Microwave–vacuum drying kinetics of carrot slices (Zheng-Wei Cui, Shi-Ying Xu, Da-Wen Sun).pdf

Journal of Food Engineering 65 (2004) 157–164

www.elsevier.com/locate/jfoodeng

Microwave–vacuum drying kinetics of carrot slices

Zheng-Wei Cui a , Shi-Ying Xu a, * , Da-Wen Sun b, *

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 X s was about 2. As 1 6 X s < 2, the experimental drying curves showed a little deviation

from the theoretical drying curves. While X s < 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 X s < 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 .

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;

Lin, Durance, & Scaman, 1999; Wadsworth, Velupillai,

& Verma, 1990; Yongsawatdigul & Gunasekaran,

1996a, 1996b).

Drying is a complex process involving simultaneous

coupled transient heat, mass and momentum transport.

They are often accompanied by chemical or biochemical

reactions and phase transformations. The drying kinet-

ics is often used to describe the combined macroscopic

and microscopic mechanisms of heat and mass transfer,

and it is aﬀected by drying conditions, types of dryer,

characteristics of materials to be dried, etc. Because on-

line measurement of temperature and moisture is di-

cult and time-consuming for microwave heating and

drying, drying kinetics models are essential for equip-

ment design, process optimization and product quality

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

the material being dried that controls the process resis-

tance, as well as on the structural and thermodynamic

assumptions made to formulate the model. Modeling of

Microwave with their ability to rapidly heat dielectric

materials is commonly used as a source of heat. In the

food industry microwave is used for heating, drying,

thawing, tempering, sterilization etc. In recent years,

microwave drying has gained popularity as an alterna-

tive drying method in the food industry. Microwave

drying is rapid, more uniform and energy ecient

compared to conventional hot-air drying (Decareau,

1985). Besides these, it dissipates energy throughout a

product, and is able to automatically level any moisture

variation within it. Microwave–vacuum drying com-

bines the advantages of both vacuum drying and

microwave drying, and it can improve energy eciency

and product quality. Microwave–vacuum drying has

been investigated as a potential method for obtaining

high-quality dried foodstuﬀs, including fruits, vegetables

* Corresponding authors.

E-mail addresses: syxu@sytu.edu.cn (S.-Y. Xu), dawen.sun@ucd.ie

(D.-W. Sun).

URL: http://www.ucd.ie/refrig

doi:10.1016/j.jfoodeng.2004.01.008

158

Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157–164

Nomenclature

c p speciﬁc heat capacity of sample (kJ/kgK)

e ð i ; j Þ error (diﬀerence) between the experimental

value and the value calculated by the model

m mass of sample (kg)

M 0 mass of dried solid (kg)

n i number of replicates of the experimental

point i

N drying rate (kg/s)

N 0 number of experimental points for each

experiment

P vacuum pressure (mbar)

Q abs energy absorbed by sample per unit time

(kW)

S E mean standard error (kg/kg db)

t microwave drying time (s)

DT temperature rise in sample (C)

T 0 initial temperature (C)

T e evaporating temperature of water at vacuum

pressure of P (C)

X 0 initial sample moisture content (kg/kg db)

X s sample moisture content (kg/kg db)

X w sample moisture content obtained by theo-

retical calculation (kg/kg db)

X s ð i ; j Þ moisture content at experiment point i and at

replicate j

X s ð i Þ mean moisture content at experiment point i

Subscripts

r p

latent heat of evaporation of water at vacuum

pressure of P (kJ/kg)

experiment point

S R

standard error between experimental point

and theoretically calculated value (kg/kg db)

replicate

drying is usually complicated by the fact that more than

one mechanism may contribute to the total mass

transfer rate and that the contributions from diﬀerent

mechanisms may change during the drying process.

Modeling of microwave heating has made signiﬁcant

progress in recent years (Chen, Singh, Haghighi, &

Nelson, 1993; Khraisheh, Cooper, & Magee, 1997; Lin,

Anantheswaran, & Puri, 1995; Oliveira & Franca, 2003;

Yand & Gunasekaran, 2001). It involves coupling the

models for microwave power absorption and tempera-

ture distribution inside the product. Modeling of

microwave drying has also made some progress in recent

years (Doland & Datta, 1993; Jansen & van der Wek-

ken, 1991; Lefeuvre, 1981; Lu, Tang, & Liang, 1998; Lu,

Tang, & Ran, 1999; Ofoli & Komolprasert, 1988;

Turner, 1994), in which the models developed range

from complicated coupled heat, mass and wave equa-

tions to empirical models expressing mass transfer

through parameters of phenomenological nature incor-

porating most process parameters aﬀecting microwave

drying, such as microwave power and vacuum. How-

ever, few literatures focus on modeling of microwave–

vacuum heating or drying. Lian, Harris, Evans, and

Warboys (1997) described the coupled heat and mois-

ture transfer during microwave–vacuum drying. The

models developed consider the moisture transfer as a

combination of simultaneous water (liquid) and vapor

transfer. Kiranoudis, Tsami, and Maroulis (1997) stud-

ied the mathematical model of microwave vacuum

drying kinetics of some fruits. An empirical mass

transfer model, involving a basic parameter of phe-

nomenological nature, was used and the inﬂuence of

process variables was examined by embodying them to

the model-drying constant. Unfortunately Kiranoudis

et al. (1997) only dried the materials without rotating,

resulting in non-uniform heating. Furthermore, micro-

wave vacuum drying process at later stages of drying

had not been well investigated.

In the current study, microwave–vacuum drying

kinetics of carrot slices is investigated by introducing a

theoretical model which is based on the balance of en-

ergy and mass. The model was tested and modiﬁed with

data produced in a laboratory microwave–vacuum dryer

using non-linear regression analysis. The study involved

a wide range of microwave power and vacuum pressure

levels.

2. Mathematical model

In microwave heating or drying, the microwave

emitted radiation is conﬁned within the cavity and there

is hardly heat loss by conduction or convection so that

the energy is mainly absorbed by a wet material placed

in the cavity. Furthermore, this energy is principally

absorbed by the water in the material, causing the

temperature to rise, some water to be evaporated, and

the moisture level to be reduced.

In our study, a theoretical model is proposed. The

model is based on the energy conservation of the sen-

sible heat, latent heat and source heat of microwave

power. The energy conservation equation is written as

Q abs t ¼ c p m ð T e T 0 Þþ r p Dm

ð 1 Þ

The mass balance equation is written as

Dm ¼ M 0 ð X 0 X w Þ

ð 2 Þ

Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157–164

159

is somewhat diﬀerent from the rated capacity that is

stated in the manufacturer’s literature, and this may be

due to a number of reasons such as magnetron ageing

and heating eﬀects. As the magnetron ages, it takes the

ﬁlament a longer time to reach the emission condition.

The power variations may also occur if the magnetron is

operated for a long period of time, as the prolonged

heating of the permanent magnets (which is part of the

magnetron) causes a reduction in the magnetic ﬁeld and

hence a reduction in the operation voltage, which in turn

leads to the reduction in the power output. Therefore, it

is essential to measure the microwave power output, and

also measures should be taken to ensure no variation in

power output. In designing our lab microwave–vacuum

dryer, cooling of the magnetron and transformer has

been enhanced for maintaining the constant power

output by the introduction of two big electric fans.

In this study, the measurement of power output of the

microwave–vacuum dryer was determined calorimetri-

cally, which was to measure the change of temperature

of a known mass of water (1000 g) for a known period

of time. The increase in temperature of water per unit

time could be given by

Q abs ¼ mC p DT

Temperature

Moisturte Content

Drying time t (min)

Fig. 1. Temperature of carrot slices during drying: power ¼ 336.5 W,

P ¼ 30 mbar, initial sample weight ¼ 220 g.

Combining Eqs. (1) and (2), the moisture content of

samples, X w (dry basis), is correlated with drying time, t,

by the following equation:

X w ¼

X 0 M 0 Q abs t c p m ð T e T 0 Þ

r p

ð 3 Þ

M 0

In microwave–vacuum drying, because the preference

vacuum pressure ranges from 25 to 45 mbar, the evap-

orating temperature of water T e is between 20 and 31 C.

During drying, the temperature is the saturation tem-

perature of water in food corresponding to the vacuum

used. This assumption is veriﬁed in the experiments. Fig.

1 also shows that sample temperature of about 30 C

during the period of X s P2 was close to the saturation

temperature of water at the vacuum pressure of 30

mbar. Compared to the value of r p Dm, the value of

c p m ð T e T 0 Þ is small so that Eq. (3) can be reduced to

X w ¼ X 0 Q abs

¼ 4187 DT

ð 6 Þ

M 0 r p t

ð 4 Þ

Eq. (6) assumes that the energy absorption was solely

due to the microwave energy, and there was no heat gain

or loss to the surroundings, furthermore, c p of water did

not change with temperature.

The standard procedure described by Schiﬀmann

(1987) was used to determine the power output.

Deionised water weighing 1000 g and equilibrating at

temperature of 5 C below room temperature, was he-

ated in the microwave–vacuum dryer at full power, 80%

full power and 50% full power, respectively. Heating was

continued for a period of time until the ﬁnal tempera-

ture of the water load reached 5 C above room tem-

perature (18 C). The water temperatures before and

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

deviation of power output was reported. In the current

study, the power output for full power, 80% full power

and 50% full power were 336.5 ± 1.7, 267.5 ± 2.1 and

162.8 ± 2.3 W, respectively.

Conventionally, the drying rate, N, is deﬁned as

N ¼ M 0 dX w

¼ Q abs

r p

ð 5 Þ

3. Material and methods

3.1. Drying equipment

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-

where (Cui et al., 2003). The rotation speed of the

turntable was 5 rpm.

3.3. Experimental procedure

A batch of fresh carrot was purchased from local

market. The initial moisture content of the carrot was

7.68 (dry basis) which was measured according to the

vacuum oven method (AOAC, 1995). Before drying, the

carrot was cut into slices of 3–5 mm and their weight

was determined by means of an electronic balance

3.2. Microwave power output measurement

Microwave ovens are usually classiﬁed according to

their power rating. In general, microwave power output

160

Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157–164

(Model MP2000D, Shanghai Electronic Balance

Instrument Co. Ltd., Shanghai, China). The sample was

spread in a single layer in a dish made of tetraﬂuoro-

ethylene and rotated with the turntable and then the

appropriate experimental conditions (vacuum and

microwave power) were imposed. For each experiment,

the vacuum was interrupted and the sample was taken

out and then weighed by electronic balance every 3 min

and the sample was dried until the moisture content was

less than 10% (wet basis) (continuous drying experiment

on similar weight was conducted to examine the eﬀect of

this interruption during drying on weight loss and it was

found the eﬀect was negligible). All the measurements

were taken within 1 min. The moisture of the dried

sample at the end of every drying period was calculated

according the loss of weight and value of initial moisture

content. Compared to the evaporation heat, the sensible

heat lost due to the above interruption was small and

could be neglected.

Microwave–vacuum drying experiments were carried

out for three levels of microwave power (336.5, 267.5,

162.8 W) and three levels of vacuum pressure (30, 51, 71

mbar). The lower power levels were obtained with the

magnetron being cycled between on and oﬀ. Three

replicates were carried out for each experiment, and the

mean value and standard error of moisture content at

each experimental point were determined. The experi-

mental data points and the process conditions are pre-

sented in Figs. 2–4. In these ﬁgures, the mean standard

error of the moisture content (experimental error, S E )

for each experimental point is presented. The standard

error (S R ) between the experimental and theoretical

calculated values is also shown. The equations for cal-

culating S E and S R are given below:

Experimental curve

Theoretical curve

(a)

Drying time t (min)

Experimental curve

Theoretical curve

(b)

Drying time t (min)

Experimental

curve

Theoretical curve

P N 0

i ¼ 1

n i 1 P n i

j ¼ 1 ð X s ð i ; j Þ X s ð i Þ Þ 2

S E ¼

ð 7 Þ

N 0

n i

e ð i ; j Þ

n i ð N 0 1 Þ

(c)

Drying time t (min)

S R ¼

ð 8 Þ

Fig. 2. Drying curves of carrot slices at examined vacuum pressure

having power output at 336.5 W. (a) P ¼ 30 mbar, initial sample

weight ¼ 220.20 g, X s P2, S R ¼ 0 : 056, S E ¼ 0 : 072; X s < 2, S R ¼ 0 : 366,

S E ¼ 0 : 091; (b) P ¼ 51 mbar, initial sample weight ¼ 220.55 g, X s P2,

S R ¼ 0 : 094, S E ¼ 0 : 078; X s < 2, S R ¼ 0 : 433, S E ¼ 0 : 089; (c) P ¼ 71

mbar, initial sample weight ¼ 220.55 g, X s P2, S R ¼ 0 : 100, S E ¼ 0 : 083;

X s < 2, S R ¼ 0 : 501, S E ¼ 0 : 097.

i ¼ 1

j ¼ 1

where n i is the number of replicates of the experimental

point i, N 0 is the number of experimental points for each

experiment, X s ð i ; j Þ is the moi st ure content at experiment

point i and at replicate j, X s ð i Þ is the mean moisture

content at experiment point i and e ð i ; j Þ 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

energy can be wholly absorbed by the load and therefore

little amount of the energy reﬂects back to the magne-

tron. Since the load level had a little eﬀect on the

absorption of microwave energy, the sample load was

reduced for the lower microwave power settings (267.5

and 162.8 W) in order to shorten the experiment time.

4. Results and discussion

Table 1 shows the weight loss of fresh carrot slices

dried for 3 min at microwave power of 336.5 W. The

results indicate that the load absorbed almost the same

quantity of microwave energy at diﬀerent load levels,

Z.-W. Cui et al. / Journal of Food Engineering 65 (2004) 157–164

161

Experimental curve

Theoretical curve

Experimental curve

Theoretical curve

(a)

Drying time t (min)

Experimental curve

Theoretical curve

(b)

Drying time t (min)

(b)

Drying time t (min)

Experimental curve

Theoretical curve

Experimental curve

Theoretical curve

(c)

Drying time t (min)

(c)

Drying time t (min)

Fig. 4. Drying curves of carrot slices at examined vacuum pressure

having power output at 162.8 W. (a) P ¼ 30 mbar, initial sample

weight ¼ 220.30 g, X s P2, S R ¼ 0 : 095, S E ¼ 0 : 078; X s < 2, S R ¼ 0 : 729,

S E ¼ 0 : 096; (b) P ¼ 51 mbar, initial sample weight ¼ 180.10 g, X s P2,

S R ¼ 0 : 136, S E ¼ 0 : 126; X s < 2, S R ¼ 0 : 441, S E ¼ 0 : 129; (c) P ¼ 71

mbar, initial sample weight ¼ 161.20 g, X s P2, S R ¼ 0 : 088, S E ¼ 0 : 823;

X s < 2, S R ¼ 0 : 554, S E ¼ 0 : 108.

Fig. 3. Drying curves of carrot slices at examined vacuum pressure

having power output at 267.5 W. (a) P ¼ 30 mbar, initial sample

weight ¼ 220.10 g, X s P2, S R ¼ 0 : 075, S E ¼ 0 : 106; X s < 2, S R ¼ 0 : 054,

S E ¼ 0 : 092; (b) P ¼ 51 mbar, initial sample weight ¼ 210.25 g, X s P2,

S R ¼ 0 : 054, S E ¼ 0 : 081; X s < 2, S R ¼ 0 : 506, S E ¼ 0 : 111; (c) P ¼ 71

mbar, initial sample weight ¼ 205.40 g, X s P2, S R ¼ 0 : 074, S E ¼ 0 : 095;

X s < 2, S R ¼ 0 : 404, S E ¼ 0 : 120.

2. Thus, the computed theoretical drying curves can be

plotted by Eq. (4) which are illustrated in Figs. 2–4.

By examining Eqs. (4) and (5), it can be found that

the drying rate is a constant during the whole micro-

wave–vacuum drying period. From Figs. 2–4, it is clear

that the experimental drying curves agree with the

computed theoretical drying curves in the period of

X s ð or X w Þ P2, indicating an initial constant drying rate

period. At moisture content X s ¼ 2, N begins to fall with

further decrease in X s . Therefore, X s ¼ 2 is the so-called

critical moisture content. The drying rate in the constant

Eqs. (4) and (5) are regarded as the theoretical drying

kinetic model and theoretical drying rate kinetic model

for microwave–vacuum drying respectively. For the

vacuum range from 30 to 71 mbar used in the experi-

ments, the latent heat of evaporation of water slightly

decreased from 2438 to 2403 kJ/kg. By using Eq. (1), the

quantity of water evaporated within 3 min at diﬀerent

microwave power output levels and vacuum pressure

levels can be calculated and the results are shown in Table

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