A multiphysics model that coupled electric fields and heat transfer was developed to simulate microwave heating of maize seeds in a dryer. The hybrid dryer with the maize seeds inside was simulated using COMSOL Multiphysics software. The dryer was equipped with three magnetrons, with a power of 800 W each, operating at a frequency of 2.45 GHz. These magnetrons create an electric field that is absorbed by the heating maize seeds. In order to increase the accuracy of the results, a study regarding the independence of the discretization grid in the field of the dryer calculation was performed. By the action of the electric field in the dryer, the temperature in the seed layer is evenly distributed, with a maximum value of 44°C after a period of 9-12 seconds. By losing moisture, the seeds become lighter, being transported around the top of the seed layer, and are discharged from the dryer every 3-4 seconds when the feed rate of maize seed is 500 kg/h. The spiral movement of the seeds in the first half of the dryer in the regions where the distribution of the electric field that alternates from maximum to minimum, makes the temperature of the seeds to be uniform in the whole volume, achieving a uniform drying. hybrid dryer, microwave drying, heat transfer
Seeds drying is a method of preservation that prevents microbial growth, increasing their shelf life.
Drying is a complex interaction of heat, mass and impulse transport, which requires time and energy
consumption. Different types of drying equipment are currently available, based on combinations of
different drying techniques. This is advantageous since it uses the best of different methods to achieve
more efficient drying [
The temperature distribution of materials of different shapes during microwave heating was
measured experimentally by mapping, and uneven heating was found to occur [
2022 Copyright for this paper by its authors.
In this study, a multiphysics simulation of a hybrid dryer was performed using a heat transfer model and an electromagnetic one. The geometric model of the dryer, the properties of the material, the equations governing the models, the initial and boundary conditions are briefly described in the following sections.
The geometry of the hybrid dryer, the seed layer to be dried, as well as the positioning of the waveguides on the dryer must be accurately described, so as not to affect the accuracy of the distribution of the electric field inside the created cavity. Any protrusion or cavity in the wall of the dryer, as well as the angles made by the walls can substantially change the distribution of the electric field inside, Figure 1. The geometric model used in the simulation must be accurate for a more accurate representation of the electric field distribution and the temperature in the dryer.
In this geometric model the electromagnetic waves generated by the magnetron enter the dryer cavity
through three parallelepipedic waveguides of 2 wavelengths = 244.9 mm (attributing in COMSOL
Multiphysics 5.6 [
Solving electromagnetic and heat transfer models required the discretization of the entire dryer in
small volumes. Thus, an appropriate mesh size in the model simulation can provide accurate simulation
results, with higher computation efficiency. The space discretization errors could be reduced to a quarter
when mesh size is halved, while the computation time will increase by almost 16 times [
ℎ ≤
6 √ , (1) magnetrons; 3 seeds subjected to drying
The model applied in the microwave-heat transfer coupled simulation was based on the following hypotheses: the geometry and volume of the seeds do not change during the simulation; the initial temperature distribution is uniform in the seed; the thermal and dielectric properties of the maize seeds are temperature dependent; density was considered at the seed (particle) level and does not vary over time; uniform heat transfer through conduction between seeds; negligible heat transfer between the walls of the dryer and the air inside the dryer.
The whole simulation combines two physical processes: the microwave propagation process and the heat transfer in solid.
The electromagnetic waves generated inside the dryer cavity are reflected multiple times by the metal walls of the dryer, forming models of stationary electromagnetic field in the dryer.
The electric field intensity ⃗ , a vector quantity, at any point in the calculation range in the dryer was calculated from
Maxwell's equations [23]. The combined waveform of Maxwell's equations is expressed by the equation: where μr is the relative permeability, ω is the angular frequency, ε0 is the permittivity of vacuum, µ0 is the permeability of vacuum, εr is the relative permittivity, σ is the electrical conductivity.
Then, the electromagnetic power loss Qe of the processing materials can be obtained from the computed electric field by the following equation [24, 25]: 1 2 = 0 ′ 1 2 | ⃗ |2 = 0 ,,| ⃗ |2, where ε0 is the permittivity of vacuum, ε’ is the real part of the relative permittivity, ε’’ is the imaginary part of the relative permittivity of the processing seeds, tan δ is the loss tangent of the processing materials.
For the heat transfer process, only the processed materials were taken into account in order to reduce the computation cost. The governing equation for heat transfer in solid is given as [26, 27, 28]: where ρ is the material density, Cp is the material heat capacity under atmospheric pressure, T is the temperature, Q is the heat source and k is the thermal conductivity.
To complete the simulation, property parameters and boundary conditions were needed. The input parameters are shown in Table 2. The thermal and dielectric properties of the maize seeds are obtained from related literature [29, 30, 31, 32].
2 − ∇ = = , air wall maize seed
Parameter relative permeability μr relative permittivity εr electrical conductivity σ (S/m)
density ρ (kg/m3) thermal conductivity k (W/mK) heat capacity Cp (J/kgK) relative permeability μr relative permittivity εr electrical conductivity σ (S/m) relative permeability μr relative permittivity εr electrical conductivity σ (S/m)
density ρ (kg/m3) thermal conductivity k (W/mK) heat capacity Cp (J/kgK)
Value 1 1 0 1 1 1 0 1.205 2.524 x10-2
1005 (4) (5) (6) (7)
The complex relative permittivity is defined as the processing materials to give a near-actual model, which is expressed as [33]: = ′ − ′′ = ′(1 − ), Other surfaces are all defined as a perfect electric conductor, which can be expressed as the equation: ⃗ × ⃗ = 0, − ⃗ ∙ = 0, where ⃗ is the unit normal vector of the corresponding surface.
The dryer wall material was defined as the thermal insulation boundary condition. The governing equation is given as: where is the heat flux.
In the simulation, the electromagnetic field distribution was first calculated in the frequency domain, and then the dissipated power was calculated. Finally, the temperature rise of the material was updated based on the heat transfer equation in the time domain. Since the electrical properties of seeds do not vary with temperature, the electromagnetic field distribution will not change and is calculated only once. The simulation time for the proposed model, for a period of 20 seconds, was about 6 hours with a workstation with two processors and a 128 Gb RAM memory.
The simulation results show the temperature distribution in the seed layer at the bottom of the dryer, and the distribution of the electric field in the dryer. In the hybrid dryer the seeds have reached a temperature of 30°C due to the warm air that transports them pneumatically. As a result of the action of the electromagnetic field, the temperature of the seeds increased progressively in volume, reaching a maximum temperature of 44°C during the simulation of the first 12 s of the process.
According to the experiments performed on this dryer, at a feed rate with maize seeds of 500 kg/h, and a warm air velocity of 20-25 m/s, the maximum stagnation time of the seeds in the dryer was 20 s. The seeds were discharged from the dryer periodically, every 3-4 seconds, and their temperature reached a maximum of 44°C. The simulation shows a maximum temperature in the seed layer of 44 °C after a period of 9 s and 12 s respectively (Figure 4).
Due to the small size of the maize seeds compared to the size of the layer formed at the base of the dryer, virtually all seeds will heat up evenly from inside to outside, depending on the location of the remaining moisture in the grain. The lighter dried maize seeds, which do not settle to the base of the dryer, are transported to the top of the layer of the warm air at an average temperature of 44 °C. The eddy currents formed in the dryer during the pneumatic transport of the maize seeds resulted in a spiral trajectory in the first half of the dryer, with a tendency to deposit in the second half of it. The spiral movement of the seeds in the first half of the dryer made them benefit from the electromagnetic waves that have maximum power in the areas near the walls of the dryer, according to the distribution of the electric field in Figure 5.
In this paper, a model was built that combines electromagnetic phenomena with heat transfer for drying cereal seeds, and a study was performed regarding the independence of the discretization grid in the field of computing for a good accuracy of the results. By simulating in the COMSOL Multiphysics software, results were obtained for the distribution of the temperature field in the maize seed layer at the base of the dryer and of the distribution of the electric field in the hybrid dryer. The results indicated that under the action of the electric field in the dryer, the maximum temperature in the seed layer was 44 °C after a period of 9-12 seconds. By losing moisture, the seeds become lighter, being transported around the top of the seed layer, and discharged from the dryer every 3-4 seconds when the feed rate of maize seed is 500 kg/h. The spiral movement of the seeds in the first half of the dryer in the regions with maximum power distribution of the electric field lead to an uniform temperature in the seed volume, thus achieving a uniform drying.
This work was supported by a grant of the Romanian Ministry of Education and Research, project number CNCS/CCCDI-UEFISCDI, project number PN-III-P2-2.1-PED-2019-3001, within PNCDI III, contract no. 378PED/2020. Thanks for all your support. 6. References [23] J. Wang, T Hong, T Xie, F. Yang, Y. Hu, H. Zhu, Impact of filled materials on the heating uniformity and safety of microwave heating solid stack materials, Processes, 6-220 (2018) 1-13. doi:10.3390/pr6110220. [24] S. A. Goldblith, D. I. Wang, Effect of microwaves on Escherichia coli and Bacillus subtilis. Appl.
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