Drying kinetics and heat mass transfer characteristics of thin layer pineapple during microwave vacuum drying

Abstract

Microwave vacuum drying of pineapple slices was carried out to investigate the microwave power degree on the drying kinetics and heat mass transfer characteristics. Numerical simulation and bench test were used to study the variation characteristic of microwave volumetric heating and temperature and moisture during the drying process, and the best drying model was selected. The result shows that the drying process of the pineapple slices belonged to the falling rate period without constant drying stage; Among 6 common thin layer drying kinetic models, the mean values of $R^{2}$ were maximum, $\chi^{2}$ and RMSE for the Two-term exponential model were minimum, which were 0.9993, 0.000107 and 0.00839, respectively. As the temperature rose to 40 $\sim$ 45 ${{}^{\circ}}$ C at the late stage of drying, the thermal runaway phenomenon appeared, and the internal temperature of pineapple slices rose sharply. Hot spots appeared at the center and edge of pineapple at the late stage of drying, and it generated by microwave volumetric heating focusing. The predicted values of moisture ratio (MR) obtained from COMSOL simulation showed good consistency with the Two-term exponential model and the experimental. In order to improve the drying quality of the pineapple, the microwave power should be varied and reasonable interval to make the drying temperature lower than the thermal runaway temperature range.

Keywords

Pineapple microwave vacuum drying numerical simulation heat and mass transfer

1. Introduction

Pineapple is a monocotyledonous crop belonging to the pineapple family that grows in tropical and subtropical regions [1]. It is rich in vitamin C, minerals, antioxidants, and other nutrients required by the human body to effectively prevent the development of diseases such as heart disease and cancer [2, 3]. Due to its high water content and susceptibility to decay and deterioration at room temperature, research on deep processing of pineapple to increase its shelf life is essential. The new generation of microwave vacuum drying technology stands out among other drying methods due to its speed, high quality, and low energy consumption. Microwave to volume heating of the material’s internal moisture quickly evaporated to form a large pressure difference, moisture and steam under the action of the pressure difference quickly migrate to the material’s surface, forming a pore with the effect of extrusion puffing moisture walking, thus quickly removing the moisture [4, 5]. In a vacuum environment, the boiling point temperature of water was significantly reduced, thereby preventing the oxidation reaction of pineapple and preserving its nutrients to the greatest extent. Material’s quality and efficiency were better by microwave vacuum drying than that by hot air or microwave drying, while energy consumption was lower than for hot air and freeze drying [6, 7, 8].

Pineapple’s high sugar content causes uneven microwave distribution in the late stages of microwave vacuum drying, which manifests itself as “thermal runaway” scorching points at the middle and the edge of the pineapple slice. As moisture content is reduced, the steady-state temperature, under the influence of microwaves, will abruptly change to a non-stationary thermal phenomenon, such as a prominent point on the surface of the pineapple, or an elongated point on the surface of the pineapple. Instantaneously, the temperature of a prominent point or the edge of the pineapple’s surface skyrockets [9]. A temperature sensor was used to measure the surface temperature of pineapple slices during the drying process, but this method has the disadvantage of measuring only a point, and distribution information of the entire temperature field, as well as the location of hot spots, cannot be obtained. By using the pineapple’s thermal physical properties (density, specific heat, dielectric properties, thermal conductivity, etc.) and heat transfer, the COMSOL Multiphysics simulation software was used to develop a coupled model to simulate microwave energy absorption and temperature distribution during microwave vacuum drying. A visual representation was provided of the uneven temperature distribution and “hot spot area”.

Researchers both domestically and internationally were currently employing numerical simulation techniques to examine the heat and mass transfer in the drying of agricultural products. In order to obtain the temperature field distribution of blackberries, avoid the location of cold spots in the heating region, establish reasonable drying parameters, and reduce inhomogeneity of temperature distribution in hot spots, Song et al. [10] carried out a numerical study on the heat transfer characteristics of microwave vacuum drying of blackberries. According to Zhang et al. [11], they used numerical simulation and bench experiments to determine the temperature range of “thermal runaway” for mushroom microwave drying, and proposed a segmented variable power drying scheme based on the hot spot phenomenon in the mushroom center. In the simulation above, mass transfer variation was not taken into account. Cheng et al. [12] developed a numerical model to simulate heat and mass transfer and deformation during the microwave drying process of minced Antarctic krill. The simulated values of the spatial temperature distribution, transient temperature profile, moisture content, and volume ratio were in good agreement with those of the experiments. Shen et al. [13] used COMSOL software to numerically simulate the brown rice under continuous microwave dying. The simulated values were in good agreement with the experimental result. The researchers conducted numerical calculations of heat and mass transfer for mashed potatoes [14], sprouted brown rice [13] and other fruits and vegetables in order to analyze the behavior of temperature, humidity, and quality, resulting in a more effective drying process.

This study investigated the kinetic characteristics of pineapple thin layer drying under different microwave power to establish a mathematical model and to select the suitable model; COMSOL software is used to simulate and analyze the transient electric field, temperature field, and moisture distribution characteristics of pineapple slices; as well as the temperature change law under different microwave power is analyzed. The critical temperature range of the scorch point was determined in order to obtain high-quality products, and a suitable drying parameter was adopted on the basis of the microwave energy absorption law.

2. Materials and methods

2.1 Samples

Pineapples with a peeled diameter of approximately 95 mm and consistent ripeness, a coring diameter of 34 mm, and an initial wet basis moisture content of 85 percent were purchased from local supermarkets. The moisture content was determined by 105 ${{}^{\circ}}$ C oven method.

2.2 Instrumentation

Microwave vacuum drying and sterilizing oven, model WZD6 by Nanjing Sanle Microwave Technology Development Co., Ltd.; Mettler Toledo XS-205DU electronic balance; slicer.

2.3 Methodology

Using a slicer, thinly slice the pineapple to a thickness of 5 mm. Takeing the pineapple diameter consistent part weighing 300 g uniformly to lay flat in the 6 rotating hanging baskets in the microwave vacuum oven.The microwave power was set as 300, 400, 500, 600, 700, 800 W for drying test, respectively. And the relative vacuum degree is $-$ 87 kPa. The MR variations was calculated at 10-minute intervals in the first test. The first test is obtained by stopping the machine to collect samples and weigh them, followed by two repetitions of the test by continuous drying until the moisture content (wet basis) falls below 15%. A temperature collector is arranged on the top of the microwave vacuum drying oven to collect the pineapple surface temperature. Each test group is repeated three times to determine the mean value. MR was calculated as according to Eq. (1).

$\displaystyle\textit{MR}=\frac{M}{M_{0}}$ (1)

Where MR is moisture ratio; $M$ is the moisture content (dry basis) at any time $t$ ; $M_{o}$ is the initial moisture content (dry basis).

The moisture content (dry basis) was calculated as according to Eq. (2).

$\displaystyle M_{0}=\frac{W_{0}-W_{K}}{W_{K}}$ (2)

Where $M_{0}$ is the initial moisture content (dry basis); $W_{0}$ is the initial mass/kg; $W_{K}$ is the dry matter mass/kg.

2.4 Mathematical model

The moisture ratio versus drying time curves for the pineapple drying process were fitted with six widely used mathematical models for thin-layer drying, as shown in Table 1. Using Origin2018 software, a non-linear regression analysis was performed to determine each drying constant in the model. Using the smallest chi-square value $\chi^{2}$ , root mean square error RMSE, and the largest coefficient of determination $R^{2}$ [21, 22], the model’s goodness of fit (goodness) was determined. Equations (3)–(5) depict the statistical equations for the goodness-of-fit [20, 23, 24, 25].

$\displaystyle R^{2}=1-\frac{\sum\nolimits_{i=1}^{N}{\left({\textit{MR}_{% \textit{pre,i}}-\textit{MR}_{\exp,i}}\right)}^{2}}{\sum\nolimits_{i=1}^{N}{% \left({\overline{\textit{MR}_{\textit{pre,i}}}-\textit{MR}_{\exp,i}}\right)}^{% 2}}$ (3)

$\displaystyle\chi^{2}=\frac{\sum\nolimits_{i=1}^{N}{\left({\textit{MR}_{% \textit{pre,i}}-\textit{MR}_{\exp,i}}\right)}^{2}}{N-n}$ (4)

$\displaystyle\textit{RMSE}=\sqrt{\frac{\sum\nolimits_{i=1}^{N}{\left({\textit{% MR}_{\textit{pre,i}}-\textit{MR}_{\exp,i}}\right)}^{2}}{N}}$ (5)

Where $\textit{MR}_{\textit{pre},i}$ represents the i-th predicted moisture ratio of the drying test; $\textit{MR}_{\exp,i}$ represents the i-th test moisture ratio of the drying test; $N$ represents the number of test measurements; and $n$ represents the model constant.

Table 1

Six commonly fitted mathematical models

Model name	Model expressions	References
Lewis	$\textit{MR}=\exp(-kt)$	[15]
Page	$\textit{MR}=\exp(-kt^{n})$	[16]
Henderson and Pabis	$\textit{MR}=\text{aexp}(-kt)$	[17]
Logarithmic	$\textit{MR}=\text{aexp}(-kt)+c$	[18]
Two-term exponential	$\textit{MR}=\text{aexp}(-kt)+(1-a)\exp(-kat)$	[19]
Wang and Singh	$\textit{MR}=1+at+bt^{2}$	[20]

2.5 Numerical simulation of microwave vacuum drying of pineapple

In this study, a simulation of the electric field intensity distribution, microwave energy absorption, temperature field, and moisture distribution characteristics inside the pineapple slices were carried out using COMSOL Multiphysics 5.5 at microwave powers of 400, 600, and 800 W and relative vacuum degree of $-$ 87 kPa.

2.5.1 Modeling

A coupled microwave heating and solid heat transfer model was constructed, and the cavity was linked to a 2.45 GHz microwave source via a TE10 mode rectangular waveguide. According to the geometry of the actual microwave vacuum drying equipment, the simulation’s geometric model is constructed as depicted in Fig. 1. The inner wall of the chamber and the waveguide were composed of copper, and the pineapple was uniformly laid flat in six rotating hanging baskets. The pineapple has the following thermophysical property parameters [26]: relative magnetic permeability $\mu_{r}=$ 1, electrical conductivity $=$ 0, thermal conductivity $k=$ 0.567 W/(m $\cdot$ K), density $\rho=$ 983 kg/m ${}^{3}$ specific heat capacity $C_{P}=$ 3.8 kJ/(kg $\cdot$ ${}^{\circ}$ C), latent heat of vaporization 28475 kJ/kg, thermal diffusion coefficient 1.52 $\times$ 107 m ${}^{2}$ /s.

Index of dielectric properties: the dielectric constant and dielectric loss factor for pineapple as a function of temperature and moisture content (wet basis), calculated using Eqs (6) and (7) [27].

$\displaystyle\varepsilon^{\prime}=56.5+0.0846T-0.00201T^{2}+7.36U-0.156\textit% {UT}+0.00174\textit{UT}^{2}-0.827U^{2}+0.0171U^{2}T-0.000191$ (6)

$\displaystyle\varepsilon{{}^{\prime\prime}}=(0.26-0.048U+0.0062U^{2})(83.4-0.6% 11T+0.00379T^{2})$ (7)

Where: $U$ is the moisture content; $T$ is the temperature/ ${}^{\circ}$ C.

Figure 1.

Geometric model of microwave vacuum oven and food product.

The grid size division is crucial to the simulation results. Different grid sizes for different domains can improve the calculation speed. The relationship between grid size and free wavelength ( $\lambda=$ 12.24 cm) and dielectric constant is calculated as shown in Eq. (8) [28].

$\displaystyle h=\frac{\lambda}{6\sqrt{\varepsilon^{\prime}}}h=\frac{\lambda}{6% \sqrt{\varepsilon^{\prime}}}$ (8)

In this study, a (tetrahedral) grid is used; the maximum and minimum sizes of the furnace gas grid were 24.47 mm and 0.7342 mm, the maximum and minimum sizes of the tray grid were 14.13 mm and 0.4239 mm, and the maximum and minimum sizes of the pineapple grid were 4.9 mm and 0.1468 mm, respectively. With the discrete time step method, the microwave vacuum heating process during rotation of the material with the basket was calculated. The microwave vacuum heating process was calculated using the discrete time step method [29], and there are 1399450 cells in the entire solution domain. The grid division results were shown in Fig. 2.

Figure 2.

Mesh of the microwave vacuum oven.

2.5.2 Model assumptions

Considering the computational efficiency of the simulation and the reliability of the numerical results, the actual drying process is modeled using appropriate assumptions and simplifications. 1) Considering pineapple slices to be homogeneous and homogeneous materials with uniform initial temperatures and moisture distributions. 2) Disregarding porous media material and multiphase transfer in order to reduce the uncertainty associated with simulation and computation. 3) Only consider the evaporation of liquid moisture, without considering changes in moisture phase. 4) Do not consider the phenomenon of volume contraction of the material. 5) The wall of the drying chamber is assumed to be adiabatic, and heat loss was not considered.

2.5.3 Control equations

Electromagnetic equation

To model the coupling between electromagnetic and heat transfer, Maxwell’s electromagnetic equations in the frequency domain are applied to the electromagnetic distribution inside the pineapple slice.

$\displaystyle\nabla\times\mu_{r}^{-1}\left({\nabla\times E}\right)-k_{0}^{2}% \left({\varepsilon_{r}-\frac{j\sigma}{\omega\varepsilon_{0}}}\right)E=0$ (9) $\displaystyle k_{0}=\omega\sqrt{\varepsilon_{0}\mu_{0}}k_{0}=\omega\sqrt{% \varepsilon_{0}\mu_{0}}$ (10) $\displaystyle\varepsilon_{r}=\left(\varepsilon^{\prime}-j{\varepsilon}^{\prime% \prime}\right)/\varepsilon_{0}$ (11)

Where $\mu_{r}$ is the relative magnetic permeability; $E$ is the electric field intensity/(V/m); $k_{0}$ is the free-space wave number; $\varepsilon_{r}$ is the relative permittivity; $\sigma$ is the conductivity/(S/m); $\varepsilon_{0}$ is the dielectric constant in vacuum; 8.854 $\times$ 10 ${}^{-12}$ /(F/m); $\mu_{0}$ is the permeability in vacuum; 1.257 $\times$ 10 ${}^{-6}$ /(NA ${}^{-2}$ ) is the dielectric constant; $\varepsilon^{\prime}$ is the dielectric constant; $\varepsilon^{\prime\prime}$ is the dielectric loss factor; $\omega$ is the angular frequency, rad/s.

Volumetric heat is generated by pineapple internal absorption of microwave energy during the microwave drying process as shown in Eq. (12) [30]:

$\displaystyle Q=2\pi f\varepsilon_{0}\varepsilon{{}^{\prime\prime}}E^{2}$ (12)

Where the frequency of $f$ Microwave is 2.45 GHz.

All walls of the dry cavity and waveguide, with the exception of the waveguide feed through, are considered perfect electrical conductors, and the boundary condition is expressed as follows:

$\displaystyle n\times E=0$ (13)

Both the interior wall of the drying oven and the outer wall of the waveguide are made of copper. The impedance boundary condition is expressed as follows:

$\displaystyle\sqrt{\frac{\mu_{0}\mu_{r}}{\varepsilon_{0}\varepsilon_{r}-{j% \sigma}/\omega}}n\times H+E-\left({n\cdot E}\right)n=\left({n\cdot E_{S}}% \right)n-E_{S}$ (14)

Where: $H$ is the magnetic field intensity, A/m; $n$ is the unit direction vector; Es is the electric field source.

Mass transfer equation

The following equation is used to calculate pineapple internal moisture concentration during drying.

$\displaystyle\frac{\partial c}{\partial t}=\nabla\left({D_{m}\nabla c}\right)-% I\frac{\partial c}{\partial t}=\nabla\left({D_{m}\nabla c}\right)-I$ (15)

Where: $c$ is the concentration of moisture within the material, mol/m ${}^{3}$ ; $D_{m}$ is the moisture diffusion coefficient, m ${}^{2}$ /s; $I$ is the evaporation rate of moisture. They are calculated using Eqs (16) and (17) [31]

$\displaystyle I=K_{\textit{vap}}\rho_{L}\left({p^{\ast}-p_{G}}\right)/p_{G}I=K% _{\textit{vap}}\rho_{L}\left({p^{\ast}-p_{G}}\right)/p_{G}$ (16) $\displaystyle p^{\ast}=10^{A-B/\left({C+T}\right)}p^{\ast}=10^{A-B/\left({C+T}% \right)}$ (17)

Where: $K_{\textit{vap}}$ is the evaporation rate constant 1/s. $\rho_{L}$ is the density of water, kg/m ${}^{3}$ ; $p_{G}$ is the vacuum pressure, Pa; A, B, C are constants.

Equation (18) shows the relationship between moisture concentration c and its wet basis moisture content.

$\displaystyle M_{\textit{wb}}=c\frac{M_{\text{H}_{2}\text{O}}}{\rho}M_{\textit% {wb}}=c\frac{M_{\text{H}_{2}\text{O}}}{\rho}$ (18)

Where: $M_{\textit{wb}}$ is the moisture content (wet basis) of the material; $M_{\text{H}_{2}\text{O}}$ is the molar mass of steam, kg/mol.

Heat transfer equation

A Fourier equation is used to determine the internal heat transfer equation of pineapple using the principle of conservation of energy [31]:

$\displaystyle\rho_{m}C_{p}\frac{\partial T}{\partial t}=\nabla\left({K_{m}% \nabla T}\right)+Q-\textit{IH}$ (19)

Where: $\rho_{m}$ is the density of the pineapple, kg/m ${}^{3}$ ; $C_{p}$ is the specific heat capacity of the material, kJ/(kg $\cdot$ K); T is the temperature $K$ ; $K_{m}$ is the thermal conductivity of the material, W/(m $\cdot$ K); Q is the microwave volume heat, W/m ${}^{3}$ ; $H$ is the latent heat of vaporization, J/mol.

Figure 3.

Drying characteristics at different microwave power.

In Eq. (20), the material surface is defined as the convective heat flux.

$\displaystyle n\cdot\left({-k\nabla T}\right)=h_{T}\left({T_{a}-T}\right)$ (20)

3. Results and analysis

3.1 Drying characteristics of pineapple slices under different microwave power

Pineapple initial moisture content was 85%, the fixed slice thickness was 5 mm, the relative vacuum degree is $-$ 87 kPa, and the pineapple mass is 300 g. To conduct the drying test, set the microwave power to 300, 400, 500, 600, 700, and 800 W and stop the test when the moisture content on the wet basis was less than 15%. Figure 3 illustrates the drying kinetic curve. In general, a higher microwave power resulted in a steeper moisture ratio curve and a shorter drying time. The drying time was reduced by 8%, 17%, 25% and 33% when compared with microwave power 400 W, 500 W, 600 W, 700 W, 800 W. A study indicates that as the power density increases, the kinetic energy of water molecules within the pineapple increases, resulting in a larger vapor pressure gradient inside and outside of the pineapple; the rapid diffusion of water to the surface forms a walking pore channel, allowing water to be discharged rapidly; and the boiling point of water was significantly lower under vacuum, allowing pineapples to be dried rapidly at lower temperatures. Since the slices were thin, the microwave penetrates the entire area, reducing the drying time as compared to traditional methods [32, 33]. After a short period of speeding up, the drying rate changes immediately to a speed-down phase. As the microwave power was small, there is no constant speed section, therefore the drying process was controlled by the speed-down phase, indicating that moisture diffusion predominates over internal moisture migration. Following the deceleration period, partly due to a reduction in the material moisture content, the drying rate decreases, and the “thermal runaway” point appears. As a result of absorbing microwave energy, a certain amount of heat was accumulated within the material, but there was insufficient water in the pineapple to produce latent heat of evaporation; thus, the dielectric loss factor increases, resulting in a raised edge or middle of the material as a consequence. Therefore, the temperature rises rapidly and the "thermal runaway" phenomenon occurs.

Table 2
Fitting parameters for different microwave power drying models

Model name	Microwave power/W	Parameters	$R^{2}$	RMSE	$\chi^{2}$
Lewis	400	$k=$ 5.064E-02	0.9825	4.591E-02	2.46E-03
	500	$k=$ 5.362E-02	0.9898	3.439E-02	1.38E-03
	600	$k=$ 6.028E-02	0.9895	3.583E-02	1.54E-03
	700	$k=$ 7.199E-02	0.9957	2.282E-02	6.25E-04
	800	$k=$ 7.708E-02	0.9959	2.270E-02	6.44E-04
Page	400	$k=$ 1.575E-02, $n=$ 1.36961	0.9992	9.21E-03	1.19E-04
	500	$k=$ 2.341E-02, $n=$ 1.2659	0.9988	1.060E-02	1.57E-04
	600	$k=$ 2.544E-02, $n=$ 1.27771	0.9965	1.191E-02	2.12E-04
	700	$k=$ 4.112E-02, $n=$ 1.19457	0.9993	8.03E-03	9.66E-05
	800	$k=$ 4.493E-02, $n=$ 1.19289	0.9992	8.75E-03	1.27E-04
Henderson	400	$k=$ 5.223E-02, $a=$ 1.03699	0.9813	4.332E-02	2.64E-03
and Pabis	500	$k=$ 5.491E-02, $a=$ 1.02782	0.9890	3.249E-02	1.48E-03
	600	$k=$ 6.148E-02, $a=$ 1.0235	0.9879	3.437E-02	1.77E-03
	700	$k=$ 7.27E-02, $a=$ 1.01226	0.9949	2.223E-02	7.41E-04
	800	$k=$ 7.769E-02, $a=$ 1.0097	0.9949	2.223E-02	2.26E-04
Logarithmic	400	$a=$ 1.12444, $k=$ 4.154E-02, $c=$ $-$ 1.0287E-01	0.9884	3.049E-02	1.63E-03
	500	$a=$ 1.08164, $k=$ 4.696E-02, $c=$ $-$ 6.473E-02	0.9917	2.535E-02	1.12E-03
	600	$a=$ 1.08037, $k=$ 5.274 E-02, $c=$ $-$ 6.568 E-02	0.9895	2.766E-02	1.53E-03
	700	$a=$ 1.04184, $k=$ 9.55 E-03, $c=$ $-$ 4.455 E-02	0.9956	2.077E-02	6.59E-04
	800	$a=$ 1.04949, $k=$ 6.963E-02, $c=$ $-$ 7.2166E-01	0.9971	1.686E-02	7.11E-04
Two-term	400	$a=$ 1.94401, $k=$ 7.578E-02	0.9989	1.061E-02	1.57E-04
exponential	500	$a=$ 1.85818, $k=$ 7.69E-02	0.9993	7.99E-03	8.95E-05
	600	$a=$ 1.89565, $k=$ 8.825E-02	0.9992	8.62E-03	1.12E-04
	700	$a=$ 1.75801, $k=$ 9.721E-02	0.9995	6.85E-03	7.03E-05
	800	$a=$ 1.7554, $k=$ 1.0412E-01	0.9994	7.88E-03	1.04E-04
Wang and	400	$a=$ -3.688E-02, $b=$ 3.45494E-04	0.9968	1.783E-02	4.45E-04
singh	500	$a=$ -3.966E-02, $b=$ 4.07409E-04	0.9961	1.940E-02	5.27E-04
	600	$a=$ -4.433E-02, $b=$ 5.05919E-04	0.9952	2.160E-02	6.99E-04
	700	a = -5.18E-02, b = 6.85214E-04	0.9958	2.0137E-02	6.08E-04
	800	$a=$ -5.584E-02, $b=$ 8.0068E-04	0.9944	2.3329E-02	9.07E-04

Figure 4.

Plots of COMSOL model MR with experimental and Two-Term modle.

Figure 5.

Temperature characteristics of COMSOL model and experimental at different microwave power.

Figure 6.

Temperature distribution during microwave vacuum drying of pineapple.

Figure 7.

Microwave volumetric heating of pineapple.

3.2 Fitting mathematical model analysis

Table 2 displays the nonlinear curve fitting results for each thin-layer model. The data analysis reveals that the two-term model has the highest $R^{2}$ mean value of 0.9993, the smallest $\chi^{2}$ mean value of 0.000107, and the RMSE mean value of 0.00839, indicating that the model can accurately describe the moisture change law of the drying process of pineapple slices and had a high prediction accuracy for the actual production.

3.3 Analysis of simulation results for moisture ratio

Under test conditions of microwave power 400, 600, and 800 W, COMSOL Multiphysics field simulation calculations were performed. Based on the RMSE, the moisture ratio under the three microwave powers was 0.08, 0.07, and 0.06, respectively, and the data consistency was good, indicating that the simulation model was correctly established. Figure 4 illustrates the relationship between test moisture ratios, thin layer drying models, and numerical calculations. It can be seen that the COMSOL simulation value for the moisture ratio was slightly lower than the test and simulation values for the first half of the drying period. Due to the fact that the relative vacuum degree was fixed at $-$ 87 kPa during simulation, but fluctuates between $-$ 82 and $-$ 93 kPa during testing, the simulation value was a bit lower than the test value.

3.4 Temperature distribution characteristics analysis

Figure 5 depicted the simulated and experimental temperature curves for each microwave power. The trend of change for the simulated and experimental values was the same, and the fit is good, indicating the correctness of the simulation equation establishment; therefore, the temperature change of the pineapple drying process can be predicted and analyzed. As depicted in Fig. 5, the temperature rises rapidly during the initial phase of drying, before entering a steady-state rising phase that culminates in a sharp rise in temperature. With an increase in microwave power, the drying time was decreased and the temperature during the middle and late stages of drying increased significantly. The testing procedure revealed that when the surface temperature of pineapple exceeded 40 degrees Celsius, a phenomenon resembling burning began to manifest, and that the drying temperature range between 40 ${{}^{\circ}}$ C and 45 ${{}^{\circ}}$ C represents a “thermal runaway”. From Eq. (12) it can be seen that the microwave frequency and electric field intensity determine the pineapple’s internal volume heat and dielectric loss factor, and that as the drying temperature rises, dielectric loss factor increases and volume heat accumulation intensifies. As the moisture content (wet basis) decreases and the latent heat of evaporation, boundary heat convection, and other heat producing processes decrease, the microwave-generated volumetric heat cannot be consumed, resulting in an increase in the material’s internal temperature, a phenomenon known as “thermal runaway”. It was difficult to determine the temperature and volume of heat distribution within a pineapple during the drying process. By using COMSOL numerical calculation method to determine microwave power of 400 W, 600 W, and 800 W, temperature and volume heat distribution can be determined as shown in Figs 6 and 7. The distribution of thermal runaway points can be observed in the center and a portion of the edge area, as well as the distribution of high and low temperatures. It was clear that the distribution of high temperature points in microwaves corresponds with the pattern of volumetric heat distribution, and the phenomenon of uneven volumetric heat distribution was of particular significance. During the drying process, the temperature should not exceed the “thermal runaway” range; best results can be achieved by suspending the microwave during the slow-down process or simply reducing the microwave intensity.

4. Conclusion

According to a non-linear fitted regression analysis of the microwave vacuum drying process of pineapple slices using six commonly used thin layer drying models, the two-term exponential drying model has the largest mean $R^{2}$ , the smallest mean $\chi^{2}$ , and the lowest RMSE. Therefore, this model was considered to be the best microwave vacuum drying kinetic model for pineapples.

With COMSOL multi-physics field coupling software, the moisture ratio variation law was simulated for each microwave power. When the moisture ratio is compared with the experimental value and the two-term exponential model, it is clear that they are consistent, indicating that the model was able to accurately predict the drying process.

The phenomenon of “thermal runaway” occurs at the surface temperature of pineapple in the range of 40 $\sim$ 45 ${}^{\circ}$ C within the later phase of drying, which has a detrimental effect on quality and burnt flavor. The internal volumetric heat distribution of the pineapple was uneven, and hot spots with excessively high volumetric thermal focus temperatures can be observed in some parts of the center and edge of the fruit. Drying products with moderately variable microwave power and slowing time can solve the problem of “thermal runaway” caused by uneven microwave distribution, save energy, and improve the quality of the final product.

Footnotes

Funding information

Yulin Scientific Research and Technology Development Program, Grant/Award Number: 20204035; Yulin Scientific Research and Technology Development Program, Grant/Award Number: 20220520; Research Starting Package for High-level Talents of Yulin Normal University, Grant/Award Number: G2022ZK14; Guangxi Science and Technology Planning Project, Grant/Award Number: AD22080002.

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Drying kinetics and heat mass transfer characteristics of thin layer pineapple during microwave vacuum drying

Abstract

Keywords

1. Introduction

2. Materials and methods

2.1 Samples

2.2 Instrumentation

2.3 Methodology

2.5.1 Modeling

2.5.3 Control equations

3.1 Drying characteristics of pineapple slices under different microwave power

Table 2 Fitting parameters for different microwave power drying models

3.3 Analysis of simulation results for moisture ratio

3.4 Temperature distribution characteristics analysis

4. Conclusion

Footnotes

Funding information

References

Table 2
Fitting parameters for different microwave power drying models