In the handling of microwave heating, it is useful to consider the same type of equations, the heat conduction equation and the diffusion equation. Due to the difference in the diffusion coefficients of each equation, there is a time delay between the energy applied by the microwave and the thermal energy. From this delay, microwave energy is stored non-thermally, which directly breaks the bonds of the crystal (it means phase transition) before it becomes thermal energy. Also, non-thermal energy is treated as acoustic phonon in the crystal. Therefore, we propose to treat phonon as an epi-thermal distribution function with an extended Bose-Einstein distribution, and in fact the application of microwaves forms a monochromatic peak in the distribution function. Its peak decays over time and becomes thermal energy. Such a process is one of the indicators of how to understand the phenomenon of microwave heating.

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The boiling experiment for a cylindrical vessel was conducted at different operating parameters such as stirring speed, microwave power, and the penetration depth of microwave. The heating rates and the time until boiling were obtained for the heating homogeneity, which is defined as ratio of the local heating within the penetration depth and the heating of the whole vessel. The ratio was estimated by correlation with two dimensionless numbers, the mixing Reynolds number (Re) and our dimensionless microwave number (As) proposed in our previous study. Although the heating ratio is linearly correlated to the simple combination of Re and As. However, it was found that the multiplier of As number depends on microwave power.

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Aluminum nitride (AlN) was synthesized by carbothermal reduction and nitridation from a mixture of Al₂O₃ and carbon black by 5.8 GHz microwave E-field irradiation using single-mode cavity. The apparent activation energy was analyzed by Arrhenius plot of the nitridation ratio of the synthesized samples. The value was smaller than that in previous research using 2.45 GHz microwave irradiation. Samples synthesized by microwaves at 1000-1100 °C were able to maintain the spherical shape of pristine alumina, but the samples at °C or higher were sintered.

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In order to discuss the mechanism of "microwave assisted chemistry" on various chemical reaction universally, the generic definition of chemical reaction enhancing effects under microwave irradiation was proposed in this paper. As the experimentally quantifiable kinetic definition, two types of correction coefficients (C_H, C_S) were proposed in this paper. These coefficients are expected to affect respectively the activation enthalpy (ΔH°^‡) and activation entropy (ΔS°^‡) of the target reaction. This definition was proposed based only on the invariance of linearity and the changes in the gradient and/or intercept of Arrhenius plot for various chemical reaction under microwave irradiation. In comparison with the deductive discussion on some mechanisms of "microwave assisted chemistry" based on various assumptions in other previous studies, it can be said that the discussion based on the proposed definition are phenomenologically guaranteed to be generic and accurate. In addition, the verifiability of some deductive discussions in other previous studies by experimentally measuring C_H and C_S were shown in this paper.

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The application of carbon composite materials in new fields such as automotive materials requires an innovative carbon fiber manufacturing process that halves manufacturing energy and CO₂ emissions while significantly increasing productivity. This study investigated the continuous heating of precursor fibers using microwaves as an innovative carbon fiber production method. As a result, carbon fibers with a high-performance index were obtained. In addition, the physical properties of composite materials using the carbon fibers obtained in this study showed good indices.

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There is a research field called a fluctuating system. In systems such as Brownian motion, the particles of interest exchange kinetic energy from white noise and perform a random walk. The Langevin equation handles these events and takes up fine particle friction and microwave irradiation to confirm the operation of the system. In this paper, we incorporate microwave irradiation into the Maxwell-Boltzmann distribution and confirm that its non-thermal energy exhibits the so-called "microwave effect". As a sample case using correlated noise, two-dimensional Ising model is proposed as a specific example of Monte Carlo simulation. Results will vary depending on the strength of the noise correlation. In this way, the noise-to-noise correlation has a strong effect on physical quantities.

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