Experimental and modeling investigation of mass transfer during combined infrared‐vacuum drying of Hayward kiwifruits

Abstract In this work, we tried to evaluate mass transfer during a combined infrared‐vacuum drying of kiwifruits. Infrared radiation power (200–300 W) and system pressure (5–15 kPa), as drying parameters, are evaluated on drying characteristics of kiwifruits. Both the infrared lamp power and vacuum pressure affected the drying time of kiwifruit slices. Nine different mathematical models were evaluated for moisture ratios using nonlinear regression analysis. The results of regression analysis indicated that the quadratic model is the best to describe the drying behavior with the lowest SE values and highest R value. Also, an increase in the power led to increase in the effective moisture diffusivity between 1.04 and 2.29 × 10−9 m2/s. A negative effect was observed on the ΔE with increasing in infrared power and with rising in infrared radiation power it was increased. Chroma values decreased during drying.

). The combined infrared-vacuum drying benefits both infrared heating and vacuum condition. Recently, infrared-vacuum drying was used to dry the wide range of food products with high quality. The high rate mass transfer and low temperature can improve the energy efficiency of process and product quality (Giri & Prasad, 2007).
In order to successful industrial design of combined infraredvacuum drying system, it is necessary to investigate the drying characteristics under various condition (McLoughlin, McMinn, & Magee, 2003).
Infrared-vacuum method can produce a high-quality product (Salehi, Kashaninejad, Asadi, & Najafi, 2016). There for, the aim of our study was to investigate the combined infrared-vacuum drying of kiwifruit slices with respect to moisture diffusivity, drying kinetics, and color changes.

| Infrared-vacuum drying
Kiwifruits (Actinidia deliciosa) were prepared from a local store. In order to decrease the respiration, the whole samples were stored at 4°C before using in experiments (Maskan, 2001b). The moisture content of kiwifruits was about 82% ±1.3 (wet basis). Before drying, all samples were peeled and cut into 0.5-mm-thick slices with a steel cutter.
A combined infrared (Philips, Germany) -vacuum (Memmert Universal, Germany) dryer was used to dry the kiwifruit slices ( Figure 1). The drying was conducted in various power of infrared radiation (200, 250, and 300 W) and pressure (5, 10, and 15 kPa). The dried samples were stored in an airtight packet till the experiments (Ghaboos et al., 2016).
Weight loss was registered using a digital scale (LutronGM-300p; Taiwan). The initial moisture content was determined based on the AOAC method (Helrich, 1990). All experiments were performed tree times and an the average was taken for data analysis (Ghaboos et al., 2016).

| Kinetics of drying
The moisture content data were calculated by Equation (1): where, MR: the dimensionless moisture ratio; M t : moisture content at any time M 0 : initial moisture content; M e : equilibrium moisture content.
The details of evaluated thin-layer drying models, presented in Table 1, these models were fitted to obtained results for MR (Doymaz, 2014;Ghaboos et al., 2016). A nonlinear estimation package (Curve Expert, Version 1.34) was used to estimate the models coefficients.
The correlation coefficient (R) and standard error (SE) were calculated to adjust the experimental results to the models A desirable fitness is achieved at low SE and high R values, (Doymaz, 2011).

| Moisture diffusivity calculation
In drying, the diffusion is suggested as the main mechanism for the moisture transport to the surface (Doymaz, 2011). For food drying process, Fick's second law of diffusion has been widely introduced to describe a falling rate stage (Sacilik, 2007). This model is presented for slab geometry as Equation (2) (Ghaboos et al., 2016): where, MR: moisture ratio; t: drying time (s); D eff : effective diffusivity (m 2 /s); L: half slab thickness of slices (m). When the drying periods is too long, Equation (2) can be abbreviated to Equation (3) (Ghaboos et al., 2016).
Applied mathematical models to kinetics modeling of kiwi drying

Model Equation
MR, moisture ratio; t, time (min) and n, k, b, l, g, c, and a are coefficients of models.
The effective diffusivity can be obtained by Equation (3). It is typically calculated using plotting lnMR versus time (as given in Equation 3) (Ghaboos et al., 2016). The slop of a straight line (K) in plot of lnMR versus time can obtained using Equation 3:

| Color measurement
An image processing system was used to determine the effect of drying condition on color indexes of dried kiwifruit, Sample images were captured with a scanner (Canon CanoScan LiDE 120; Japan). The color space of images was in RGB system and they were converted into L*a*b* system. In the L*a*b* space, the color perception is more uniform (Mashkour, Shahraki, Mirzaee, & Garmakhany, 2014;Salehi & Kashaninejad, 2014;Salehi et al., 2016).

| Effect of drying condition
The absorption of infrared radiation by water content is the most important parameter, which affects drying rate. In general, infrared radiation can be absorbed by materials in the thin surface layer of sample (Ghaboos et al., 2016;Nowak & Lewicki, 2004). During drying, the radiation properties of exposed material is affected by removal of the water content, so the absorptivity of the sample is decreased due to increasing in the reflection of the waves. Figures 2 and 3, present the changes in water content under studied infrared power and vacuum pressure, respectively. As can be seen, an increase in the power decreased the moisture content due to increasing temperature. In the fixed pressure (5 kPa), the drying periods of kiwifruit samples were 80, 60, and 47.5 min at 200, 250, and 300 W, respectively. Finally, the obtained results indicated that the power of infrared significantly affects the removal of moisture content.
In vacuum drying operation, drying is performed in low pressures.
The reduction in temperature in the subatmospheric pressure leads to obtaining a higher quality compared to conventional air drying at atmospheric pressure (Ghaboos et al., 2016). With decreasing in the drying time from 92.5 to 80 min at a fixed infrared power, the vacuum pressure was decreased from 150 to 50 kPa (200 W). It seems that drying of thin layers had a higher efficiency at far-infrared (25-100 μm) compared to near-infrared radiation (NIR, 0.75-3.00 μm) for thicker samples (Salehi et al., 2016).

| Drying curves fitting
The experimental data were fitted with the mathematical models (Table 1) and the quadratic model was the best model to describe the drying rate because it had the lowest SE and the highest R values.
Statistical data obtained for this model and estimated parameters are presented in Table 2. The results indicated that for all models, the R values were higher than .997, stating a good correlation. Figure 4 shows the very good correlation between experimental and the predicted results using the quadratic model for dried kiwifruit slices at 200 W and 15 kPa.

| Moisture diffusivity
The parameter of effective diffusivities was obtained using plotting lnMR versus time. The changes in lnMR under various infrared radiation power, vacuum pressure, and thickness are presented in Figures 5 and 6, respectively. The D eff values for food samples are in Variations of moisture content with drying time of kiwi slices at different infrared power (15 kPa) Variations of moisture content with drying time of kiwi slices at different system pressure (300 W) range 10 −11 to 10 −9 m 2 /s (Doymaz & Göl, 2011). The values of D eff at different condition drying of kiwifruit slice obtained by Equation (4) and predicted results are indicated in Table 3. The effective diffusivity of kiwifruit samples were obtained from 1.04 to 2.29 × 10 −9 m 2 /s.

| Color measurement
Color is an important quality factor for food production  shows the saturation degree of color and is corresponding to the color strength (Maskan, 2001b). The variation in Hue angle values was not considerable compared to drying processes. Ghaboos et al. (2016) found that high temperature is responsible for increasing ΔE values during drying of mint leaves.

| CONCLUSIONS
Kiwifruit samples were dried using a combined infrared-vacuum dryer.
The dryer was Equipped with near-infrared (NIR) heaters. The drying times of kiwifruit were 80, 60, and 47.5 min at 200, 250, and 300 W, respectively. It was reduced when the system pressure was decreased.
The drying kinetics were described by quadratic model with the latter providing the best representation of the experimental data. It was observed that the obtained effective moisture diffusivity values for kiwifruit samples were from 1.04 and 2.29 × 10 −9 m 2 /s. This study verified that the color of kiwifruit was affected by the parameters of drying pro-