 (Nov 2020) 121–130, https://doi.org/10.1016/j.fbp.2020.08.013. [30] M.B. Gawande, S.N. Shelke, R. Zboril, R.S. Varma, Microwave-assisted chemistry: synthetic applications for rapid assembly of nanomaterials and organics, Acc. Chem. Res. 47 (4) (2014) 1338–1348, 2014-04-15, https://doi.org/10.1021/ar 400309b. [31] A.F. Porto, B.L. Sadicoff, M.C.V. Amorim, M.C.S. de Mattos, Microwave-assisted free radical bulk-polyaddition reactions in a domestic microwave oven, Polym. Test. 21 (2) (Apr 2002) 145–148, https://doi.org/10.1016/s0142-9418(01) 00061-7. [32] H.L. Chen, T. Li, Z. Wang, R.Z. Ye, Q.L. Li, Effect of dielectric properties on heat transfer characteristics of rubber materials via microwave heating, Int. J. Therm. Sci. 148 (Feb 2020), https://doi.org/10.1016/j.ijthermalsci.2019.106162. Art no. 106162. [33] T.P. Naik, I. Singh, A.K. Sharma, Processing of polymer matrix composites using microwave energy: a review, Comp. Part a-Appl. Sci. Manufact. 156 (May 2022), https://doi.org/10.1016/j.compositesa.2022.106870. Art no. 106870. [34] I. Singh, P.K. Bajpai, D. Malik, A.K. Sharma, P. Kumar, Feasibility study on microwave joining of ‘green’ composites, Akademeia 1 (1) (2011). Art no. ea0101. [35] V. Ramopoulos, G. Link, S. Soldatov, J. Jelonnek, Industrial scale microwave applicator for high temperature alkaline hydrolysis of PET, Int. J. Microw. Wirel. Technol. 10 (05 2018) 1–8, https://doi.org/10.1017/S1759078718000727. [36] M. Dua, Q. Zhang, P. Mertiny, Microwave heating of graphene nanoplatelet polymer composites: experimental and finite element study, Polym. Compos. 44 (8) (Aug 2023) 4924–4936, https://doi.org/10.1002/pc.27460. [37] J. Zhou, Y.G. Li, Z.X. Zhu, E. Xu, S.P. Li, S.C. Sui, Microwave heating and curing of metal-like CFRP laminates through ultrathin and flexible resonance structures, Compos. Sci. Technol. 218 (Feb 2022), https://doi.org/10.1016/j. compscitech.2021.109200. Art no. 109200. [38] J. Zhou, Y.G. Li, D. Li, Y.Y. Wen, Online learning based intelligent temperature control during polymer composites microwave curing process, Chem. Eng. J. 370 (Aug 2019) 455–465, https://doi.org/10.1016/j.cej.2019.03.204. [39] M. Baker-Fales, T.Y. Chen, D.G. Vlachos, Scale-up of microwave-assisted, continuous flow, liquid phase reactors: application to 5-Hydroxymethylfurfural production, Chem. Eng. J. 454 (Feb 2023), https://doi.org/10.1016/j. cej.2022.139985. Art no. 139985. [40] K. Martina, G. Cravotto, R.S. Varma, Impact of microwaves on organic synthesis and strategies toward flow processes and scaling up, J. Organomet. Chem. 86 (20) (Oct 2021) 13857–13872, https://doi.org/10.1021/acs.joc.1c00865. [41] L. Bonaccorsi, E. Proverbio, Influence of process parameters in microwave continuous synthesis of zeolite LTA, Microporous Mesoporous Mater. 112 (1–3) (Jul 2008) 481–493, https://doi.org/10.1016/j.micromeso.2007.10.028. [42] I. Polaert, L. Estel, M. Delmotte, D. Luart, C. Len, A new and original microwave continuous reactor under high pressure for future chemistry, AICHE J. 63 (1) (Jan 2017) 192–199, https://doi.org/10.1002/aic.15515. [43] H. Saggadi, I. Polaert, D. Luart, C. Len, L. Estel, Microwaves under pressure for the continuous production of quinoline from glycerol, Catal. Today 255 (Oct 2015) 66–74, https://doi.org/10.1016/j.cattod.2014.10.050. [44] R. Bell and M. Robbins, "ELECTROMAGNETIC HEATING REACTOR," Patent Appl. GB2020051499W, 2020. [45] H. Qiu, "Microwave catalysis continuous pipe reactor," Patent Appl. CN108355595A, 2018. [46] Z. Jicheng, Y. Pengfei, and W. Zhe, "Microwave catalytic reactor system," Patent Appl. CN102133516A, 2011. [47] R. Parosa, "A method for hydrothermal liquefaction of biomass and a system for hydrothermal liquefaction of biomass," Patent Appl. WO2014008954A1, 2014. [48] C.R. Ellison, R. Hoff, C. Marculescu, D. Boldor, Investigation of microwaveassisted pyrolysis of biomass with char in a rectangular waveguide applicator with built-in phase-shifting, Appl. Energy 259 (Feb 2020), https://doi.org/ 10.1016/j.apenergy.2019.114217. Art no. 114217. [49] H. Topcam, F. Erdogdu, Designing system cavity geometry and optimizing process variables for continuous flow microwave processing, Food Bioprod. Process. 127 (May 2021) 295–308, https://doi.org/10.1016/j.fbp.2021.03.006. [50] S. Tuta, T.K. Palazoglu, Finite element modeling of continuous-flow microwave heating of fluid foods and experimental validation, J. Food Eng. 192 (Jan 2017) 79–92, https://doi.org/10.1016/j.jfoodeng.2016.08.003. [51] P. Kumar, et al., Overcoming issues associated with the scale-up of a continuous flow microwave system for aseptic processing of vegetable purees, Food Res. Int. 41 (5) (2008) 454–461, https://doi.org/10.1016/j.foodres.2007.11.004. [52] P. Ratanadecho, K. Aoki, M. Akahori, A numerical and experimental investigation of the modelling of microwave melting of frozen packed beds using a rectangular wave guide, Int. Commun. Heat Mass Transf. 28 (6) (Aug 2001) 751–762, https:// doi.org/10.1016/s0735-1933(01)00279-2. [53] P. Ratanadecho, K. Aoki, M. Akahori, The characteristics of microwave melting of frozen packed beds using a rectangular waveguide, Ieee Trans. Microwave Theory Tech. 50 (6) (Jun 2002) 1495–1502, https://doi.org/10.1109/ tmtt.2002.1006410. Art no. Pii s0018–9480(02)05204–3. [54] P. Ratanadecho, K. Aoki, M. Akahori, Influence of irradiation time, particle sizes, and initial moisture content during microwave drying of multi-layered capillary porous materials, J. Heat Transf. Trans. Asme 124 (1) (Feb 2002) 151–161, https://doi.org/10.1115/1.1423951. [55] A. Idris, K. Khalid, W. Omar, Drying of silica sludge using microwave heating, Appl. Therm. Eng. 24 (5–6) (Apr 2004) 905–918, https://doi.org/10.1016/j. applthermaleng.2003.10.001. [56] H. Zhang, A.K. Datta, Microwave power absorption in singleand multiple-item foods, Food Bioprod. Process. 81 (C3) (Sep 2003) 257–265, https://doi.org/ 10.1205/096030803322438027. [57] L.H. Huang, Computer-controlled microwave heating to in-package pasteurize beef frankfurters for elimination of listeria monocytogenes, J. Food Process Eng. 28 (5) (Oct 2005) 453–477, https://doi.org/10.1111/j.1745-4530.2005.033.x. [58] G. Cuccurullo, L. Giordano, D. Albanese, L. Cinquanta, M. Di Matteo, Infrared thermography assisted control for apples microwave drying, J. Food Eng. 112 (4) (Oct 2012) 319–325, https://doi.org/10.1016/j.jfoodeng.2012.05.003. [59] H. Zhang, A.K. Datta, I.A. Taub, C. Doona, Electromagnetics, heat transfer, and thermokinetics in microwave sterilization, AICHE J. 47 (9) (Sep 2001) 1957–1968, https://doi.org/10.1002/aic.690470907. [60] X. Zhou, P.D. Pedrow, Z.W. Tang, S. Bohnet, S.S. Sablani, J.M. Tang, Heating performance of microwave ovens powered by magnetron and solid-state generators, Innovative Food Sci. Emerg. Technol. 83 (Jan 2023), https://doi.org/ 10.1016/j.ifset.2022.103240. Art no. 103240. [61] A.W. Fliflet, et al., Application of microwave heating to ceramic processing: design and initial operation of a 2.45-GHz single-mode furnace, IEEE Trans. Plasma Sci. 24 (3) (Jun 1996) 1041–1049, https://doi.org/10.1109/27.533111. [62] B.W. Li, H.X. Li, X.F. Zhang, X.L. Jia, Z.C. Sun, Nucleation and crystallization of tailing-based glass-ceramics by microwave heating, Int. J. Miner. Metall. Mater. 22 (12) (Dec 2015) 1342–1349, https://doi.org/10.1007/s12613-015-1203-y. [63] R.M.C. Mimoso, D.M.S. Albuquerque, J.M.C. Pereira, J.C.F. Pereira, Simulation and control of continuous glass melting by microwave heating in a single-mode cavity with energy efficiency optimization, Int. J. Therm. Sci. 111 (Jan 2017) 175–187, https://doi.org/10.1016/j.ijthermalsci.2016.08.015. [64] X. Sun, J.-Y. Hwang, X. Huang, B. Li, S. Shi, Effects of microwave on molten metals with low melting temperatures, J. Miner. Mater. Charact. Eng. 4 (01 2005) 107–112, https://doi.org/10.4236/jmmce.2005.42010. [65] S. Gedevanishvili, D. Agrawal, R. Roy, and B. Vaidhyanathan, "Microwave processing using highly microwave absorbing powdered material layers " Patent Appl. 6512216 B2, 2003. [66] L. Yongguang, L. Tianqi, Y. Xia, L. Jing, Z. Libo, X. Yunhao, Dielectric properties and microwave heating behavior of neutral leaching residues from zinc metallurgy in the microwave field, Green Proc. Synth. 9 (1) (2020) 97–106, https://doi.org/10.1515/gps-2020-0011. [67] Y.D. Xu, B.Z. Mu, T. Li, H.L. Chen, Effect of carbon nanotube mass fraction and distribution on microwave heating effect of rubber composites, J. Therm. Anal. Calorim. 148 (12) (Jun 2023) 5347–5356, https://doi.org/10.1007/s10973-02312088-2. [68] Y.J. Zhu, F. Chen, Microwave-assisted preparation of inorganic nanostructures in liquid phase, Chem. Rev. 114 (12) (Jun 2014) 6462–6555, https://doi.org/ 10.1021/cr400366s. [69] A.R. Harutyunyan, B.K. Pradhan, J.P. Chang, G.G. Chen, P.C. Eklund, Purification of single-wall carbon nanotubes by selective microwave heating of catalyst particles, J. Phys. Chem. B 106 (34) (Aug 2002) 8671–8675, https://doi.org/ 10.1021/jp0260301. [70] W.H. Sutton, Microwave processing of ceramics - an overview, in: 3rd Symp on Microwave Processing of Materials, at the 1992 Spring Meeting of the Materials Research Soc, San Francisco, Ca, Apr 27-May 01 1992, vol. 269, in Materials Research Society Symposium Proceedings, 1992, pp. 3–20, https://doi.org/ 10.1557/proc-269-3 [Online]. Available: ://WOS:A1992BX05V00001. [71] L.F. Chen, C. Leonelli, T. Manfredini, C. Siligardi, Processing of a silicon-carbidewhisker-reinforced glass-ceramic composite by microwave heating, J. Am. Ceram. Soc. 80 (12) (Dec 1997) 3245–3249. [72] R. Vasudevan, T. Karthik, S. Ganesan, R. Jayavel, Effect of microwave sintering on the structural and densification behavior of sol-gel derived zirconia toughened alumina (ZTA) nanocomposites, Ceram. Int. 39 (3) (Apr 2013) 3195–3204, https://doi.org/10.1016/j.ceramint.2012.10.004. [73] Y. Fang, J.P. Cheng, R. Roy, D.M. Roy, D.K. Agrawal, Enhancing densification of zirconia-containing ceramic-matrix composites by microwave processing, C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 17 J. Mater. Sci. 32 (18) (Sep 1997) 4925–4930, https://doi.org/10.1023/a: 1018624223909. [74] S. Chandrasekaran, T. Basak, S. Ramanathan, Experimental and theoretical investigation on microwave melting of metals, J. Mater. Process. Technol. 211 (3) (2011) 482–487, https://doi.org/10.1016/j.jmatprotec.2010.11.001. [75] R.M. Anklekar, K. Bauer, D.K. Agrawal, R. Roy, Improved mechanical properties and microstructural development of microwave sintered copper and nickel steel PM parts, Powder Metall. 48 (1) (Mar 2005) 39–46, https://doi.org/10.1179/ 003258905x37657. [76] A. Mondal, A. Shukla, A. Upadhyaya, D. Agrawal, Effect of porosity and particle size on microwave heating of copper, Sci. Sinter. 42 (2) (May-Aug 2010) 169–182, https://doi.org/10.2298/sos1002169m. [77] K. Hara, M. Hayashi, M. Sato, K. Nagata, Continuous pig Iron making by microwave heating with 12.5 kW at 2.45 GHz, J. Microw. Power Electromagn. Energy. 45 (3) (2011) 137–147. [78] S. Tamang, S. Aravindan, Joining of dissimilar metals by microwave hybrid heating: 3D numerical simulation and experiment, Int. J. Therm. Sci. 172 (Feb 2022), https://doi.org/10.1016/j.ijthermalsci.2021.107281. Art no. 107281. [79] J. Zhou, Y.G. Li, T. Yang, W.Z. Xue, X.Z. Hao, A.M. Gao, Microwave heating and processing of solid metals using electromagnetic resonators, Int. J. Adv. Manuf. Technol. 123 (3–4) (Nov 2022) 1111–1121, https://doi.org/10.1007/s00170022-10244-w. [80] W.L.E. Wong, M. Gupta, Development of mg/cu nanocomposites using microwave assisted rapid sintering, Compos. Sci. Technol. 67 (7–8) (Jun 2007) 1541–1552, https://doi.org/10.1016/j.compscitech.2006.07.015. [81] W.L.E. Wong, M. Gupta, Improving overall mechanical performance of magnesium using nano-alumina reinforcement and energy efficient microwave assisted processing route, Adv. Eng. Mater. 9 (10) (Oct 2007) 902–909, https:// doi.org/10.1002/adem.200700169. [82] W.W.L. Eugene, M. Gupta, Simultaneously improving strength and ductility of magnesium using nano-size SiC particulates and microwaves, Adv. Eng. Mater. 8 (8) (Aug 2006) 735–740, https://doi.org/10.1002/adem.200500209. [83] K.S. Tun, M. Gupta, Improving mechanical properties of magnesium using nanoyttria reinforcement and microwave assisted powder metallurgy method, Compos. Sci. Technol. 67 (13) (Oct 2007) 2657–2664, https://doi.org/10.1016/j. compscitech.2007.03.006. [84] S. Dabrowska, T. Chudoba, J. Wojnarowicz, W. Lojkowski, Current trends in the development of microwave reactors for the synthesis of nanomaterials in laboratories and industries: a review, Crystals 8 (10) (Oct 2018), https://doi.org/ 10.3390/cryst8100379. Art no. 379. [85] C. Lv, H.-X. Yin, Y.-L. Liu, X.-X. Chen, M.-H. Sun, H.-L. Zhao, Preparation of cerium oxide via microwave heating: research on effect of temperature field on particles, Crystals 12 (6) (2022) 843, 2022-06-15, https://doi.org/10.3390/crys t12060843. [86] H. Li, et al., Food waste pyrolysis by traditional heating and microwave heating: a review, Fuel 324 (Sep 2022), https://doi.org/10.1016/j.fuel.2022.124574. Art no. 124574. [87] S. Anis, R. Alhakim, A.M. Khoiron Wahyudi, A. Kusumastuti, Microwave-assisted pyrolysis and distillation of cooking oils for liquid bio-fuel production, J. Anal. Appl. Pyrolysis 154 (Mar 2021), https://doi.org/10.1016/j.jaap.2020.105014. Art no. 105014. [88] R.G. Bosisio, J.L. Cambon, C. Chavarie, D. Klvana, Exprimental result on the hesting of athabasca tar sand samples with microwave power, J. Microwave Power 12 (4) (1977) 301–307, 1977/01/01, https://doi.org/10.1080/16070 658.1977.11689058. [89] A. Rosin, M.A. Willert-Porada, T. Gerdes, A. Schmidt-Rodenkirchen, Ieee, High pressure microwave flow reactor for raw oil treatment, in: 2016 Ieee Mtt-S International Microwave Symposium (Ims), 2016. [90] R. Morschh¨ auser, et al., Microwave-assisted continuous flow synthesis on industrial scale, Green Proc. Synth. 1 (3) (2012), https://doi.org/10.1515/gps2012-0032, 2012-01-01. [91] H. Shang, et al., Effect of microwave irradiation on the viscosity of crude oil: a view at the molecular level, Fuel Process. Technol. 170 (Feb 2018) 44–52, https://doi.org/10.1016/j.fuproc.2017.10.021. [92] L. Combemale, G. Caboche, D. Stuerga, D. Chaumont, Microwave synthesis of yttria stabilized zirconia, Mater. Res. Bull. 40 (3) (Mar 2005) 529–536, https:// doi.org/10.1016/j.materresbull.2004.10.024. [93] M. Gupta, W.L.E. Wong, Enhancing overall mechanical performance of metallic materials using two-directional microwave assisted rapid sintering, Scr. Mater. 52 (6) (Mar 2005) 479–483, https://doi.org/10.1016/j.scriptamat.2004.11.006. [94] A. Borrell, M.D. Salvador, F.L. Pe˜ naranda-Foix, J.M. Cat´ ala-Civera, Microwave sintering of zirconia materials: mechanical and microstructural properties, Int. J. Appl. Ceram. Technol. 10 (2) (Mar–Apr 2013) 313–320, https://doi.org/ 10.1111/j.1744-7402.2011.02741.x. [95] M. Rozainee, W. Khairuddin, W. Ali, K.G. Tan, C.H. Tan, A.C. Kumoro, Comparison of sludge drying performance between microwave and convective drying, in: Presented at the 5th Symposium of Malaysian Chemical Engineers, 2001. [96] D.A. Papargyris, R.J. Day, A. Nesbitt, D. Bakavos, Comparison of the mechanical and physical properties of a carbon fibre epoxy composite manufactured by resin transfer moulding using conventional and microwave heating, Compos. Sci. Technol. 68 (7–8) (Jun 2008) 1854–1861, https://doi.org/10.1016/j. compscitech.2008.01.010. [97] S. Sharifvaghefi, B. Shirani, M. Eic, Y. Zheng, Application of microwave in hydrogen production from methane dry reforming: comparison between the conventional and microwave-assisted catalytic reforming on improving the energy efficiency, Catalysts 9 (7) (Jul 2019), https://doi.org/10.3390/ catal9070618. Art no. 618. [98] K.G. Ayappa, H.T. Davis, G. Crapiste, E.A. Davis, J. Gordon, Microwave-heating - an evaluation of power formulations, Chem. Eng. Sci. 46 (4) (1991) 1005–1016, https://doi.org/10.1016/0009-2509(91)85093-d. [99] G.S.J. Sturm, G.D. Stefanidis, M.D. Verweij, T.D.T. Van Gerven, A.I. Stankiewicz, Design principles of microwave applicators for small-scale process equipment, Chem. Eng. Proc. Proc. Intensific. 49 (9) (Sep 2010) 912–922, https://doi.org/ 10.1016/j.cep.2010.07.017. [100] A.K. Datta, Heat and mass-transfer in the microwave processing of food, Chem. Eng. Prog. 86 (6) (Jun 1990) 47–53. [101] J. Tang, Unlocking potentials of microwaves for food safety and quality, J. Food Sci. 80 (8) (2015) E1776–E1793, 2015-08-01, https://doi.org/10.1111/1750-3 841.12959. [102] G.P. Lewis, et al., Monitoring and control system for tuneable high frequency microwave assisted chemistry, J. Phys. Conf. Ser. 76 (1) (2007) 012058, 2007/ 07/01, https://doi.org/10.1088/1742-6596/76/1/012058. [103] D.B. Oliveira, E.J. Silva, Hybrid analytical-FEM method for microwave heating analysis in a single mode cavity, IEEE Trans. Magn. 46 (8) (Aug 2010) 2767–2770, https://doi.org/10.1109/tmag.2010.2044152. [104] B.J. Pangrle, K.G. Ayappa, H.T. Davis, E.A. Davis, J. Gordon, Microwave thawing of cylinders, AICHE J. 37 (12) (Dec 1991) 1789–1800, https://doi.org/10.1002/ aic.690371204. [105] X. Zeng, A. Faghri, Experimental and numerical study of microwave thawing heat-transfer for food materials, J. Heat Transf. Trans. Asme 116 (2) (May 1994) 446–455, https://doi.org/10.1115/1.2911417. [106] J.P. Robinson, C.E. Snape, S.W. Kingman, H. Shang, Thermal desorption and pyrolysis of oil contaminated drill cuttings by microwave heating, J. Anal. Appl. Pyrolysis 81 (1) (Jan 2008) 27–32, https://doi.org/10.1016/j.jaap.2007.07.004. [107] J.P. Robinson, S.W. Kingman, O. Onobrakpeya, Microwave-assisted stripping of oil contaminated drill cuttings, J. Environ. Manag. 88 (2) (Jul 2008) 211–218, https://doi.org/10.1016/j.jenvman.2007.02.009. [108] P. Rattanadecho, N. Suwannapum, B. Chatveera, D. Atong, N. Makul, Development of compressive strength of cement paste under accelerated curing by using a continuous microwave thermal processor, Mater. Sci. Eng. a-Struct. Mater. Prop. Microstruct. Proc. 472 (1–2) (Jan 2008) 299–307, https://doi.org/ 10.1016/j.msea.2007.03.035. [109] P. Rattanadecho, N. Suwannapum, Drying of dielectric materials using a continuous microwave belt drier (case study: ceramics and natural rubber), J. Manufact. Sci. Eng. Trans. Asme 129 (1) (Feb 2007) 157–163, https://doi.org/ 10.1115/1.2386166. [110] J.M. Catala-Civera, A.J. Canos, P. Plaza-Gonzalez, J.D. Gutierrez, B. Garcia-Banos, F.L. Penaranda-Foix, Dynamic measurement of dielectric properties of materials at high temperature during microwave heating in a dual mode cylindrical cavity, IEEE Trans. Microwave Theory Tech. 63 (9) (2015) 2905–2914, 2015-09-01, htt ps://doi.org/10.1109/tmtt.2015.2453263. [111] B. Garcia-Ba˜ nos, J. Catal´ a-Civera, F. Pe˜ naranda-Foix, P. Plaza-Gonz´ alez, G. Llorens-Vall´ es, In situ monitoring of microwave processing of materials at high temperatures through dielectric properties measurement, Materials 9 (5) (2016) 349, 2016-05-07, https://doi.org/10.3390/ma9050349. [112] J.D. Gutierrez-Cano, P. Plaza-Gonzalez, A.J. Canos, B. Garcia-Banos, J.M. CatalaCivera, F.L. Penaranda-Foix, A new stand-alone microwave instrument for measuring the complex permittivity of materials at microwave frequencies, IEEE Trans. Instrum. Meas. 69 (6) (2020) 3595–3605, 2020-06-01, https://doi.org/1 0.1109/tim.2019.2941038. [113] R. P´ erez-Campos, et al., Permittivity measurements for cypress and rockrose biomass versus temperature, density, and moisture content, Sensors 20 (17) (Sep 2020), https://doi.org/10.3390/s20174684. Art no. 4684. [114] A.L. Cullen, P.K. Yu, Accurate measurement of permittivity by means of an open resonator, Proc. Royal Soc. London Series a-Math. Phys. Sci. 325 (1563) (1971) 493, https://doi.org/10.1098/rspa.1971.0181. [115] J. Krupka, Frequency domain complex permittivity measurements at microwave frequencies, Meas. Sci. Technol. 17 (6) (Jun 2006) R55–R70, https://doi.org/ 10.1088/0957-0233/17/6/r01. [116] R. P´ erez-Campos, et al., Dynamic permittivity measurement of ground-tire rubber (GTR) during microwave-assisted devulcanization, Polymers 14 (17) (Sep 2022), https://doi.org/10.3390/polym14173543. Art no. 3543. [117] C. Leonelli, T.J. Mason, Microwave and ultrasonic processing: now a realistic option for industry, Chem. Eng. Process. Process Intensif. 49 (9) (2010) 885–900, 2010-09-01, https://doi.org/10.1016/j.cep.2010.05.006. [118] P. Plaza-Gonzalez, J. Monzo-Cabrera, J.M. Catala-Civera, D. Sanchez-Hernandez, Effect of mode-stirrer configurations on dielectric heating performance in multimode microwave applicators, IEEE Trans. Microwave Theory Tech. 53 (5) (2005) 1699–1706, 2005-05-01, https://doi.org/10.1109/tmtt.2005.847066. [119] J. Monzo-Cabrera, et al., A novel bandstop filter based on two-port coaxial cavities for the installation of metallic mode stirrers in microwave ovens, Electronics 11 (13) (Jul 2022), https://doi.org/10.3390/electronics11131989. Art no. 1989. [120] M. Sparks, R. Loudon, C. Kittel, Ferromagnetic relaxation. I. Theory of the relaxation of the uniform precession and the degenerate spectrum in insulators at low temperatures, Phys. Rev. 122 (3) (05/01/ 1961) 791–803, https://doi.org/ 10.1103/PhysRev.122.791. [121] K.G. Ayappa, Modelling transport processes during microwave heating: a review, Rev. Chem. Eng. 13 (2) (1997) 1–69. [122] A. Metaxas, Microwave heating, Power Eng. J. 5 (10 1991) 237–247, https://doi. org/10.1049/pe:19910047. C. Valverde et al. International Communications in Heat and Mass Transfer 156 (2024) 107594 18 [123] D.E. Clark, D.C. Folz, J.K. West, Processing materials with microwave energy, Mater. Sci. Eng. a-Struct. Mater. Prop. Microstruct. Proc. 287 (2) (Aug 2000) 153–158, https://doi.org/10.1016/s0921-5093(00)00768-1. [124] P. Veggi, J. Martinez, M.A. Meireles, Fundamentals of microwave, in: Extraction Microwave-Assisted Extraction for Bioactive Compounds: Theory and Practice, Springer US, Boston, MA, 2013, pp. 15–52. [125] A.M. Paola, S.B. Juliano, A.G. Ricardo, Chapter 2 - microwave heating, in: F. ´ Erico Marlon de Moraes (Ed.), Microwave-Assisted Sample Preparation for Trace Element Analysis, Elsevier, Amsterdam, 2014, pp. 59–75. [126] M. Gupta, E.W.W. Leong, Microwaves and Metals, 2008. [127] E. Kubel, Advancement in Microwave Heating Technology, 2005. [128] C.O. Kappe, Controlled microwave heating in modern organic synthesis, Angew. Chem. Int. Ed. 43 (46) (2004) 6250–6284, 2004–11–26, https://doi.org/10. 1002/anie.200400655. [129] R. Behrend, C. Dorn, V. Uhlig, H. Krause, Investigations on container materials in high temperature microwave applications, Energy Procedia 120 (2017) 417–423, https://doi.org/10.1016/j.egypro.2017.07.191. [130] T.A. Baeraky, Determination of microwave electrical characteristics of boron nitride at high temperature, Phys. Status Solidi C - Conf. Critic. Rev. 2 (7) (2005) 2577–2580, https://doi.org/10.1002/pssc.200461281. [131] S. Hahn, K. Dornich, M. Reichmann, G. Walter, Contactless measurement of the dielectric parameters of ceramic materials for microwave processing, Cfi-Ceramic Forum Int. 87 (5) (May 2010) E43–E46. [132] B.W. William, S. Aina, Dielectric Constant and Loss Data, 1972 [Online]. Available: https://api.semanticscholar.org/CorpusID:137029977. [133] C.H. Chan, R. Yusoff, G.C. Ngoh, Modeling and prediction of extraction profile for microwave-assisted extraction based on absorbed microwave energy, Food Chem. 140 (1–2) (Sep 2013) 147–153, https://doi.org/10.1016/j. foodchem.2013.02.057. [134] M.S. Spotz, D.J. Skamser, D.L. Johnson, Thermal-stability of ceramic materials in microwave-heating, J. Am. Ceram. Soc. 78 (4) (Apr 1995) 1041–1048, https:// doi.org/10.1111/j.1151-2916.1995.tb08434.x. [135] G. Roussy, A. Bennani, J.M. Thiebaut, Temperature runaway of microwave irradiated materials, J. Appl. Phys. 62 (4) (Aug 1987) 1167–1170, https://doi. org/10.1063/1.339666. [136] A. Birnboim, et al., Comparative study of microwave sintering of zinc oxide at 2.45, 30, and 83 GHz, J. Am. Ceram. Soc. 81 (6) (Jun 1998) 1493–1501. [137] A.W. Fliflet, et al., A study of millimeter-wave sintering of fine-grained alumina compacts, Ieee Trans. Plasma Sci. 28 (3) (Jun 2000) 924–935. [138] S. Singh, D. Gupta, V. Jain, A.K. Sharma, Microwave processing of materials and applications in manufacturing industries: a review, Mater. Manuf. Process. 30 (1) (Jan 2015) 1–29, https://doi.org/10.1080/10426914.2014.952028. [139] M.S. Srinath, A.K. Sharma, P. Kumar, A novel route for joining of austenitic stainless steel (SS-316) using microwave energy, Proc. Inst. Mech. Eng. Part B-J. Eng. Manufact. 225 (B7) (Jul 2011) 1083–1091, https://doi.org/10.1177/ 2041297510393451. [140] P.K. Loharkar, A. Ingle, S. Jhavar, Parametric review of microwave-based materials processing and its applications, J. Mater. Res. Technol. 8 (3) (May–Jun 2019) 3306–3326, https://doi.org/10.1016/j.jmrt.2019.04.004. [141] D. Gupta, A.K. Sharma, Development and microstructural characterization of microwave cladding on austenitic stainless steel, Surf. Coat. Technol. 205 (21–22) (Aug 2011) 5147–5155, https://doi.org/10.1016/j.surfcoat.2011.05.018. [142] E.T. Kostas, D. Beneroso, J.P. Robinson, The application of microwave heating in bioenergy: a review on the microwave pre-treatment and upgrading technologies for biomass, Renew. Sust. Energ. Rev. 77 (Sep 2017) 12–27, https://doi.org/ 10.1016/j.rser.2017.03.135. [143] Y. Sun, Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources, KIT Scientific Publishing, 2016. [144] A.N. Magunov, Laser thermometry of solids, in: Tempmeko 2001: 8th International Symposium on Temperature and Thermal Measurement in Industry and Science, Vol 1 & 2, Proceedings, 2002, pp. 205–209. [145] L.S. Gangurde, G.S.J. Sturm, T.J. Devadiga, A.I. Stankiewicz, G.D. Stefanidis, Complexity and challenges in noncontact high temperature measurements in microwave-assisted catalytic reactors, Ind. Eng. Chem. Res. 56 (45) (Nov 2017) 13380–13392, https://doi.org/10.1021/acs.iecr.7b02091. [146] D.J. Grellinger, M. Janney, Temperature measurement in A 2. 45 GHZ microwave furnace, Ceram. Trans. 36 (1993) 529–538. [147] E. Pert, et al., Temperature measurements during microwave processing: the significance of thermocouple effects, J. Am. Ceram. Soc. 84 (9) (Sep 2001) 1981–1986. [148] A. Arzhannikov, T. Akhmetov, P. Kalinin, Stand for Research on Microwave Heating and Transformation of Substances, IYaF im. Budkera, Novosibirsk, 10 2004. [149] S.M. Bradshaw, E.J.V. Wyk, J.B.D. Swardt, Microwave heating principles and the application to the regeneration of granular activated carbon, J. South. Afr. Inst. Min. Metall. 98 (1998) 201–210. [150] F.R. Vandevoort, M. Laureano, J.P. Smith, G.S.V. Raghavan, A practical thermocouple for temperature-measurement in microwave-ovens, Can. Inst. Food Sci. Technol. J. 20 (4) (Oct 1987) 279–284, https://doi.org/10.1016/s0315-5463 (87)71200-0. [151] H.S. Ramaswamy, J.M. Rauber, G.S.V. Raghavan, F.R. van de Voort, Evaluation of shielded thermocouples for measuring temperature of foods in a microwave oven, J. Food Sci. Technol. Mysore 35 (4) (Jul-Aug 1998) 325–329. [152] I. Kalinke, P. Kubbutat, S.T. Dinani, S. Ambros, M. Ozcelik, U. Kulozik, Critical assessment of methods for measurement of temperature profiles and heat load history in microwave heating processes-a review, Compr. Rev. Food Sci. Food Saf. 21 (3) (May 2022) 2118–2148, https://doi.org/10.1111/1541-4337.12940. [153] D.L. Luan, J.M. Tang, P.D. Pedrow, F. Liu, Z.W. Tang, Performance of mobile metallic temperature sensors in high power microwave heating systems, J. Food Eng. 149 (Mar 2015) 114–122, https://doi.org/10.1016/j.jfoodeng.2014.09.041. [154] D.L. Luan, J. Tang, P.D. Pedrow, F. Liu, Z.W. Tang, Using mobile metallic temperature sensors in continuous microwave assisted sterilization (MATS) systems, J. Food Eng. 119 (3) (Dec 2013) 552–560, https://doi.org/10.1016/j. jfoodeng.2013.06.003. [155] J. Tang and F. Liu, "Method for recording temperature profiles in food packages during microwave heating using a metallic data logger," Patent Appl. US 2012/ 0241443 A1, 2015. [156] K. Knoerzer, M. Regier, H. Schubert, Measuring temperature distributions during microwave processing, in: Microwave Processing of Foods, 2nd edition, 2017, pp. 327–349, https://doi.org/10.1016/b978-0-08-100528-6.00015-2. [157] D. Obermayer, C.O. Kappe, On the importance of simultaneous infrared/fiberoptic temperature monitoring in the microwave-assisted synthesis of ionic liquids, Org. Biomol. Chem. 8 (1) (2010) 114–121, https://doi.org/10.1039/b918407d. [158] T. Juming, Fiber-Optic Measurement Systems: Microwave and Radio Frequency Heating Applications, 2006 [Online]. Available: https://api.semanticscholar.or g/CorpusID:31343436. [159] S.W. Harun, M. Yasin, H.A. Rahman, H. Arof, H. Ahmad, Fiber Optic Temperature Sensors, 2012. [160] V. Trudel, Y. St-Amant, One-dimensional single-mode fiber-optic displacement sensors for submillimeter measurements, Appl. Opt. 48 (26) (2009) 4851–4857, 2009/09/10, https://doi.org/10.1364/AO.48.004851. [161] T. Ano, et al., In situ temperature measurements of reaction spaces under microwave irradiation using photoluminescent probes, Phys. Chem. Chem. Phys. 18 (19) (May 2016) 13173–13179, https://doi.org/10.1039/c6cp02034h. [162] B. Bacsa, K. Horv´ ati, S. Bosze, F. Andreae, C.O. Kappe, Solid-phase synthesis of difficult peptide sequences at elevated temperatures:: A critical comparison of microwave and conventional heating technologies, J. Organomet. Chem. 73 (19) (Oct 2008) 7532–7542, https://doi.org/10.1021/jo8013897. [163] X. Yang, B. Wei, Exact research on the theory of the blackbody thermal radiation, Scientific Reports 6 (1) (2016) 37214, https://doi.org/10.1038/srep37214. [164] C. Abrudean, M. Panoiu, C. Panoiu, I. Sora, Using finite difference time-domain method to simulate the electromagnetic field in a multimode microwave oven, in: Proceedings of the 13th Wseas International Conference on Computers, 2009, pp. 193− +. [165] A. Protasov, Reconstruction of the thermal field image from measurements in separate points, in: 2017 5th Ieee Microwaves, Radar and Remote Sensing Symposium (Mrrs), 2017, pp. 89–92. [166] A. Amini, K. Ohno, T. Maeda, K. Kunitomo, Effect of the ratio of magnetite particle size to microwave penetration depth on reduction reaction behaviour by H₂, Sci. Rep. 8 (Oct 2018), https://doi.org/10.1038/s41598-01833460-5. Art no. 15023. [167] S. Ryyn¨ anen, P.O. Risman, T. Ohlsson, Hamburger composition and microwave heating uniformity, J. Food Sci. 69 (7) (Sep 2004) M187–M196. [168] W. Minkina, S. Dudzik, Infrared Thermography, 09 2015. [169] A.N. Magunov, Spectral pyrometry (review), Instrum. Exp. Tech. 52 (4) (Jul 2009) 451–472, https://doi.org/10.1134/s0020441209040010. [170] M. Vollmer, K.-P. M¨ ollmann, Infrared Thermal Imaging: Fundamentals, Research and Applications, 2013. [171] C. Mirabito, et al., "FEMLAB Model of a Coupled Electromagnetic-Thermal Boundary Value Problem," 01, 2005. [172] J.L. He, Y. Yang, H.C. Zhu, K. Li, W. Yao, K.M. Huang, Microwave heating based on two rotary waveguides to improve efficiency and uniformity by gradient descent method, Appl. Therm. Eng. 178 (Sep 2020), https://doi.org/10.1016/j. applthermaleng.2020.115594. Art no. 115594. [173] Y. Zhang, et al., Continuous flow microwave system with helical tubes for liquid food heating, J. Food Eng. 294 (2021) 110409, https://doi.org/10.1016/j. jfoodeng.2020.110409. [174] A. Shadi, et al., Numerical and experimental analysis of fully coupled electromagnetic and thermal phenomena in microwave heating of rocks, Miner. Eng. 178 (Mar 2022), https://doi.org/10.1016/j.mineng.2022.107406. Art no. 107406. [175] "SIMUTOOL." http://www.simutool.com/the-project/ (accessed 10 July, 2023). [176] M. Olszewska-Placha, D. Gryglewski, W. Wojtasiak, M. Celuch, Demonstration of a combined active-passive methodology for the design of solid-state-fed microwave ovens, in: Presented at the Proc. AMPERE 2021, 2021. [177] S.L. Birla, K. Pitchai, 18 - Simulation of microwave processes, in: S. Marc Regier, Kai Knoerzer, Helmar (Eds.), The Microwave Processing of Foods (Second Edition), Second Edition ed. no, Woodhead Publishing Series in Food Science, Technology and Nutrition), Woodhead Publishing, 2017, pp. 407–431. [178] M. Vinatoru, Microwave and Ultrasounds Together – A Challenge, 2019. [179] N.A. Mohamad Aziz, R. Yunus, D. Kania, H. Abd Hamid, Prospects and challenges of microwave-combined technology for biodiesel and biolubricant production through a transesterification: a review, Mol., Rev. 26 (4) (Feb 2021), https://doi. org/10.3390/molecules26040788. Art no. 788. C. Valverde et al.