mass transfer characteristics during convective, microwave and combined microwave–convective...

Research ArticleReceived: 15 October 2011 Revised: 23 April 2012 Accepted: 31 May 2012 Published online in Wiley Online Library:

(wileyonlinelibrary.com) DOI 10.1002/jsfa.5786

Mass transfer characteristics duringconvective, microwave and combinedmicrowave–convective drying of lemon slicesMorteza Sadeghi,∗ Omid Mirzabeigi Kesbi and Seyed Ahmad Mireei

Abstract

BACKGROUND: The investigation of drying kinetics and mass transfer phenomena is important for selecting optimum operatingconditions, and obtaining a high quality dried product. Two analytical models, conventional solution of the diffusion equationand the Dincer and Dost model, were used to investigate mass transfer characteristics during combined microwave-convectivedrying of lemon slices. Air temperatures of 50, 55 and 60 ◦C, and specific microwave powers of 0.97 and 2.04 W g−1 were theprocess variables.

RESULTS: Kinetics curves for drying indicated one constant rate period followed by one falling rate period in convective andmicrowave drying methods, and only one falling rate period with the exception of a very short accelerating period at thebeginning of microwave-convective treatments. Applying the conventional method, the effective moisture diffusivity variedfrom 2.4 × 10−11 to 1.2 × 10−9 m2 s−1. The Biot number, the moisture transfer coefficient, and the moisture diffusivity,respectively in the ranges of 0.2 to 3.0 (indicating simultaneous internal and external mass transfer control), 3.7 × 10−8 to4.3 × 10−6 m s−1, and 2.2 × 10−10 to 4.2 × 10−9 m2 s−1 were also determined using the Dincer and Dost model.

CONCLUSIONS: The higher degree of prediction accuracy was achieved by using the Dincer and Dost model for all treatments.Therefore, this model could be applied as an effective tool for predicting mass transfer characteristics during the drying oflemon slices.c© 2012 Society of Chemical Industry

Keywords: lemon; mass transfer; microwave–convective drying; moisture diffusivity

INTRODUCTIONAlthough juice production is the most important process for citrusfruits,1 the development of a drying process for the productionof powders, flakes and slices also promotes their consumption.2

Lemon (Citrus limon (L.) Burm. f) and lime (Citrus aurantiflia (Chrism)Swing.) are two of the most familiar citrus fruits grown, withexcellent quality in semi-arid irrigated and coastal areas.3 In 2008,Iran, with an annual production of about 695 000 tonnes of lemonand lime, was the sixth producing country in the world.4 Thetraditional method of open-sun drying is still practised for Iranianlime and lemon dehydration. In this method, exposure to sunlight isrequired so that a characteristic flavour and moisture are achieved.However, the process faces a problem of hygiene; also, the productquality fluctuates in very humid climates.5

In spite of the considerable number of studies reported inthe literature for drying various agricultural products, studiesperformed on lemon drying are limited and researchers have notaddressed this matter adequately. Chen et al.5 used a closed-typesolar dryer to dehydrate lemon slices and studied its effect onquality parameters of the dried product.

Drying is a complicated process of simultaneous heat andmass transfer phenomena. A significant number of mechanismshave been proposed to explain moisture transportation withinthe porous materials during drying. Nevertheless, diffusionmechanisms have been mostly used to interpret experimental

observations through various models.6 Moisture diffusivity andmoisture transfer coefficient are two important mass transferparameters. Moisture diffusivity is required for calculating andmodelling of the drying process. However, according to the exper-imental measurement techniques and analysis methods, data aredependent on researcher.7 Zogzas et al.8 reviewed the reportedexperimental moisture diffusivity data in foodstuff materials.

Researchers have mostly characterised the moisture diffusivitybased on adopting a numerical solution of a diffusion equation forhomogenous materials and proposed simplified models for thedetermination of moisture diffusivity from experimental dryingcurves.6,9 – 16 However, the use of different models could resultin significant differences in the calculated values of moisturediffusivity.

Dincer and Dost17,18 developed and verified an analyticalmodel to determine mass transfer coefficients for both regularand irregular shaped objects during drying. They introduceddrying parameters, namely drying coefficients and lag factors,

∗ Correspondence to: Morteza Sadeghi, Department of Farm Machinery, Collegeof Agriculture, Isfahan University of Technology, Isfahan 84156-83111, Iran.E-mail: [email protected]

Department of Farm Machinery, College of Agriculture, Isfahan University ofTechnology, Isfahan 84156-83111, Iran

J Sci Food Agric (2012) www.soci.org c© 2012 Society of Chemical Industry

www.soci.org M Sadeghi, O Mirzabeigi Kesbi, SA Mireei

based on an analogy between cooling and drying profiles, andboth these factors exhibit an exponential function with time.McMinn et al.7 evaluated moisture diffusivity and moisture transfercoefficient of slab and cylindrical potato samples by adopting thismodel. The samples were dried under convective, microwave andcombined convective–microwave conditions. The results showeda reasonably good agreement between the values predicted fromthe correlation and the experimental observations.

Employing microwave power radiation in the drying processcauses internal rapid heating as a result of friction generatedby dipoles (polar molecule, such as water) rotating and ionmovement in the drying body. This heating method is particularlyadvantageous in thermal drying, since favourable properties ofwater and other polar liquids cause heat to be generated inthe wet parts of the drying material and, hence, moisture tobe extracted.19 This method considerably reduces drying time.However, when internal heating extracts moisture to the surface,the presence of a convective flow can remove it from the surfacerapidly. Therefore, the combined microwave–convective methodcould be more useful.20 – 24

This study aimed to investigate and compare mass transfercharacteristics of lemon slices dried under convective, microwaveand combined microwave–convective conditions by using twoanalytical methods: (1) conventional solution of the diffusionequation, and (2) the Dincer and Dost model.

MATERIALS AND METHODSSample preparationLemon samples were obtained from a local market in Isfahan(central Iran) and stored at 6 ◦C until the experiments wereconducted. Prior to the drying experiments, lemons were placedat room temperature for 24 h and cut perpendicular to the fruitaxis in approximately equal slices (5 mm thick and 50 ± 3 mmdiameter). Lemon slices (with peel) had the initial moisture contentof about 85% wet basis (W.B.), which was determined by vacuumdrying method at 70 ◦C until constant weight was achieved.25

Biochemical analyses were also conducted to provide data onchemical composition of the raw material according to AOAC.25

Water content, carbohydrates, fat, protein, fibre, and ash were950.96, 18.7, 17.2, 2.9, 2.1 and 2.2 g kg−1 lemon flesh, respectively.

Experimental set-upThe schematic diagram of the drying system and instrumentationused to conduct the experiments are shown in Fig. 1. A 2450 MHzdomestic microwave oven (LG, MC-8047; LG Electronics Inc., Seoul,South Korea) with 180, 360, 540, 720 and 900 W power and cavitydimensions of 400 (width) × 380 (depth) × 260 (height) mm wasmodified and developed as the microwave-assisted hot-air dryer.Since these ranges are the nominal power values, the accuratepower of the system for two desired levels in the experiments(180 and 360 W) was measured by the IMPI-2 litre test powermeasurement procedure test.26 The power measurement was runthree times and the final power was reported as the mean of threereadings. In this way, the accurate powers corresponding to thenominal values of 180 and 360 W were determined as 185.5 and388.5 W, respectively.

In the centre of the oven chamber base, a circular area of 170 mmdiameter was drilled in regular 4 mm diameter holes. A cone shapepipe was fixed at the drilled area from bottom to supply hot air tothe chamber. The sample basket (200 × 200 mm) was suspendedby nylon wires from a digital balance (Kern 572-57, with ±0.1 gaccuracy; KERN & Sohn GmbH, Balingen, Germany) bracket righttop of the holes in the chamber. Therefore, continuous sampleweight monitoring was possible. The sample weights were sentto the PC through a RS232 port and recorded there. Also, for theair outlet a rectangular area (60 × 100 mm) was drilled in regular5 mm holes in the left wall of the chamber and a duct was fixed tolead the air out.

The drying air was supplied by a centrifugal fan, powered bya 2 hp three-phase motor. The air was blown by a blower into anelectrical heater through an 80 mm diameter metal duct. A one-to three-phase frequency inverter (TECO, 7300 CV, with ±0.01 Hzaccuracy; TECO Electric & Machinery Co. Ltd., Taipei, Taiwan) wasused to adjust and control the airflow rate in the range of 0–0.4 m3

s−1. Ten 0.7-kW electrical coils were used in the heating chamberto supply enough thermal energy to heat up the drying air tothe desired temperature. The coils were connected to the electricmains (power supply) through a temperature controller. Thecontroller was designed to control the temperature of hot air withan accuracy of ±0.1 ◦C and acted accordingly to increase/decreasethe electrical current to the heating elements. The temperature of

Inverter

Blower

Power supply

Balance

Sample basket

Air outlet

MC oven

Nylon wire

Temperature sensor

Electric heater

Control unit

PC

Figure 1. A schematic view of the experimental microwave–convective drying set-up.

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the inlet hot air was measured by a thermometer (PT100, 0.1 ◦Cresolution; Testo GmbH & Co., Lenzkirch, Germany).

Prior to the drying tests, the air velocity was measured underthe basket (top of the holes) in the centre of the circular area byan anemometer (LT lutron, AM-4204, with ±0.1 m s−1 accuracy;Lutron Electronic Enterprise Co., Ltd., Taipei, Taiwan) and wasadjusted through changing the coming electrical frequency tothe blower by the inverter. An ultrasonic humidifier equippedwith a microcontroller was used to adjust and control the relativehumidity of the isolated drying room where the experiments wereconducted. The ambient relative humidity was measured by asensor (Philips H8302 model; Philips Electronics, Eindhoven, TheNetherlands) with an accuracy of ±2% and a linearity of ±2%, foran operating range of 20–95% relative humidity.

Drying proceduresFor each experiment, about 190 g of initial sample (10 sliceswith peel around) was placed in the holding basket (monolayer)floor. Experiments were carried out by using three methods:(1) convective (hot air) drying at the inlet hot air temperatures of50, 55 and 60 ◦C; (2) microwave drying at a power of 185.5 W(specific microwave power of 0.97 W g−1); and (3) combinedmicrowave–convective drying at inlet hot-air temperatures of 50,55 and 60 ◦C, and microwave powers of 185.5 and 388.5 W (specificmicrowave powers of 0.97 and 2.04 W g−1, respectively) with threereplicates. All experiments were performed by the set-up shown inFig. 1 with microwave power being off in the convective method,and the blower/heater being off in the microwave drying method.The treatments were dried until reaching a final moisture contentof approximately 0.15 g g−1 dry basis (D.B.). The air velocity (insidethe cavity; under the basket) and relative humidity were kept atconstant levels of 1.5 m s−1 and 25%, respectively. By continuoussample weight monitoring during the process, drying rate curves(drying rate vs. moisture content) were available.

Theoretical basisTwo analytical models, conventional solution of the second Fickequation for infinite plane sheet and the Dincer and Dost model,were performed to determine and evaluate the mass transfercharacteristics of lemon slices. In these models, the moistureratio (MR) is defined as MR = (M − Me)/(M0 − Me), where M isthe moisture content of the product at each moment, M0 is theinitial moisture content of the product, and Me is the equilibriummoisture content. The equilibrium moisture content was measuredby having the samples dry in the apparatus for an extended periodof time until no significant weight loss was detected.

Conventional solution of the diffusion equationMany authors have used Crank’s solution of the second Fickequation for sheet (slab), sphere, and cylinder to determineeffective moisture diffusivity of several crops. Thin-layer drying ofmaterials is usually simulated with the solution of the equation foran infinite plane sheet, whose definition is described by Equation 1as follows:

MR = 8

π2

∞∑n=0

1

(2n + 1)2 exp

[−(2n + 1)2 π2

4

Defft

L2

](1)

where Deff is the effective moisture diffusivity (m2 s−1), L is thehalf thickness of the plane sheet (m), n is the number of terms

of the Fourier series, MR is the moisture ratio (dimensionless),and t is the drying time (s). In this study, the effectivemoisture diffusivities of lemon slices were calculated using thedimensionless moisture ratio by taking into account the first fiveterms of the series.

The Dincer and Dost modelApplying a number of assumptions, such as constant thermo-physical properties and negligible effect of heat transfer onmass transfer, Dincer and Dost17 proposed another solutionfor the one-dimensional transient diffusion equation. Based ondifferent initial and boundary conditions for infinite slab, infi-nite cylinder and sphere, the governing equations were solvedand further simplified to give the dimensionless moisture ratioat any point of the product. This was developed to providea simple but efficient tool for predicting the mass transferparameters during drying operations. Drying coefficient, Biotnumber, moisture diffusivity, and moisture transfer coefficientare four significant mass transfer characteristics obtained by thismethod.

To apply the Dincer and Dost model for dehydrating lemonslices, which were considered as an infinite slab, in the first step,experimental drying data, i.e. the dimensionless moisture ratio(MR), were fitted to Equation 2, by which MR is defined in terms ofthe drying coefficient and dimensionless lag factor:

MR = J1 exp(−St) (2)

where J1 is the lag factor (dimensionless) and S is the dryingcoefficient (s−1). By determining J1 values, the dimensionless Biotnumber (Bi) was calculated from Equation 3:

J1 = exp

(0.2533 × Bi

1.3 + Bi

)(3)

Then, moisture diffusivity was obtained by using Equation 4 asfollows:

D = S × L2

µ21

(4)

where D is the moisture diffusivity (m2 s−1), L is the half thicknessof slab (m) and µ1 is the root of the transcendental characteristicequation (dimensionless). For the purpose of practical dryingapplications, a simplified expression (Equation 5) was developedto calculate µ1 with respect to Biot number for infinite slabgeometry:

{µ1 = π

2 Bi ≥ 100

µ1 = tan−1(0.640443 Bi + 0.380397) 0 < Bi < 100(5)

Finally, the moisture transfer coefficient was determined byEquation 6:

km = Bi × D

L(6)

where km is the moisture transfer coefficient (m s−1).

Error analysisThe goodness of fitting experimental drying data to modelsequations was evaluated by means of coefficient of determination

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(R2), and the root mean square of error (RMSE) as follows:

R2 =

n∑i=1

(MRpre,i − MR)2

n∑i=1

(MRexp,1 − MR)2

= 1 −

n∑i=1

(MRexp,i − MRpre,i)2

n∑i=1

(MRexp,i − MR)2

(7)

and

RMSE =[

1

n

n∑i=1

(MRexp,i − MRpre,i)2

]1/2

(8)

where MRexp,i is the i-th experimental moisture ratio, MRpre,i is thei-th predicted moisture ratio, MR is the average of all experimentalmoisture ratios, and n is the number of observations. Allmathematical operations were performed with MATLAB software.

RESULTS AND DISCUSSIONDrying kinetics and mass transferThe investigation of drying kinetics and internal–external masstransfer rate is important for controlling the process, selecting theoptimum operating conditions, and obtaining dried productswith an acceptable quality. Drying durations of lemon slicesunder different drying conditions (average of three replications±1 standard deviation) are shown in Table 1. The results show thatapplying microwave power reduced drying time considerably.The same results have been reported for several natural materialssuch as grape,20 apple and mushroom,21 banana,22 orange slices2

and apple and strawberry.15 Microwave radiation causes bipolarmolecules to rotate with high frequency into the lemon slices.Because of friction against the bipolar rotation, the heat generatedinside the slices causes moisture to be diffused outside. Due to thehigh value of moisture content in the lemon slices, employingmicrowave power during drying improves moisture diffusionconsiderably. In combined drying treatments, the presence ofthe hot-air flow helps moisture extract and leave the slicessurface. Therefore, drying time was reduced about 17 and 31times, respectively, when applying 0.97 and 2.04 W g−1 microwavepower as compared with convective drying method (average ofthree temperatures).

Examples of drying rate curves (drying rate vs. moisture content)are illustrated in Fig. 2 for combined microwave–convective (0.97and 2.04 W g−1, 55 ◦C), and in Fig. 3, for convective (50, 55 and60 ◦C) and microwave (0.97 W g−1) treatments. As expected,drying rate under the combined method was higher than thatfor microwave, and much greater than the drying rate for theconvective method. In the initial stage of dehydration under thecombined drying method, the maximum drying rate took placeafter a short delay (Fig. 2). This delay indicates the warming-upperiod, which is due to the short drying duration for combinedtreatments. Because of the long drying time in the convectivedrying method, this period had a low share of total drying durationand, hence, was not observable in drying rate curves.

As shown, in combined drying treatments (Fig. 2), drying ratecurves had only one falling rate period with the exception of a

Table 1. Drying durations for convective, microwave and combineddrying of lemon slices

Hot-airtemperature ( ◦C)

Specific microwavepower (W g−1)

Dryingduration (min)

50 0 1850 ± 70a

55 0 1150 ± 56

60 0 980 ± 61

50 0.97 80 ± 3

55 0.97 78 ± 2

60 0.97 73 ± 4

50 2.04 44 ± 1

55 2.04 45 ± 3

60 12.04 38 ± 1

– 0.97 145 ± 7

a Results are given as the mean ±1 SD.

Figure 2. Variations in drying rate with moisture content for lemon slicesdehydrated under combined microwave–convective drying method atinlet hot air temperature of 55 ◦C.

very short accelerating period (warming-up) at the start. This is inaccordance with prior microwave-assisted drying studies.14,27 – 29

High initial moisture content of lemon slices results in a higherabsorption of microwave, and therefore, higher drying rates.Moisture content reduction during drying decreases microwaveabsorption. As a result, a fall in the drying rate is induced. However,under convective and microwave drying methods (Fig. 3), theprocess occurred in one constant rate period followed by a fallingrate period after removing moisture content to a critical amount ofapproximately 2 g g−1 (d.b.). Drying rate in the falling rate periodinvolves two processes, including the movement of moisturewithin the material to the surface and removal of the moisturefrom the surface.30 These processes occur poorly for treatmentsdehydrated under convective and microwave drying methods,respectively.

Models application: moisture diffusivity and moisture transfercoefficientCrank’s solution methodEffective moisture diffusivity (Deff ) values of lemon slices fordifferent drying treatments were obtained by conventionalsolution of the diffusion equation as shown in Table 2. The



(a)

(b)

Figure 3. Variations in drying rate with moisture content for lemon slicesdehydrated under convective (50, 55 and 60 ◦C) and microwave (0.97 Wg−1) drying methods.

goodness parameters of fits (R2 and RMSE) are also given in thetable. The lowest value of R2 (0.756) and the highest value of RMSE(0.1487) were related to the microwave drying method. The reasoncould be the higher resistance to mass transfer at the surface underthis condition, which is neglected in comparison to the internalresistance of the sample in Crank’s solution method. On the otherhand, for the convective and combined microwave–convectivemethods, the air flow with velocity of 1.5 m s−1, which passes overthe samples, reduces surface resistance.

The values of Deff ranged from 2.41 × 10−11 (for convectivetreatment at 50 ◦C) to 1.25 × 10−9 m2 s−1 (for combinedmicrowave–convective treatment at 2.04 W g−1 and 60 ◦C). It isobserved that the values of Deff increased with microwave powerand drying hot-air temperature. The same results have beenreported by Wang et al.14 for apple pomace, Dadali et al.13 forspinach, and Contreras et al.15 for apple and strawberry. However,microwave power was found to have more influence on moisturediffusivity of lemon slices. In the combined microwave–convectivedrying method, Deff was increased 21 and 38 times, respectively,when applying 0.97 and 2.04 W g−1 as compared with theconvective drying method (average of three temperatures).Increasing microwave power makes bipolar molecules rotate at

Table 2. Values of effective moisture diffusivity (Deff ) for convective,microwave and combined drying of lemon slices obtained by aconventional solution of the diffusion equation

Hot-airtemperature( ◦C)

Specificmicrowave

power(W g−1) Deff (m2 s−1) R2 RMSE

50 0 2.41 × 10−11 0.9057 0.08469

55 0 2.84 × 10−11 0.8512 0.1055

60 0 2.73 × 10−11 0.7919 0.1245

50 0.97 5.45 × 10−10 0.8472 0.1073

55 0.97 5.58 × 10−10 0.8589 0.1033

60 0.97 5.78 × 10−10 0.8426 0.1078

50 2.04 1.15 × 10−9 0.8828 0.08582

55 2.04 1.12 × 10−9 0.8845 0.08988

60 2.04 1.25 × 10−9 0.872 0.09399

– 0.97 1.92 × 10−10 0.756 0.1487

R2, coefficient of determination; RMSE, root mean square error.

higher velocities. In fact, the higher electric field amplitude (whichis proportional to microwave power) inputs more force to them.Consequently, more heat is produced, which, in turn, enhancesDeff . The results confirm the principle that the increase in Deff

decreases the drying time. Values show that 21 and 38 timesincreases in Deff exert 17 and 31 times reductions in drying time.

The Dincer and Dost methodRegressing the dimensionless moisture ratio values against thedrying time in the exponential form of Equation 2 and using theleast squares curve fitting method, we obtained values of dryingcoefficient (S), and lag factor (J1) as presented in Table 3. S is aparameter indicating the drying capability of the solid object, andhas a direct effect on moisture diffusivity.7 Therefore, the dryingprocess is directly related to this parameter. The higher value of Sindicates more moisture extraction and reduction in drying time.As shown in Table 3, the drying coefficient varied from 2.01×10−5

to 1.16 × 10−3 s−1. The values of S increased with both dryinghot air temperature and microwave power. However, microwavepower had a more significant effect on drying coefficient.

The lag factor (J1) is a criterion indicating the magnitude ofthe internal resistance to moisture transfer and has a direct effecton the moisture transfer coefficient as a function of Biot number(Equation 3). For the convective drying method the increase in J1

with hot air temperature (1.035 for 50 ◦C to 1.092 for 60 ◦C) revealsthat the internal mass transfer resistance was the controlling factor.Increasing microwave power for combined treatments, however,decreased J1 at a constant temperature, confirming the reductionin the magnitude of the internal resistance. The microwave dryingmethod exhibited the highest J1 value (1.198). This confirms thatthe movement of moisture within lemon slices to the surface andremoval of the moisture from the surface are slow under thiscondition.

Using drying coefficient and lag factor values, we determinedthe Biot number (Bi), µ1, moisture diffusivity (D), and moisturetransfer coefficient (km) as indicted in Table 4. Biot number is one ofthe most important dimensionless parameters in drying, indicatingthe resistance to moisture diffusion within the material. The Bivalues were in the range of 0.204 to 3.033, indicating simultaneousinternal and external mass transfer control, which mostly occurs in



Table 3. Values of the lag factor (J1) and the drying coefficient (S) for convective, microwave and combined drying of lemon slices obtained by theDincer and Dost model

Hot-air temperature ( ◦C) Specific microwave power (W g−1) Lag factor Drying coefficient (s−1) R2 RMSE

50 0 1.035 2.01 × 10−5 0.9647 0.05207

55 0 1.067 2.60 × 10−5 0.9441 0.06524

60 0 1.092 2.65 × 10−5 0.9154 0.08019

50 0.97 1.188 5.12 × 10−4 0.9726 0.04606

55 0.97 1.160 5.14 × 10−4 0.9741 0.04491

60 0.97 1.194 5.51 × 10−4 0.9721 0.04605

50 2.04 1.182 1.04 × 10−3 0.9864 0.03002

55 2.04 1.158 1.01 × 10−3 0.9838 0.03446

60 2.04 1.189 1.16 × 10−3 0.9866 0.03123

– 0.97 1.198 1.98 × 10−4 0.9215 0.08494

Note that the lag factor is dimensionless.R2, coefficient of determination; RMSE, root mean square error.

Table 4. Values of the Biot number, the root of the transcendental characteristic equation (µ1), moisture diffusivity (D) and mass transfer coefficientfor convective, microwave and combined drying of lemon slices (km) obtained by the Dincer and Dost model

Hot-air temperature ( ◦C) Specific microwave power (W g−1) Biot number µ1 D (m2 s−1) km (m s−1)

50 0 0.204 0.473 3.560 × 10−10 3.677 × 10−8

55 0 0.447 0.588 3.006 × 10−10 6.724 × 10−8

60 0 0.692 0.689 2.233 × 10−10 7.727 × 10−8

50 0.97 2.764 1.135 1.588 × 10−9 2.195 × 10−6

55 0.97 1.839 1.000 2.054 × 10−9 1.890 × 10−6

60 0.97 3.033 1.164 1.626 × 10−9 2.466 × 10−6

50 2.04 2.525 1.107 3.397 × 10−9 4.288 × 10−6

55 2.04 1.789 0.991 4.116 × 10−9 3.681 × 10−6

60 2.04 2.806 1.140 3.568 × 10−9 5.007 × 10−6

– 0.97 1.946 1.020 7.618 × 10−10 7.413 × 10−7

Note that the Biot number and µ1 are dimensionless.

practice. In the convective drying method, Bi increased as the airtemperature increased, showing internal resistance to moisturediffusion within lemon slices. But in the combined drying method,as the microwave power increased, the Biot number decreased,consequently enhancing surface resistance.

Moisture diffusivity (D) values were between 2.233 × 10−10 and4.116 × 10−9 m2 s−1. As explained, increasing microwave powerenhances moisture diffusivity through rotating bipolar moleculesat higher velocities. It is observed that applying microwave poweraffected the magnitude of the diffusivity during microwave andcombined microwave–convective drying. Also, duplicating thepower level in the combined method improved diffusivity twice.

Moisture transfer coefficient (km) values were in the range of3.677 × 10−8 to 5.007 × 10−6 m s−1. This coefficient showed thesame variation as D with the process variables, providing furtherconfirmation of the mass transfer characteristics. As shown, thelower the value of km, the longer the drying time.

Validation and comparison of modelsIn order to verify the models, their accuracy and applicabilitywere evaluated using the goodness parameters of fitting, andcomparing the experimental average dimensionless moisture ratioprofiles with the predicted ones. The goodness parameters offitting presented in Tables 2 and 3 reveal that for all treatmentsthe values of R2 and RMSE were higher and lower for the Dincer

and Dost model, as compared with corresponding values forconventional solution of the diffusion equation method. Therefore,it is concluded that application of the Dincer and Dost model canbetter predict experimental drying data for dehydration of lemonslices.

Typical experimental and predicted data for two oper-ating conditions (convective at 50 ◦C, and combined mi-crowave–convective at 2.04 W g−1, and 50 ◦C) are illustratedin Fig. 4 and Fig. 5, respectively. It is clear that for both models theagreement between experimental and predicted data was betterat microwave level of 2.04 W g−1. Comparison of models indicatesthat the predictions by the Dincer and Dost model agreed betterwith the experimental moisture ratio data. For all treatments, theaverage error between the experimental and predicted resultsvaried from 3% to 7.3% for the Dincer and Dost method, and from7.9% to 16.7% for Crank’s solution method, respectively. The worstand the best prediction belonged to the microwave method, andthe combined microwave–convective method with a microwavepower of 2.04 W g−1, respectively.

CONCLUSIONSThe main findings of this study can be summarised as:

• Applying microwave power during drying of lemon slicesreduced drying time considerably compared to the convective



Figure 4. Experimental and predicted values of average moisture ratio forlemon slices dehydrated under the convective method at 50 ◦C.

Figure 5. Experimental and predicted values of average moisture ratio forlemon slices dehydrated under combined microwave–convective methodat 2.04 W g−1 and 50 ◦C.

method. In the combined drying method, drying rate curveshad only one falling rate period with the exception of avery short accelerating period at the start. In contrast, underthe convective and microwave drying methods, the processoccurred in one constant rate period followed by a falling rateperiod.

• The values of effective moisture diffusivity were increasedwith both microwave power and air temperature. However,microwave power had more influence on moisture diffusivityof lemon slices.

• The Biot number values indicated the presence of simultaneousinternal and external resistances.

• Validation of the models revealed that the model developedby Dincer and Dost was more effective for calculating themass transfer characteristics during convective, microwaveand combined drying of lemon slices as compared withconventional solution of the diffusion equation.

ACKNOWLEDGEMENTSFinancial support for this research was received from IsfahanUniversity of Technology, which is gratefully acknowledged. Theauthors are also grateful to Dr N. Hamdami, Dept. of Food Scienceand Technology, Isfahan University of Technology, for his help andthe technical support.

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