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ÿþJournal of Food Engineering 65 (2004) 157 164 www.elsevier.com/locate/jfoodeng Microwave vacuum drying kinetics of carrot slices a a,* b,* Zheng-Wei Cui , Shi-Ying Xu , Da-Wen Sun a School of Food Science and Technology, Southern Yangtze University, Wuxi, Jiangsu 214036, PR China b Department of Biosystems Engineering, University College Dublin, National University of Ireland, Earlsfort Terrace, Dublin 2, Ireland Received 25 September 2003; accepted 6 January 2004 Abstract The kinetics of microwave vacuum drying of thin layer carrot slices was studied by introducing a theoretical model. The model is based on the energy conservation of sensible heat, latent heat and source heat of microwave power. The model was tested with data produced in a lab microwave vacuum dryer in which the materials to be dried could rotate in the cavity. The theoretical and experimental drying curves showed that the theoretical model was in agreement with experimental data, and drying rate was a constant until the dry-basis moisture content Xs was about 2. As 1 6 Xs < 2, the experimental drying curves showed a little deviation from the theoretical drying curves. While Xs < 1, the experimental drying curves showed a sharp deviation from the theoretical drying curves. To predict the changing of moisture content with time by the theoretical model in the period of Xs < 2, a correction factor, u, was introduced and obtained using non-linear regression analysis. The investigation involved a wide range of microwave power and vacuum pressure levels. Both the theoretical model and experimental data also showed that the drying rate was linear to the microwave power output, and inversely proportional to the first order of latent heat of evaporation for water at the vacuum pressure of P. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Microwave vacuum drying; Microwave; Kinetic; Drying; Carrot slice; Thin-layer drying 1. Introduction and grains (Cui, Xu, & Sun, 2003, 2004; Drouzas & Schubert, 1996; Kaensup, Chutima, & Wongwises, 2002; Microwave with their ability to rapidly heat dielectric Lin, Durance, & Scaman, 1999; Wadsworth, Velupillai, materials is commonly used as a source of heat. In the & Verma, 1990; Yongsawatdigul & Gunasekaran, food industry microwave is used for heating, drying, 1996a, 1996b). thawing, tempering, sterilization etc. In recent years, Drying is a complex process involving simultaneous microwave drying has gained popularity as an alterna- coupled transient heat, mass and momentum transport. tive drying method in the food industry. Microwave They are often accompanied by chemical or biochemical drying is rapid, more uniform and energy efficient reactions and phase transformations. The drying kinet- compared to conventional hot-air drying (Decareau, ics is often used to describe the combined macroscopic 1985). Besides these, it dissipates energy throughout a and microscopic mechanisms of heat and mass transfer, product, and is able to automatically level any moisture and it is affected by drying conditions, types of dryer, variation within it. Microwave vacuum drying com- characteristics of materials to be dried, etc. Because on- bines the advantages of both vacuum drying and line measurement of temperature and moisture is diffi- microwave drying, and it can improve energy efficiency cult and time-consuming for microwave heating and and product quality. Microwave vacuum drying has drying, drying kinetics models are essential for equip- been investigated as a potential method for obtaining ment design, process optimization and product quality high-quality dried foodstuffs, including fruits, vegetables improvement. A mathematical model for drying kinetics is normally based on the physical mechanisms of internal heat and mass transfer and on heat transfer conditions external to * Corresponding authors. the material being dried that controls the process resis- E-mail addresses: syxu@sytu.edu.cn (S.-Y. Xu), dawen.sun@ucd.ie tance, as well as on the structural and thermodynamic (D.-W. Sun). URL: http://www.ucd.ie/refrig assumptions made to formulate the model. Modeling of 0260-8774/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.01.008 158 Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157 164 Nomenclature cp specific heat capacity of sample (kJ/kg K) SE mean standard error (kg/kg db) eði;jÞ error (difference) between the experimental t microwave drying time (s) value and the value calculated by the model DT temperature rise in sample (°C) m mass of sample (kg) T0 initial temperature (°C) M0 mass of dried solid (kg) Te evaporating temperature of water at vacuum ni number of replicates of the experimental pressure of P (°C) point i X0 initial sample moisture content (kg/kg db) N drying rate (kg/s) Xs sample moisture content (kg/kg db) N0 number of experimental points for each Xw sample moisture content obtained by theo- experiment retical calculation (kg/kg db) P vacuum pressure (mbar) Xsði;jÞ moisture content at experiment point i and at Qabs energy absorbed by sample per unit time replicate j (kW) X mean moisture content at experiment point i sði Þ rp latent heat of evaporation of water at vacuum Subscripts pressure of P (kJ/kg) i experiment point SR standard error between experimental point j replicate and theoretically calculated value (kg/kg db) drying is usually complicated by the fact that more than the model-drying constant. Unfortunately Kiranoudis one mechanism may contribute to the total mass et al. (1997) only dried the materials without rotating, transfer rate and that the contributions from different resulting in non-uniform heating. Furthermore, micro- mechanisms may change during the drying process. wave vacuum drying process at later stages of drying Modeling of microwave heating has made significant had not been well investigated. progress in recent years (Chen, Singh, Haghighi, & In the current study, microwave vacuum drying Nelson, 1993; Khraisheh, Cooper, & Magee, 1997; Lin, kinetics of carrot slices is investigated by introducing a Anantheswaran, & Puri, 1995; Oliveira & Franca, 2003; theoretical model which is based on the balance of en- Yand & Gunasekaran, 2001). It involves coupling the ergy and mass. The model was tested and modified with models for microwave power absorption and tempera- data produced in a laboratory microwave vacuum dryer ture distribution inside the product. Modeling of using non-linear regression analysis. The study involved microwave drying has also made some progress in recent a wide range of microwave power and vacuum pressure years (Doland & Datta, 1993; Jansen & van der Wek- levels. ken, 1991; Lefeuvre, 1981; Lu, Tang, & Liang, 1998; Lu, Tang, & Ran, 1999; Ofoli & Komolprasert, 1988; 2. Mathematical model Turner, 1994), in which the models developed range from complicated coupled heat, mass and wave equa- In microwave heating or drying, the microwave tions to empirical models expressing mass transfer emitted radiation is confined within the cavity and there through parameters of phenomenological nature incor- is hardly heat loss by conduction or convection so that porating most process parameters affecting microwave the energy is mainly absorbed by a wet material placed drying, such as microwave power and vacuum. How- in the cavity. Furthermore, this energy is principally ever, few literatures focus on modeling of microwave absorbed by the water in the material, causing the vacuum heating or drying. Lian, Harris, Evans, and temperature to rise, some water to be evaporated, and Warboys (1997) described the coupled heat and mois- the moisture level to be reduced. ture transfer during microwave vacuum drying. The In our study, a theoretical model is proposed. The models developed consider the moisture transfer as a model is based on the energy conservation of the sen- combination of simultaneous water (liquid) and vapor sible heat, latent heat and source heat of microwave transfer. Kiranoudis, Tsami, and Maroulis (1997) stud- power. The energy conservation equation is written as ied the mathematical model of microwave vacuum drying kinetics of some fruits. An empirical mass Qabst ¼ cpmðTe T0Þ þrpDm ð1Þ transfer model, involving a basic parameter of phe- The mass balance equation is written as nomenological nature, was used and the influence of Dm ¼ M0ðX0 XwÞð2Þ process variables was examined by embodying them to Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157 164 159 is somewhat different from the rated capacity that is 50 9 stated in the manufacturer s literature, and this may be 8 40 due to a number of reasons such as magnetron ageing 7 and heating effects. As the magnetron ages, it takes the 6 30 filament a longer time to reach the emission condition. 5 Temperature The power variations may also occur if the magnetron is 4 Moisturte Content 20 operated for a long period of time, as the prolonged 3 heating of the permanent magnets (which is part of the 2 10 magnetron) causes a reduction in the magnetic field and 1 hence a reduction in the operation voltage, which in turn 0 0 leads to the reduction in the power output. Therefore, it 0 5 10 15 20 25 30 is essential to measure the microwave power output, and Drying time t (min) also measures should be taken to ensure no variation in power output. In designing our lab microwave vacuum Fig. 1. Temperature of carrot slices during drying: power ¼ 336.5 W, P ¼ 30 mbar, initial sample weight ¼ 220 g. dryer, cooling of the magnetron and transformer has been enhanced for maintaining the constant power Combining Eqs. (1) and (2), the moisture content of output by the introduction of two big electric fans. samples, Xw (dry basis), is correlated with drying time, t, In this study, the measurement of power output of the by the following equation: microwave vacuum dryer was determined calorimetri- cally, which was to measure the change of temperature Qabst cpmðTe T0Þ X0M0 rp of a known mass of water (1000 g) for a known period Xw ¼ ð3Þ M0 of time. The increase in temperature of water per unit time could be given by In microwave vacuum drying, because the preference vacuum pressure ranges from 25 to 45 mbar, the evap- mCpDT 4187 DT Qabs ¼ ¼ ð6Þ orating temperature of water Te is between 20 and 31 °C. t t During drying, the temperature is the saturation tem- Eq. (6) assumes that the energy absorption was solely perature of water in food corresponding to the vacuum due to the microwave energy, and there was no heat gain used. This assumption is verified in the experiments. Fig. or loss to the surroundings, furthermore, cp of water did 1 also shows that sample temperature of about 30 °C not change with temperature. during the period of Xs P 2 was close to the saturation The standard procedure described by Schiffmann temperature of water at the vacuum pressure of 30 (1987) was used to determine the power output. mbar. Compared to the value of rpDm, the value of Deionised water weighing 1000 g and equilibrating at cpmðTe T0Þ is small so that Eq. (3) can be reduced to temperature of 5 °C below room temperature, was he- Qabs ated in the microwave vacuum dryer at full power, 80% Xw ¼ X0 t ð4Þ M0rp full power and 50% full power, respectively. Heating was continued for a period of time until the final tempera- Conventionally, the drying rate, N, is defined as ture of the water load reached 5 °C above room tem- M0dXw Qabs perature (18 °C). The water temperatures before and N ¼ ¼ ð5Þ dt rp after heating were measured using a k-type thermocou- ple probe after the water was thoroughly stirred for uniform temperature. Three replicates were performed for each measurement, and the mean value and standard 3. Material and methods deviation of power output was reported. In the current study, the power output for full power, 80% full power 3.1. Drying equipment and 50% full power were 336.5 ± 1.7, 267.5 ± 2.1 and 162.8 ± 2.3 W, respectively. The lab scale microwave vacuum dryer in which the materials to be dried can be rotated in the cavity was developed by the authors and described in details else- 3.3. Experimental procedure where (Cui et al., 2003). The rotation speed of the turntable was 5 rpm. A batch of fresh carrot was purchased from local market. The initial moisture content of the carrot was 3.2. Microwave power output measurement 7.68 (dry basis) which was measured according to the vacuum oven method (AOAC, 1995). Before drying, the Microwave ovens are usually classified according to carrot was cut into slices of 3 5 mm and their weight their power rating. In general, microwave power output was determined by means of an electronic balance o s Temperature ( C ) Moisture content X (kg/kgdb) 160 Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157 164 (Model MP2000D, Shanghai Electronic Balance 10 Instrument Co. Ltd., Shanghai, China). The sample was 8 spread in a single layer in a dish made of tetrafluoro- Experimental curve ethylene and rotated with the turntable and then the Theoretical curve 6 appropriate experimental conditions (vacuum and microwave power) were imposed. For each experiment, 4 the vacuum was interrupted and the sample was taken 2 out and then weighed by electronic balance every 3 min and the sample was dried until the moisture content was 0 less than 10% (wet basis) (continuous drying experiment 0102030 on similar weight was conducted to examine the effect of (a) Drying time t (min) this interruption during drying on weight loss and it was found the effect was negligible). All the measurements 10 were taken within 1 min. The moisture of the dried 8 sample at the end of every drying period was calculated according the loss of weight and value of initial moisture Experimental curve 6 content. Compared to the evaporation heat, the sensible Theoretical curve heat lost due to the above interruption was small and 4 could be neglected. Microwave vacuum drying experiments were carried 2 out for three levels of microwave power (336.5, 267.5, 162.8 W) and three levels of vacuum pressure (30, 51, 71 0 mbar). The lower power levels were obtained with the 010 20 30 magnetron being cycled between on and off. Three (b) Drying time t (min) replicates were carried out for each experiment, and the mean value and standard error of moisture content at 10 each experimental point were determined. The experi- mental data points and the process conditions are pre- 8 Experimental sented in Figs. 2 4. In these figures, the mean standard curve error of the moisture content (experimental error, SE) Theoretical curve 6 for each experimental point is presented. The standard error (SR) between the experimental and theoretical 4 calculated values is also shown. The equations for cal- culating SE and SR are given below: 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN0 Pn 1 i ðXsði;jÞ X Þ2 sði Þ i¼1 j¼1 ni 1 0 SE ¼ ð7Þ 01020 30 N0 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Drying time t (min) uX X (c) N0 ni u e2 ði;jÞ t SR ¼ ð8Þ Fig. 2. Drying curves of carrot slices at examined vacuum pressure ni ðN0 1Þ i¼1 j¼1 having power output at 336.5 W. (a) P ¼ 30 mbar, initial sample weight ¼ 220.20 g, Xs P 2, SR ¼ 0:056, SE ¼ 0:072; Xs < 2, SR ¼ 0:366, where ni is the number of replicates of the experimental SE ¼ 0:091; (b) P ¼ 51 mbar, initial sample weight ¼ 220.55 g, Xs P 2, point i, N0 is the number of experimental points for each SR ¼ 0:094, SE ¼ 0:078; Xs < 2, SR ¼ 0:433, SE ¼ 0:089; (c) P ¼ 71 experiment, Xsði;jÞ is the moisture content at experiment mbar, initial sample weight ¼ 220.55 g, Xs P 2, SR ¼ 0:100, SE ¼ 0:083; Xs < 2, SR ¼ 0:501, SE ¼ 0:097. point i and at replicate j, X is the mean moisture sði Þ content at experiment point i and eði;jÞ is the error (dif- ference) between the experimental value and the value calculated by the model, i.e., Eq. (4). that is to say, the load had little effect on the microwave power output. The reason may be that when there is still enough free water available in the load, the microwave 4. Results and discussion energy can be wholly absorbed by the load and therefore little amount of the energy reflects back to the magne- Table 1 shows the weight loss of fresh carrot slices tron. Since the load level had a little effect on the dried for 3 min at microwave power of 336.5 W. The absorption of microwave energy, the sample load was results indicate that the load absorbed almost the same reduced for the lower microwave power settings (267.5 quantity of microwave energy at different load levels, and 162.8 W) in order to shorten the experiment time. Moisture content (kg/kg db) Moisture content (kg/kg db) Moisture content (kg/kg db) Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157 164 161 10 10 8 8 Experimental curve Experimental curve 6 6 Theoretical curve Theoretical curve 4 4 2 2 0 0 020 40 60 80 010 20 30 40 (a) Drying time t (min) Drying time t (min) (a) 10 10 Experimental curve 8 8 Experimental curve Theoretical curve Theoretical curve 6 6 4 4 2 2 0 0 0 10 20 30 40 50 010 20 30 40 (b) Drying time t (min) (b) Drying time t (min) 10 10 Experimental curve 8 8 Theoretical curve 6 Experimental curve 6 4 Theoretical curve 4 2 2 0 0 10203040 0 (c) Drying time t (min) 0 10203040 Fig. 4. Drying curves of carrot slices at examined vacuum pressure Drying time t (min) (c) having power output at 162.8 W. (a) P ¼ 30 mbar, initial sample Fig. 3. Drying curves of carrot slices at examined vacuum pressure weight ¼ 220.30 g, Xs P 2, SR ¼ 0:095, SE ¼ 0:078; Xs < 2, SR ¼ 0:729, having power output at 267.5 W. (a) P ¼ 30 mbar, initial sample SE ¼ 0:096; (b) P ¼ 51 mbar, initial sample weight ¼ 180.10 g, Xs P 2, weight ¼ 220.10 g, Xs P 2, SR ¼ 0:075, SE ¼ 0:106; Xs < 2, SR ¼ 0:054, SR ¼ 0:136, SE ¼ 0:126; Xs < 2, SR ¼ 0:441, SE ¼ 0:129; (c) P ¼ 71 SE ¼ 0:092; (b) P ¼ 51 mbar, initial sample weight ¼ 210.25 g, Xs P 2, mbar, initial sample weight ¼ 161.20 g, Xs P 2, SR ¼ 0:088, SE ¼ 0:823; SR ¼ 0:054, SE ¼ 0:081; Xs < 2, SR ¼ 0:506, SE ¼ 0:111; (c) P ¼ 71 Xs < 2, SR ¼ 0:554, SE ¼ 0:108. mbar, initial sample weight ¼ 205.40 g, Xs P 2, SR ¼ 0:074, SE ¼ 0:095; Xs < 2, SR ¼ 0:404, SE ¼ 0:120. 2. Thus, the computed theoretical drying curves can be plotted by Eq. (4) which are illustrated in Figs. 2 4. Eqs. (4) and (5) are regarded as the theoretical drying By examining Eqs. (4) and (5), it can be found that kinetic model and theoretical drying rate kinetic model the drying rate is a constant during the whole micro- for microwave vacuum drying respectively. For the wave vacuum drying period. From Figs. 2 4, it is clear vacuum range from 30 to 71 mbar used in the experi- that the experimental drying curves agree with the ments, the latent heat of evaporation of water slightly computed theoretical drying curves in the period of decreased from 2438 to 2403 kJ/kg. By using Eq. (1), the Xs ðor XwÞ P 2, indicating an initial constant drying rate quantity of water evaporated within 3 min at different period. At moisture content Xs ¼ 2, N begins to fall with microwave power output levels and vacuum pressure further decrease in Xs. Therefore, Xs ¼ 2 is the so-called levels can be calculated and the results are shown in Table critical moisture content. The drying rate in the constant Miosture content (kg/kg db) Moisture content (kg/kg db) Moisture content (kg/kg db) Moisture content (kg/kg db) Moisture content (kg/kg db) Moisture content (kg/kg db) 162 Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157 164 Table 1 Weight loss of fresh carrot slices dried for 3 min at microwave power of 336.5 W Load (g) 980 600 200 100 70 Loss of weight (g) 25.56 ± 0.63 24.88 ± 0.59 24.64 ± 0.75 23.21 ± 0.68 22.42 ± 0.58 Table 2 10 The quantity of water evaporated within 3 min at different microwave power output levels and vacuum pressure levels 8 Vacuum pressure Microwave power (mbar) 336.5 W 267.5 W 162.8 W 6 Õ =1.3662X w-0.5741 30.0 24.80 g 19.75 g 12.02 g 51.0 25.05 g 19.91 g 12.12 g R2 = 0.9397 4 71.0 25.21 g 20.04 g 12.19 g Dm ¼ Qabst=rp and t ¼ 3 min. 2 0 rate period (Xs P 2) is governed fully by the rate of 2 1.5 1 0.5 0 external heat and mass transfer, since a film of free water Moisture content X (kg/kg db) w is always available at the evaporating surface. In our experiments, potato slices and pumpkin slices were also Fig. 5. Non-linear regression curve of correction coefficient versus dried and almost the same data were obtained. It is theoretical moisture content. therefore deduced that the drying rate in this period remains almost constant for most of sliced vegetables where u is mainly affected by the moisture content, as and fruits as the main component of vegetable and fruits well as the characteristic or composition of the material is water, and the amounts of salt, fat and other com- being dried, and it can be defined in the current study as ponents are very small. Figs. 2 4 also show that N be- gins to drop at Xs ¼ 2 since water molecules cannot u ¼ f ðXwÞ P 1 ð10Þ migrate immediately to the surface because of internal If Xs is divided by Xw, the values of u could then be transport limitation. Under these conditions, the drying obtained. Fig. 5 shows the plot of u versus Xw. By non- surface becomes first partially unsaturated and then linear regression analysis, the value of u as a function of fully unsaturated until it reaches the equilibrium mois- Xw was obtained as follows: ture content. Furthermore, as the moisture content is below 2, a little amount of water is available, and con- u ¼ 1:3662Xw 0:5741 ð11Þ sequently the volumetric heating due to microwave In summary, the moisture content, Xs, of the mate- power dissipation is reduced because the power dissi- rials being dried in microwave vacuum dryer can be pation of microwave strongly depends on the moisture predicted by the following equations: content of the material (Lian et al., 1997) and part of 8 Qabst microwave power reflects back to the magnetron. When Xw ¼ X0 > M0rp > > > the moisture content is very low, the dielectric loss factor > < 8ðXw P 2Þ decreases and the sample temperature may increase. Qabst > Xs ¼ ð12Þ < uXw ¼ u X0 M0rp > Therefore, it is very difficult to predict moisture loss rate > > > u ¼ 1:3662Xw 0:5741 > > based on the balance between the absorbed microwave : : ð0 < Xw < 2Þ heat and the released heat of water evaporation, thus the theoretical drying kinetic model (Eq. (4)) must be Fig. 6 presents the effect of microwave power on the modified in the period of Xs < 2. drying curves. For constant vacuum pressure levels, the The drying rate begins to decline slowly as drying rate produced higher values if microwave power 1 < Xs < 2, and the drying rate declines sharply as was greater. The experimental data agree with the result Xs < 1. As the true moisture content, Xs, is larger than predicted by Eq. (5), which shows that the drying rate is that (Xw) calculated by Eq. (4), a correction coefficient, the first order of power output. u, is introduced to modify Eq. (4) which is then The effect of vacuum pressure on the drying curves is rewritten as presented in Fig. 7. When microwave power level re- mained constant, the drying rate produced a little higher Qabs value if the vacuum pressure (residual absolute pressure) Xs ¼ uXw ¼ u X0 t ; 0 < Xw < 2 ð9Þ M0rp was higher. This result was in contrary to those reported Correction cofficient Õ Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157 164 163 10 10 8 8 336.3w 30 mbar 6 6 51 mbar 267.5W 71 mbar 162.8W 4 4 2 2 0 0 0 10203040 0 10 20 30 40 50 (a) Drying time t (min) (a) Drying time t (min) 10 10 8 8 30 mbar 336.5W 6 51 mbar 6 267.5W 71 mbar 4 162.8W 4 2 2 0 0 10203040 0 (b) Drying time t (min) 0 10 20 30 40 50 (b) Drying time t (min) 10 10 30 mbar 8 51 mbar 8 6 71 mbar 336.5W 4 6 267.5W 162.8W 2 4 0 2 0 10 20 30 40 50 60 (c) Drying time t (min) 0 0 10203040Fig. 7. Effect of vacuum pressure on experimental drying curves: (c) initial sample weight ¼ 220 g. (a) Q ¼ 336:5 W; (b) Q ¼ 267:5 W; Drying time t (min) (c) Q ¼ 162:8 W. Fig. 6. Effect of microwave power on experimental drying curves: initial sample weight ¼ 220 g. (a) P ¼ 30 mbar; (b) P ¼ 51 mbar; (c) P ¼ 71 mbar. 5. Conclusions by Kiranoudis et al. (1997), Lin et al. (1999) and In this paper, a theoretical model for microwave Kaensup et al. (2002), but it was confirmed by the result vacuum drying of carrot slices was developed and predicted by Eq. (5), indicating the drying rate is in in- modified for the later stages of drying. The model and verse proportion to the value of rp. The reason may be experimental data reveal that the drying rate is a con- that as the carrots were sliced into 3 5 mm in the current stant one until the moisture content is about 2 dry-basis experiments, the drying rate was controlled by heat and remains essentially unchanged for most of sliced dissipation rate, and the higher drying temperature at vegetables and fruits in this period due to the initial high higher vacuum pressure caused higher drying rate. moisture content of the samples, and then the drying However, the samples used in the previous experiments rate declines. As Xs < 2, the correction coefficient, u reported by Lin et al. (1999) and Kaensup et al. (2002) must be introduced as a function of Xw. In the earlier were not sliced and therefore had much larger size, while period of the drying (high moisture content, Xs P 2), the the sample used in the experiment by Kiranoudis et al. drying rate can be estimated to range from 1474 to 1498 (1997) were spherical particles with 30 mm in diameter, g water/kW h at the vacuum pressure from 30 to 70 therefore, the drying rate was controlled by moisture mbar. diffusion and affected by the vacuum level with lower The model and experimental data also show that the vacuum pressure leading to higher drying rate. microwave power and vacuum pressure affect the drying s s Moisture content X (kg/kg db) Moisture content X (kg/kg db) s s Moisture content X (kg/kg db) s s Moisture content X (kg/kg db) Moisture content X (kg/kg db) Moisture content X (kg/kg db) 164 Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157 164 Kiranoudis, C. T., Tsami, E., & Maroulis, Z. B. (1997). Microwave rate. 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