Microwave coupled with hot air drying kinetics and characteristics of hawthorn slices at different drying hot air temperatures, hot air velocities, and microwave power densities was investigated. The research results showed that drying occurred mainly in the falling rate period and in the accelerating period. Twelve mathematical models were selected to describe and compare the drying kinetics of hawthorn slices. By comparing three criterions including correlation coefficient, chi-square, and root mean square error, we determined that Weibull distribution model obtained the best fit and could best predict the experimental values. Consequently, Weibull distribution model could be used to aid dryer design and promote the efficiency of dryer operation by simulation and optimization of the drying processes. Moisture transfer from hawthorn slice was described by applying Fick’s second law and the effective diffusivity values were calculated by simplified Fick’s second law. The variable law of effective diffusivity values was consistent with the variable law of moisture ratio.
Hawthorn is a kind of plant that belongs to hawthorn genus, which belongs to Rosaceae, is a unique fruit originated from China, and has 3000 years of cultural history. Currently, it mainly distributed in China, Europe, and North America [
Drying is one of the widely used methods for postharvest preservation of fruit products. The basic objective in drying fruit products is the removal of water in the solids up to a certain level, at which microorganism and deterioration chemical reactions are greatly minimized [
The dried slices of hawthorn fruits are much-loved hawthorn processed products; in addition to medical applications, it also can be made into drinks and raw or auxiliary material for other processed products. One of the main concerns of the commercial dried slices of hawthorn fruits is to obtain dried products of good quality. The quality of dried slices of hawthorn fruits can be affected by drying methods. Currently, there are mainly two kinds of drying methods including sun-drying and hot air drying for the slices of hawthorn fruits. Sun-drying is the most frequently used method for the slices of hawthorn fruits. This drying method is simple and there are no drying costs substantially, but drying takes a long time and the drying slices of hawthorn fruits are exposed to environmental contamination such as dust, rodents, birds, and microorganisms. Therefore, the quality of the dried products may be lowered significantly [
In recent years, the microwave drying technology is more widely applied. In microwave drying, microwave interaction with water molecules and internally generated heat throughout the drying of samples, which greatly reduces the drying time, improves energy efficiency and reduces the loss of trace elements in dried fruits. But there is a trouble of temperature uneven if it simply relies on the method of microwave heating, especially in the later stage of drying; the dried material is easy to cause gelatinization, which leads to poor quality of the dried product [
Microwave coupled with hot air (MCHA) drying is an innovative technique that dries the materials by microwave and hot air simultaneously and combines the advantages of microwave and hot air drying as well as overcomes the disadvantages associated with the application of each method alone [
Various mathematical models describing the drying characteristics of different fruits and vegetables had been proposed to optimize the drying process and design efficient dryers [
Therefore, the present study is conducted with the following objectives: (1) to dry the hawthorn slices in a microwave coupled with hot air dryer, and to determine the effect of hot air temperature, hot air velocity, and microwave power density on the dry characteristic, and to obtain drying characteristic curves; (2) to calculate the effective diffusivity of hawthorn slices samples; (3) to fit the experimental drying data obtained to drying models widely for predicting the drying characteristics of microwave coupled with hot air drying of hawthorn slices at different drying hot air temperature, hot air velocity, and microwave power density conditions.
North hawthorn is one of the main species among hawthorns cultured in Shandong, Hebei, Jilin, Henan, Liaoning, and Heilongjiang, China. Hawthorn used in experiment was cultured in Shandong, they were selected as the dried materials in December 2013. They were classified according to color, size, degree of mechanical damage, and decay after being bought. Those test samples of fresh color, the same size, no mechanical damage, and decay were packed into plastics bags in 0.5 kg lots after being washed and drained and stored in a refrigerator at 4°C. The fresh hawthorns and the dried hawthorn slices were shown in Figure
The appearances of hawthorn: (a) fresh hawthorn; (b) dry hawthorn slices.
The drying tests of hawthorn slicks were mainly completed by microwave coupled with hot air dryer (YHMW900-100), which was manufactured at College of Engineering, Heilongjiang Bayi Agricultural University, Daqing, Heilongjiang. The schematic view and photograph of experimental setup were shown in Figure
Photograph of experimental setup and schematic illustration of microwave coupled with hot air dryer. 1: Electric control part; 2: control buttons; 3: indicator; 4: control panel; 5: regulator; 6: temperature control device; 7: microwave control digital display; 8: air flow velocity indicator; 9: magnetron; 10: temperature sensor; 11: microwave cavity; 12: hot air distributor inlet; 13: rotating glass plate; 14: heater; 15: stainless steel inlet duct; 16: air flow velocity sensor; 17: centrifugal blower; 18: stainless steel air outlet duct; 19: axial fan.
The size of the microwave coupled with hot air dryer was 1570 × 1000 × 505 mm, which mainly consisted of microwave drying system and hot air drying system. Microwave drying system consisted of the magnetron, control systems, and microwave resonator cavity. The frequency of magnetron was 2450 MHz, the microwave input power was 1300 W, and the microwave output power was 900 W. The control system was used to control the microwave power and the drying time, the microwave output power could be adjusted to 900, 720, 540, 360, and 180 W, and the drying time could be controlled to the range of 0–180 min. Microwave resonator cavity was made of 304 stainless steel and structural dimensions were of 330 × 215 × 350 mm. Hot air drying system mainly consisted of air flow distributor, a heater, a control system, and a centrifugal fan powered of 550 W. The air flow distributor was made of 304 stainless steel, structural dimensions were of 150 × 150 × 30 mm, and the outlet was composed of 106 holes with 8 mm diameter. There was a row of 3 mm diameter holes on the side wall of the microwave cavity for discharging the wet air after drying. The heater consisted of three far-infrared carbon fiber heating tubes power of 800 W and stainless steel tube with diameter of 89 mm. Control system consisted of a Pt100 temperature sensor with an accuracy of ±0.5°C (HGB300, China), a frequency converter with an accuracy of ±0.5% maximum air flow velocity (MT-B-0R7G-4-1010, the output frequency was 0–400 Hz, China), an air flow velocity sensor with an accuracy of ±0.2 m/s + 3% mv (WD, range was 0–30 m/s, China), and a digital display control instrument with an accuracy better than ±0.5% FS (ch6, display range −1999–9999, China). The temperature sensor was installed in the upper part of the microwave cavity for the inside hot air temperature measurement; hot air temperature was controlled between 30°C and 100°C (dry bulb temperature). Since the normal operating temperature of the air flow velocity sensor is below 60°C, to protect the air flow velocity sensor, it was installed at the outlet of the centrifugal blower to measure the air flow velocity. The air flow velocity was controlled between 0–5 m/s inside microwave cavity. There was an interconnection between the microwave cavity of microwave drying system and distributor of hot air drying system, which can feed hot air uniformly into the microwave cavity.
The moisture loss of test samples was weighed by a digital electronic balance (Model T1000, American Twin Brothers Co. Ltd., China) with the measurement range of 0–1000 g and an accuracy of 0.1 g. The hawthorn initial moisture content was measured by a digital electronic balance (Model JA2003N, Shanghai Jingke Trade Co. Ltd., China) with the measurement range of 0–210 g and an accuracy of 0.001 g. A digital anemometer with an accuracy of ±0.1 dgts (Model MT826, Hong Kong Mattel Electronics Technology Co. Ltd., Hong Kong, China) was used to measure the air velocity.
According to the china pharmacopoeia, thickness of dried hawthorn slices was 2~4 mm; therefore, the thickness of fresh hawthorn slices used in each drying test was 5 mm. According to the China pharmacopoeia, the dry experiment would be finished when moisture content of hawthorn slices was at 12% (w. b.). In most of the fruits and vegetables drying experiments, drying temperature was not more than 70°C. It might affect the color and nutrients of fruit and vegetables if the temperature exceeded 70°C, declining in the drying quality [
It was necessary to run the hot air drying system for 10 to 20 min before the experiment; when the hot air temperature inside the microwave cavity reached the presetting temperature and stabilized, the fresh hawthorn slices on the plastic drying tray were put into the microwave cavity; a microwave drying system was started to dry. Drying experiments were carried out at different drying hot air temperatures of 50, 55, 60, 65, and 70°C and different hot air velocities of 1, 1.5, 2, 2.5, and 3 m/s and different microwave power densities of 3, 6, 9, 12, and 15 w/g. During the drying process, the weight of the dry sample was weighed once every 60 s. The weight of the drying samples was weighted once every 10 s or 20 s when the moisture content of hawthorn slices was about 25% (w. b.). It did not impact the drying process since weighing was done within a few seconds [
Moisture ratio of drying experiment expresses the residual moisture content (d. b.) of the material under certain conditions, the Moisture ratio is determined by the following [
Hawthorn drying rate was an important parameter in the drying kinetics; in order to determine the relationship among hawthorn drying time, drying rate, and drying moisture content (d. b.), hawthorn slice drying rate was determined by the following [
To further describe and forecast the moisture loss of hawthorn slices during the drying process of microwave coupled with hot air, 12 mathematical models (Table
Mathematical models for fitting of the moisture ratio values.
Number | Model name | Model | Reference |
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1 | Newton |
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2 | Page |
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3 | Henderson and Pabis |
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4 | Two term |
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5 | Two-term exponential |
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6 | Verma et al. |
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7 | Logarithmic |
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8 | Wang and Singh |
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9 | Approximation of diffusion |
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10 | Midilli et al. |
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11 | Modified page |
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12 | Weibull distribution |
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There were three evaluation criteria in determining the optimum drying mathematical model: the correlation coefficient
Effectivemoisture diffusion coefficient described moisture migration mechanism and reflected the important characteristics of drying model in the food and other materials drying process and was one of the essential parameters to calculate and simulate moisture migration mechanism of food and other materials. Effective moisture diffusion coefficient of hawthorn dried slices using microwave coupled with hot air could be calculated by simplifying Fick’s second law. General series solution of this Fick’s law written in spherical coordinates, with the assumptions of moisture migration being by diffusion, negligible shrinkage, constant diffusion coefficients, and temperature, was given as follows [
For long drying periods, (
Equation (
Hawthorn effective moisture diffusion coefficient could be calculated from the slope method, which was shown as follows:
Uncertainties and errors in experiments can arise from instrument selection, condition, calibration, environment, observation, reading, and test planning. In the drying experiments of hawthorn slices, the hot air temperatures, hot air velocity, dry sample weight, and weight losses were measured with appropriate instruments [
Uncertainties of the parameters during drying of hawthorn slices.
Parameter | Unit | Comment |
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Hot air distributor inlet temperature | °C | ±0.35 |
Hot air distributor outlet temperature | °C | ±0.35 |
Microwave cavity inlet temperature | °C | ±0.35 |
Centrifugal blower outlet temperature | °C | ±0.35 |
Ambient air temperature | °C | ±0.5 |
Heater outlet temperature | °C | ±0.5 |
Mass loss values | min | ±0.1 |
Temperature value | min | ±0.1 |
Uncertainty in the air velocity measurement | m/s | 0.12 |
Uncertainty in the hawthorn slices weight measurement | g | 0.1 |
Uncertainty in the initial moisture content measurement of hawthorn slices | g | 0.001 |
Uncertainty in the mass loss measurement | g | 0.1 |
Uncertainty in reading values of table ( |
% | ±0.1-0.2 |
The hawthorn moisture ratio curve varied with time, at different hot air temperatures, power density, and hot air velocity, which was shown in Figure
The experimental moisture ratios at different drying conditions: (a) experimental moisture ratios at different hot air temperatures; (b) experimental moisture ratios at different microwave power density; (c) the experimental moisture ratios at different drying hot air velocity.
Under the drying conditions with different temperatures, the power density, and hot air velocity, the curve of the drying rate of the hawthorn slices varying with moisture content (d. b.) was shown in Figure
The experimental drying rate at different drying conditions: (a) experimental drying rate at different hot air temperatures; (b) experimental drying rate at different microwave power density; (c) experimental drying rate at different drying hot air velocity.
As can be seen from Figure
Data of continuous moisture content (d. b.) obtained under conditions of different hot air temperature, microwave power density, and hot air velocity were converted into moisture ratio. They were fitted by 12 mathematical models with drying time as the independent variables. The mathematical models were shown in Table
Statistical results of 12 models at different drying conditions.
Model | Experimental factors | Evaluation criteria | Experimental factors | Evaluation criteria | Experimental factors | Evaluation criteria | ||||||||||||
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Newton | 50 | 2 | 9 | 0.93996 | 0.00463 | 0.06802 | 60 | 1 | 9 | 0.95211 | 0.00419 | 0.06471 | 60 | 2 | 3 | 0.96803 | 0.00284 | 0.05327 |
55 | 2 | 9 | 0.95286 | 0.004 | 0.06322 | 60 | 1.5 | 9 | 0.95682 | 0.00399 | 0.06317 | 60 | 2 | 6 | 0.93824 | 0.00567 | 0.07527 | |
60 | 2 | 9 | 0.95059 | 0.00475 | 0.06891 | 60 | 2 | 9 | 0.95625 | 0.0042 | 0.06478 | 60 | 2 | 9 | 0.95589 | 0.00414 | 0.06433 | |
65 | 2 | 9 | 0.96072 | 0.00337 | 0.05807 | 60 | 2.5 | 9 | 0.94461 | 0.00449 | 0.06701 | 60 | 2 | 12 | 0.93763 | 0.00563 | 0.07502 | |
70 | 2 | 9 | 0.93896 | 0.00438 | 0.06615 | 60 | 3 | 9 | 0.95038 | 0.00455 | 0.06745 | 60 | 2 | 15 | 0.9328 | 0.00645 | 0.08034 | |
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Page | 50 | 2 | 9 | 0.97907 | 0.0017 | 0.0412 | 60 | 1 | 9 | 0.98064 | 0.00181 | 0.0425 | 60 | 2 | 3 | 0.99839 | 0.000150 | 0.01226 |
55 | 2 | 9 | 0.99489 | 0.000461 | 0.02146 | 60 | 1.5 | 9 | 0.99206 | 0.000783 | 0.02798 | 60 | 2 | 6 | 0.99895 | 0.000103 | 0.01013 | |
60 | 2 | 9 | 0.99472 | 0.000542 | 0.02327 | 60 | 2 | 9 | 0.99622 | 0.000386 | 0.01965 | 60 | 2 | 9 | 0.99367 | 0.000633 | 0.02517 | |
65 | 2 | 9 | 0.99165 | 0.000756 | 0.0275 | 60 | 2.5 | 9 | 0.98102 | 0.00164 | 0.04052 | 60 | 2 | 12 | 0.99898 | 0.0000990 | 0.00995 | |
70 | 2 | 9 | 0.96146 | 0.00293 | 0.05409 | 60 | 3 | 9 | 0.99003 | 0.000962 | 0.03102 | 60 | 2 | 15 | 0.99471 | 0.000551 | 0.02347 | |
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Henderson and Pabis | 50 | 2 | 9 | 0.94659 | 0.06415 | 0.06415 | 60 | 1 | 9 | 0.96106 | 0.00363 | 0.06027 | 60 | 2 | 3 | 0.98414 | 0.00148 | 0.03845 |
55 | 2 | 9 | 0.9702 | 0.00268 | 0.05181 | 60 | 1.5 | 9 | 0.96854 | 0.0031 | 0.05569 | 60 | 2 | 6 | 0.96072 | 0.00384 | 0.062 | |
60 | 2 | 9 | 0.96562 | 0.00352 | 0.05937 | 60 | 2 | 9 | 0.9703 | 0.00304 | 0.05512 | 60 | 2 | 9 | 0.96795 | 0.00321 | 0.05663 | |
65 | 2 | 9 | 0.97023 | 0.0027 | 0.05194 | 60 | 2.5 | 9 | 0.95489 | 0.0039 | 0.06246 | 60 | 2 | 12 | 0.95652 | 0.0042 | 0.06483 | |
70 | 2 | 9 | 0.94336 | 0.0043 | 0.06557 | 60 | 3 | 9 | 0.96314 | 0.00356 | 0.05964 | 60 | 2 | 15 | 0.94608 | 0.00561 | 0.07491 | |
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Two term | 50 | 2 | 9 | 0.99662 | 0.000307 | 0.01752 | 60 | 1 | 9 | 0.99647 | 0.000380 | 0.01948 | 60 | 2 | 3 | 0.99653 | 0.000359 | 0.01895 |
55 | 2 | 9 | 0.97991 | 0.00207 | 0.04548 | 60 | 1.5 | 9 | 0.99865 | 0.000154 | 0.0124 | 60 | 2 | 6 | 0.99717 | 0.000320 | 0.01788 | |
60 | 2 | 9 | 0.97662 | 0.00277 | 0.05259 | 60 | 2 | 9 | 0.99831 | 0.000200 | 0.01414 | 60 | 2 | 9 | 0.99938 | 0.0000721 | 0.00849 | |
65 | 2 | 9 | 0.99803 | 0.000201 | 0.01417 | 60 | 2.5 | 9 | 0.96088 | 0.0039 | 0.06247 | 60 | 2 | 12 | 0.97758 | 0.00253 | 0.05029 | |
70 | 2 | 9 | 0.9972 | 0.000241 | 0.01551 | 60 | 3 | 9 | 0.99938 | 0.0000666 | 0.00816 | 60 | 2 | 15 | 0.9665 | 0.00414 | 0.06433 | |
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Two-term exponential | 50 | 2 | 9 | 0.93992 | 0.00487 | 0.06981 | 60 | 1 | 9 | 0.97811 | 0.00204 | 0.04518 | 60 | 2 | 3 | 0.99829 | 0.000160 | 0.01263 |
55 | 2 | 9 | 0.99275 | 0.000653 | 0.02556 | 60 | 1.5 | 9 | 0.98915 | 0.00107 | 0.0327 | 60 | 2 | 6 | 0.99549 | 0.000441 | 0.02101 | |
60 | 2 | 9 | 0.99106 | 0.000917 | 0.03028 | 60 | 2 | 9 | 0.99344 | 0.000671 | 0.02591 | 60 | 2 | 9 | 0.99051 | 0.000950 | 0.03082 | |
65 | 2 | 9 | 0.98941 | 0.000959 | 0.03097 | 60 | 2.5 | 9 | 0.97733 | 0.00196 | 0.04428 | 60 | 2 | 12 | 0.99531 | 0.000454 | 0.0213 | |
70 | 2 | 9 | 0.96033 | 0.00301 | 0.05488 | 60 | 3 | 9 | 0.986 | 0.00135 | 0.03675 | 60 | 2 | 15 | 0.98566 | 0.00149 | 0.03863 | |
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Verma et al. | 50 | 2 | 9 | 0.95331 | 0.004 | 0.06323 | 60 | 1 | 9 | 0.96704 | 0.00329 | 0.05739 | 60 | 2 | 3 | 0.99211 | 0.000774 | 0.02782 |
55 | 2 | 9 | 0.97991 | 0.00193 | 0.04394 | 60 | 1.5 | 9 | 0.97738 | 0.00239 | 0.04888 | 60 | 2 | 6 | 0.97418 | 0.00271 | 0.05202 | |
60 | 2 | 9 | 0.97662 | 0.00257 | 0.05068 | 60 | 2 | 9 | 0.98047 | 0.00214 | 0.04627 | 60 | 2 | 9 | 0.97683 | 0.00248 | 0.04984 | |
65 | 2 | 9 | 0.9755 | 0.00235 | 0.04848 | 60 | 2.5 | 9 | 0.96088 | 0.00362 | 0.0602 | 60 | 2 | 12 | 0.97758 | 0.00233 | 0.04832 | |
70 | 2 | 9 | 0.9455 | 0.0044 | 0.0663 | 60 | 3 | 9 | 0.9707 | 0.00299 | 0.05464 | 60 | 2 | 15 | 0.96685 | 0.00376 | 0.06134 | |
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Logarithmic | 50 | 2 | 9 | 0.99579 | 0.000361 | 0.01899 | 60 | 1 | 9 | 0.99224 | 0.000775 | 0.02784 | 60 | 2 | 3 | 0.97221 | 0.00273 | 0.05222 |
55 | 2 | 9 | 0.99309 | 0.000664 | 0.02577 | 60 | 1.5 | 9 | 0.99425 | 0.000607 | 0.02464 | 60 | 2 | 6 | 0.99275 | 0.000760 | 0.02756 | |
60 | 2 | 9 | 0.99496 | 0.000554 | 0.02354 | 60 | 2 | 9 | 0.99054 | 0.00104 | 0.03219 | 60 | 2 | 9 | 0.99495 | 0.000542 | 0.02328 | |
65 | 2 | 9 | 0.99309 | 0.000663 | 0.02576 | 60 | 2.5 | 9 | 0.99711 | 0.000268 | 0.01637 | 60 | 2 | 12 | 0.98199 | 0.00188 | 0.0433 | |
70 | 2 | 9 | 0.98706 | 0.00104 | 0.03231 | 60 | 3 | 9 | 0.99695 | 0.000310 | 0.01762 | 60 | 2 | 15 | 0.99658 | 0.000388 | 0.0197 | |
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Wang and Singh | 50 | 2 | 9 | 0.995 | 0.000405 | 0.02013 | 60 | 1 | 9 | 0.99358 | 0.000599 | 0.02447 | 60 | 2 | 3 | 0.99388 | 0.000571 | 0.02389 |
55 | 2 | 9 | 0.99593 | 0.000367 | 0.01916 | 60 | 1.5 | 9 | 0.99847 | 0.000151 | 0.01228 | 60 | 2 | 6 | 0.99336 | 0.000649 | 0.02548 | |
60 | 2 | 9 | 0.99846 | 0.000158 | 0.01259 | 60 | 2 | 9 | 0.99774 | 0.000231 | 0.01519 | 60 | 2 | 9 | 0.99927 | 0.000730 | 0.00855 | |
65 | 2 | 9 | 0.99805 | 0.000176 | 0.01328 | 60 | 2.5 | 9 | 0.99673 | 0.000282 | 0.01681 | 60 | 2 | 12 | 0.98791 | 0.00117 | 0.03419 | |
70 | 2 | 9 | 0.03501 | 0.00123 | 0.03501 | 60 | 3 | 9 | 0.99904 | 0.0000931 | 0.00965 | 60 | 2 | 15 | 0.99672 | 0.000341 | 0.01848 | |
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Approximation of diffusion | 50 | 2 | 9 | 0.99501 | 0.000427 | 0.02067 | 60 | 1 | 9 | 0.99378 | 0.000621 | 0.02492 | 60 | 2 | 3 | 0.993 | 0.000687 | 0.02621 |
55 | 2 | 9 | 0.99587 | 0.000396 | 0.01991 | 60 | 1.5 | 9 | 0.99848 | 0.000161 | 0.01268 | 60 | 2 | 6 | 0.99332 | 0.000700 | 0.02645 | |
60 | 2 | 9 | 0.9984 | 0.000176 | 0.01326 | 60 | 2 | 9 | 0.99755 | 0.000269 | 0.01639 | 60 | 2 | 9 | 0.99924 | 0.0000812 | 0.00901 | |
65 | 2 | 9 | 0.998 | 0.000189 | 0.01375 | 60 | 2.5 | 9 | 0.99674 | 0.000302 | 0.01737 | 60 | 2 | 12 | 0.98754 | 0.0013 | 0.03602 | |
70 | 2 | 9 | 0.98392 | 0.0013 | 0.03602 | 60 | 3 | 9 | 0.99908 | 0.0000936 | 0.00967 | 60 | 2 | 15 | 0.99671 | 0.000373 | 0.01931 | |
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Midilli et al. | 50 | 2 | 9 | 0.99366 | 0.000574 | 0.02397 | 60 | 1 | 9 | 0.99405 | 0.000641 | 0.02531 | 60 | 2 | 3 | 0.69049 | 0.03206 | 0.17904 |
55 | 2 | 9 | 0.30344 | 0.07171 | 0.26779 | 60 | 1.5 | 9 | 0.99855 | 0.000165 | 0.01283 | 60 | 2 | 6 | 0.31333 | 0.07752 | 0.27843 | |
60 | 2 | 9 | 0.99915 | 0.000101 | 0.01004 | 60 | 2 | 9 | 0.99905 | 0.000112 | 0.01056 | 60 | 2 | 9 | 0.33137 | 0.07721 | 0.27787 | |
65 | 2 | 9 | 0.38454 | 0.06274 | 0.25048 | 60 | 2.5 | 9 | 0.99716 | 0.000284 | 0.01684 | 60 | 2 | 12 | 0.16359 | 0.09434 | 0.30715 | |
70 | 2 | 9 | 0.98799 | 0.00103 | 0.03214 | 60 | 3 | 9 | 0.99919 | 0.0000869 | 0.00932 | 60 | 2 | 15 | 0.43633 | 0.07038 | 0.2653 | |
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Modified page | 50 | 2 | 9 | 0.97907 | 0.0017 | 0.0412 | 60 | 1 | 9 | 0.98064 | 0.00181 | 0.0425 | 60 | 2 | 3 | 0.99839 | 0.0001.0 | 0.01226 |
55 | 2 | 9 | 0.99489 | 0.000461 | 0.02146 | 60 | 1.5 | 9 | 0.99206 | 0.000783 | 0.02797 | 60 | 2 | 6 | 0.99895 | 0.000103 | 0.01013 | |
60 | 2 | 9 | 0.99472 | 0.000542 | 0.02327 | 60 | 2 | 9 | 0.99622 | 0.000386 | 0.01965 | 60 | 2 | 9 | 0.99367 | 0.000633 | 0.02517 | |
65 | 2 | 9 | 0.99165 | 0.000756 | 0.0275 | 60 | 2.5 | 9 | 0.98102 | 0.00164 | 0.04051 | 60 | 2 | 12 | 0.999 | 0.0000990 | 0.00995 | |
70 | 2 | 9 | 0.96146 | 0.00293 | 0.05409 | 60 | 3 | 9 | 0.99003 | 0.000962 | 0.03102 | 60 | 2 | 15 | 0.99471 | 0.000551 | 0.02346 | |
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Weibull distribution | 50 | 2 | 9 | 0.99578 | 0.000383 | 0.01956 | 60 | 1 | 9 | 0.99477 | 0.000563 | 0.02373 | 60 | 2 | 3 | 0.99866 | 0.000139 | 0.01177 |
55 | 2 | 9 | 0.99762 | 0.000245 | 0.01565 | 60 | 1.5 | 9 | 0.9986 | 0.000159 | 0.01262 | 60 | 2 | 6 | 0.99961 | 0.0000444 | 0.00666 | |
60 | 2 | 9 | 0.99915 | 0.000101 | 0.01005 | 60 | 2 | 9 | 0.99896 | 0.000123 | 0.01107 | 60 | 2 | 9 | 0.99941 | 0.0000678 | 0.00823 | |
65 | 2 | 9 | 0.99802 | 0.000201 | 0.01419 | 60 | 2.5 | 9 | 0.99722 | 0.000277 | 0.01665 | 60 | 2 | 12 | 0.99912 | 0.0000994 | 0.00997 | |
70 | 2 | 9 | 0.98706 | 0.00111 | 0.03336 | 60 | 3 | 9 | 0.99918 | 0.0000884 | 0.0094 | 60 | 2 | 15 | 0.99822 | 0.000222 | 0.0149 |
Note: “
The coefficient and constant values of the Weibull distribution model were obtained by using nonlinear regression procedure, after analyzing the Weibull distribution model according to the conditions of different drying air temperature, power density, and hot air velocity, which were shown in Table
Statistical results of Weibull distribution model and its constants and coefficients at different drying conditions.
Power density |
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In order to further describe the influence of drying variables on Weibull distribution model, the relationship between the coefficients or constants (
At hot air velocity of 2 m/s and power density of 9 w/g,
In order to verify whether the Weibull distribution model could be well predicted to the characteristics of microwave coupled with hot air drying of hawthorn slices, (
Comparison of experimental and predicted MR from the Weibull distribution model at different drying hot air temperatures.
Comparison of experimental and predicted MR from the Weibull distribution model at different drying hot air velocity.
Comparison of experimental and predicted MR from the Weibull distribution model at different microwave power density.
During the falling rate drying period, the internal resistance governed the mass transfer and the moisture transfer during drying was controlled by internal diffusion. In this case, Fick’s second law of diffusion could be used as an effective prediction. According to the drying time
Effective moisture diffusivity values of hawthorn slices.
Power density (w/g) | Hot air velocity (m/s) | Hot air temperature (°C) | Slope | Deff |
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In this paper, the effects of dry factor on moisture ratio and drying rate of microwave coupled with hot air drying were systematically studied and the reason for the drying curve trends was analyzed, under the drying conditions of hot air temperature being ranged from 50°C to 70°C, microwave density being ranged from 3 to 15 w/g, and hot air velocity being ranged from 1 to 3 m/s. In this study, it was found that the drying process occurred only in accelerating period and falling rate period and no significant constant rate drying period existed. The drying curves were fitted to 12 different drying mathematical models which were often used and it was found in this study that there were a maximum value of
Empirical constants in the drying models
Empirical coefficients in the drying models
Moisture content (d. b.) at
Equilibrium moisture content (d. b.),
Initial moisture content (d. b.),
Dimensionless moisture ratio
Experimental dimensionless moisture ratio
Predicted dimensionless moisture ratio
Number of observations
Chi-square
Coefficient of determination
Root mean square error
Number of drying constants
Drying time, min
Temperature,
Velocity, m/s
Dry basis,
Drying rate,
Effective moisture diffusivity coefficient,
Half-thickness of the slab,
Wet basis,
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was funded by the National Natural Science Foundation of China (no. 51175223). It was also financially supported by the key disciplines of the agricultural mechanization engineering of Heilongjiang Bayi Agricultural University.