A spectral method for numerical modeling of radial microwave heating in cylindrical samples with temperature dependent dielectric properties

Navarro, M. C.; Burgos, J.

doi:10.1016/j.apm.2016.10.062

Cited by 18 publications

(11 citation statements)

References 20 publications

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“…Validation. The results based on current numerical simulation have been validated with the experimental data(Navarro and Burgos, 2017) and earlier simulation resultsNavarro and Burgos, 2017) for cylindrical sample (circular cross section) in the presence of radial irradiation as demonstrated in Figures3(a)-3(b). Earlier work…”

supporting

confidence: 65%

“…It may be noted that the intensity of the static source can be obtained from the wattage of microwave emitting source, volume of the microwave system and frequency of microwave radiation. As mentioned earlier, the azimuthally symmetric irradiation of the static sample with I R 0 ¼ (Navarro and Burgos, 2017) considered a few lossy samples (agar gel and mashed potato). The thermal and dielectric data of lossy materials (agar gel and mashed potato) were also reported in the earlier work (Navarro and Burgos, 2017).…”

Section: Finite Element (Gfem) Simulationsmentioning

confidence: 99%

“…As mentioned earlier, the azimuthally symmetric irradiation of the static sample with I R 0 ¼ (Navarro and Burgos, 2017) considered a few lossy samples (agar gel and mashed potato). The thermal and dielectric data of lossy materials (agar gel and mashed potato) were also reported in the earlier work (Navarro and Burgos, 2017). Although the temperature-dependent dielectric properties for mashed potato were reported by Navarro and Burgos (2017), the variation of properties with temperature may be negligible and average dielectric properties even validate reasonably well current and earlier (Navarro and Burgos, 2017) numerical predictions as shown in Figure 3(b).…”

Section: Finite Element (Gfem) Simulationsmentioning

confidence: 99%

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Finite element (GFEM) simulations on the effect of microwave heating for lossy dielectric samples with various shapes (circle, square and triangle)

Basak

2020

HFF

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Purpose This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of temperature and larger penetration of heating within samples vs shapes of samples (circle, square and triangular). Design/methodology/approach Galerkin finite element method (GFEM) with adaptive meshing in a composite domain (free space and sample) is used in an in-house computer code. The finite element meshing is done in a composite domain involving triangle embedded within a semicircular hypothetical domain. The comparison of heating pattern is done for various shapes of samples involving identical cross-sectional area. Test cases reveal that triangular samples can induce larger penetration of heat and multiple heating fronts. A representative material (beef) with high dielectric loss corresponding to larger microwave power or heat absorption in contrast to low lossy samples is considered for the current study. The average power absorption within lossy samples has been computed using the spatial distribution and finite element basis sets. Four regimes have been selected based on various local maxima of the average power for detailed investigation. These regimes are selected based on thin, thick and intermediate limits of the sample size corresponding to the constant area of cross section, Ac involving circle or square or triangle. Findings The thin sample limit (Regime 1) corresponds to samples with spatially invariant power absorption, whereas power absorption attenuates from exposed to unexposed faces for thick samples (Regime 4). In Regimes 2 and 3, the average power absorption non-monotonically varies with sample size or area of cross section (Ac) and a few maxima of average power occur for fixed values of Ac involving various shapes. The spatial characteristics of power and temperature have been critically analyzed for all cross sections at each regime for lossy samples. Triangular samples are found to exhibit occurrence of multiple heating fronts for large samples (Regimes 3 and 4). Practical implications Length scales of samples of various shapes (circle, square and triangle) can be represented via Regimes 1-4. Regime 1 exhibits the identical heating rate for lateral and radial irradiations for any shapes of lossy samples. Regime 2 depicts that a larger heating rate with larger temperature non-uniformity can occur for square and triangular-Type 1 lossy sample during lateral irradiation. Regime 3 depicts that the penetration of heat at the core is larger for triangular samples compared to circle or square samples for lateral or radial irradiation. Regime 4 depicts that the penetration of heat is still larger for triangular samples compared to circular or square samples. Regimes 3 and 4 depict the occurrence of multiple heating fronts in triangular samples. In general, current analysis recommends the triangular samples which is also associated with larger values of temperature variation within samples. Originality/value GFEM with generalized mesh generation for all geometries has been implemented. The dielectric samples of any shape are surrounded by the circular shaped air medium. The unified mesh generation within the sample connected with circular air medium has been demonstrated. The algorithm also demonstrates the implementation of various complex boundary conditions in residuals. The numerical results compare the heating patterns for all geometries involving identical areas. The thermal characteristics are shown with a few generalized trends on enhanced heating or targeted heating. The circle or square or triangle (Type 1 or Type 2) can be selected based on specific heating objectives for length scales within various regimes.

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supporting

confidence: 65%

Section: Finite Element (Gfem) Simulationsmentioning

confidence: 99%

Section: Finite Element (Gfem) Simulationsmentioning

confidence: 99%

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Finite element (GFEM) simulations on the effect of microwave heating for lossy dielectric samples with various shapes (circle, square and triangle)

Basak

2020

HFF

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“…By heating limestone rocks to 882 °C, there is initially an increase in its volume. Once their surfaces are calcined, pore volume increases which allows releasing carbon dioxide (Navarro and Burgos, 2017). The input temperature of the reaction is 882 °C.…”

Section: Introductionmentioning

confidence: 99%

New process to obtain unslaked lime through microwave hybrid heating and its fluid dynamics computational modeling

Corrêa

Neto

França

et al. 2021

jCEC

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This study aimed to analyze the advantages of limestone calcination through a conventional microwave heating technique. For such a purpose, the microwave was merged by hybrid heating and a refractory ceramic internally coated with copper oxide was used with a conventional muffle furnace. It has also been analyzed the behavior of calcining limestone with different masses and variations in retention time using a muffle furnace and microwaves, both with and without using the refractory ceramic. Afterwards, the process has been modeled so as to analyze temperature versus retention time. As a result, calcination using a microwave susceptor with the refractory ceramic substance proved to be a process that takes 35% less time than conventional methods. Furthermore, there has been a reduction in 66.1% of energy expenditure. It was also observed that the new procedure offers advantages in reduced greenhouse gases emissions on account of the release of only a single substance, ease of air treatment in industrial environments and being a more economically viable process for limestone calcination, which can be further utilized by companies belonging to such a sector. Its patent deposit number BR 202018073002-4 U2 in INPI.

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“…A novel numerical method, i.e., spectral method [16], has recently been developed, which establishes the functional Hilbert spaces to overcome the infinite-dimensional characteristics of microwave heating model. By capturing the dominated dynamical characteristics, the PDE model can be transformed into a low-order one to improve the computational efficiency dramatically.…”

Section: Introductionmentioning

confidence: 99%

A Data-Driven Based Spatiotemporal Model Reduction for Microwave Heating Process with the Mixed Boundary Conditions

Zhong

Liang

2021

Processes

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In this paper, a data-driven based spatiotemporal model reduction approach is proposed for predicting the temperature distribution and developing the computation speeds in the microwave heating process. Due to the mixed boundary conditions, it is difficult for the traditional spectral method to directly obtain the analytical eigenfunctions. Motivated by the time/space separation theory, we first propose a general framework of spatiotemporal model reduction, which can effectively develop the computation speeds in the numerical analysis of multi-physical fields. Subsequently, the empirical eigenfunctions are generated by applying the Karhunen–Loève theory to decompose the snapshots. Then, the partial differential Equation (PDE) model is discretized into a class of recursive equations and transformed as the reduced-order ordinary differential Equation (ODE) model. Finally, the effectiveness and superiority of the proposed approach is demonstrated by a comparison study with a traditional method on the microwave heating Debye medium.

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A spectral method for numerical modeling of radial microwave heating in cylindrical samples with temperature dependent dielectric properties

Cited by 18 publications

References 20 publications

Finite element (GFEM) simulations on the effect of microwave heating for lossy dielectric samples with various shapes (circle, square and triangle)

Finite element (GFEM) simulations on the effect of microwave heating for lossy dielectric samples with various shapes (circle, square and triangle)

New process to obtain unslaked lime through microwave hybrid heating and its fluid dynamics computational modeling

A Data-Driven Based Spatiotemporal Model Reduction for Microwave Heating Process with the Mixed Boundary Conditions

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