Microwave–vacuum drying kinetics of carrot slices

Zheng-Wei Cui

, Shi-Ying Xu

a,*

, Da-Wen Sun

b,*

School of Food Science and Technology, Southern Yangtze University, Wuxi, Jiangsu 214036, PR China

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

was about 2. As 1 6 X

2, the experimental drying curves showed a little deviation

from the theoretical drying curves. While X

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

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

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 eﬃcient
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 eﬃciency
and product quality. Microwave–vacuum drying has
been investigated as a potential method for obtaining
high-quality dried foodstuﬀs, including fruits, vegetables

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 diﬃ-
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

Journal of Food Engineering 65 (2004) 157–164

www.elsevier.com/locate/jfoodeng

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

0260-8774/$ - see front matter

doi:10.1016/j.jfoodeng.2004.01.008

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

abs

¼ c

ðT

Þ þ r

ð1Þ

The mass balance equation is written as

¼ M

ðX

ð2Þ

Nomenclature

speciﬁc heat capacity of sample (kJ/kg K)

ði;jÞ

error (diﬀerence) between the experimental
value and the value calculated by the model

mass of sample (kg)

mass of dried solid (kg)

number of replicates of the experimental
point i

drying rate (kg/s)

number of experimental points for each
experiment

vacuum pressure (mbar)

abs

energy absorbed by sample per unit time
(kW)

latent heat of evaporation of water at vacuum
pressure of P (kJ/kg)

standard error between experimental point
and theoretically calculated value (kg/kg db)

mean standard error (kg/kg db)

microwave drying time (s)

temperature rise in sample (

°C)

initial temperature (

°C)

evaporating temperature of water at vacuum
pressure of P (

°C)

initial sample moisture content (kg/kg db)

sample moisture content (kg/kg db)

sample moisture content obtained by theo-
retical calculation (kg/kg db)

ði;jÞ

moisture content at experiment point i and at
replicate j

ðiÞ

mean moisture content at experiment point i

Subscripts
i

experiment point

replicate

158

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

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

(dry basis), is correlated with drying time, t,

by the following equation:

abs

ðT

ð3Þ

In microwave–vacuum drying, because the preference

vacuum pressure ranges from 25 to 45 mbar, the evap-
orating temperature of water T

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

2 was close to the saturation

temperature of water at the vacuum pressure of 30
mbar. Compared to the value of r

, the value of

ðT

Þ is small so that Eq. (3) can be reduced to

¼ X

abs

ð4Þ

Conventionally, the drying rate, N , is deﬁned as

abs

ð5Þ

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.

3.2. Microwave power output measurement

Microwave ovens are usually classiﬁed according to

their power rating. In general, microwave power output

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

abs

4187

ð6Þ

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

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.

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

Drying time t (min)

Temperature

Moisturte Content

Temperature (

C )

Moisture content X

(kg/kgdb)

Fig. 1. Temperature of carrot slices during drying: power

¼ 336.5 W,

¼ 30 mbar, initial sample weight ¼ 220 g.

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

159

(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

)

for each experimental point is presented. The standard
error (S

) between the experimental and theoretical

calculated values is also shown. The equations for cal-
culating S

and S

are given below:

¼1

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

¼1

ðX

ði;jÞ

ðiÞ

ð7Þ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

¼1

2
ði;jÞ

ðN

1Þ

ð8Þ

where n

is the number of replicates of the experimental

point i, N

is the number of experimental points for each

experiment, X

ði;jÞ

is the moisture content at experiment

point i and at replicate j, X

ðiÞ

is the mean moisture

content at experiment point i and e

ði;jÞ

is the error (dif-

ference) between the experimental value and the value
calculated by the model, i.e., Eq. (4).

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,

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.

Drying time t (min)

Moisture content (kg/kg db)

Experimental curve

Theoretical curve

Drying time t (min)

Moisture content (kg/kg db)

Experimental curve

Theoretical curve

Drying time t (min)

Moisture content (kg/kg db)

Experimental

curve
Theoretical curve

(a)

(b)

(c)

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

2, S

¼ 0:056, S

¼ 0:072; X

2, S

¼ 0:366,

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

¼ 0:094, S

¼ 0:078; X

2, S

¼ 0:433, S

¼ 0:089; (c) P ¼ 71

mbar, initial sample weight

¼ 220.55 g, X

2, S

¼ 0:100, S

¼ 0:083;

2, S

¼ 0:501, S

¼ 0:097.

160

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

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

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

ðor X

Þ P 2, indicating an initial constant drying rate

period. At moisture content X

¼ 2, N begins to fall with

further decrease in X

. Therefore, X

¼ 2 is the so-called

critical moisture content. The drying rate in the constant

Drying time t (min)

Miosture content (kg/kg db)

Experimental curve

Theoretical curve

Drying time t (min)

Moisture content (kg/kg db)

Experimental curve

Theoretical curve

Drying time t (min)

Moisture content (kg/kg db)

Experimental curve

Theoretical curve

(a)

(b)

(c)

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

2, S

¼ 0:075, S

¼ 0:106; X

2, S

¼ 0:054,

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

¼ 0:054, S

¼ 0:081; X

2, S

¼ 0:506, S

¼ 0:111; (c) P ¼ 71

mbar, initial sample weight

¼ 205.40 g, X

2, S

¼ 0:074, S

¼ 0:095;

2, S

¼ 0:404, S

¼ 0:120.

Drying time t (min)

Moisture content (kg/kg db)

Experimental curve

Theoretical curve

Drying time t (min)

Moisture content (kg/kg db)

Experimental curve

Theoretical curve

Drying time t (min)

Moisture content (kg/kg db)

Experimental curve

Theoretical curve

(c)

(b)

(a)

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

2, S

¼ 0:095, S

¼ 0:078; X

2, S

¼ 0:729,

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

¼ 0:136, S

¼ 0:126; X

2, S

¼ 0:441, S

¼ 0:129; (c) P ¼ 71

mbar, initial sample weight

¼ 161.20 g, X

2, S

¼ 0:088, S

¼ 0:823;

2, S

¼ 0:554, S

¼ 0:108.

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

161

rate period (X

2) is governed fully by the rate of

external heat and mass transfer, since a ﬁlm of free water
is always available at the evaporating surface. In our
experiments, potato slices and pumpkin slices were also
dried and almost the same data were obtained. It is
therefore deduced that the drying rate in this period
remains almost constant for most of sliced vegetables
and fruits as the main component of vegetable and fruits
is water, and the amounts of salt, fat and other com-
ponents are very small. Figs. 2–4 also show that N be-
gins to drop at X

¼ 2 since water molecules cannot

migrate immediately to the surface because of internal
transport limitation. Under these conditions, the drying
surface becomes ﬁrst partially unsaturated and then
fully unsaturated until it reaches the equilibrium mois-
ture content. Furthermore, as the moisture content is
below 2, a little amount of water is available, and con-
sequently the volumetric heating due to microwave
power dissipation is reduced because the power dissi-
pation of microwave strongly depends on the moisture
content of the material (Lian et al., 1997) and part of
microwave power reﬂects back to the magnetron. When
the moisture content is very low, the dielectric loss factor
decreases and the sample temperature may increase.
Therefore, it is very diﬃcult to predict moisture loss rate
based on the balance between the absorbed microwave
heat and the released heat of water evaporation, thus the
theoretical drying kinetic model (Eq. (4)) must be
modiﬁed in the period of X

The

drying

rate

begins

decline

slowly

1 < X

2, and the drying rate declines sharply as

1. As the true moisture content, X

, is larger than

that (X

) calculated by Eq. (4), a correction coeﬃcient,

, is introduced to modify Eq. (4) which is then

rewritten as

¼ uX

¼ u X

abs

;

0 < X

ð9Þ

where u is mainly aﬀected by the moisture content, as
well as the characteristic or composition of the material
being dried, and it can be deﬁned in the current study as

¼ f ðX

Þ P 1

ð10Þ

If X

is divided by X

, the values of u could then be

obtained. Fig. 5 shows the plot of u versus X

. By non-

linear regression analysis, the value of u as a function of
X

was obtained as follows:

¼ 1:3662X

0:5741

ð11Þ

In summary, the moisture content, X

, of the mate-

rials being dried in microwave–vacuum dryer can be
predicted by the following equations:

¼ X

abs

ðX

¼ u X

abs

¼ 1:3662X

0:5741

ð0 < X

ð12Þ

Fig. 6 presents the eﬀect of microwave power on the

drying curves. For constant vacuum pressure levels, the
drying rate produced higher values if microwave power
was greater. The experimental data agree with the result
predicted by Eq. (5), which shows that the drying rate is
the ﬁrst order of power output.

The eﬀect of vacuum pressure on the drying curves is

presented in Fig. 7. When microwave power level re-
mained constant, the drying rate produced a little higher
value if the vacuum pressure (residual absolute pressure)
was higher. This result was in contrary to those reported

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

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
The quantity of water evaporated within 3 min at diﬀerent microwave
power output levels and vacuum pressure levels

Vacuum pressure
(mbar)

Microwave power

336.5 W

267.5 W

162.8 W

30.0

24.80 g

19.75 g

12.02 g

51.0

25.05 g

19.91 g

12.12 g

71.0

25.21 g

20.04 g

12.19 g

¼ Q

abs

t=r

and t

¼ 3 min.

0.5

1.5

Moisture content X

(kg/kg db)

Correction cofficient

R2 = 0.9397

ϕ =1.3662X

-0.5741

Fig. 5. Non-linear regression curve of correction coeﬃcient versus
theoretical moisture content.

162

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

by Kiranoudis et al. (1997), Lin et al. (1999) and
Kaensup et al. (2002), but it was conﬁrmed by the result
predicted by Eq. (5), indicating the drying rate is in in-
verse proportion to the value of r

. The reason may be

that as the carrots were sliced into 3–5 mm in the current
experiments, the drying rate was controlled by heat
dissipation rate, and the higher drying temperature at
higher vacuum pressure caused higher drying rate.
However, the samples used in the previous experiments
reported by Lin et al. (1999) and Kaensup et al. (2002)
were not sliced and therefore had much larger size, while
the sample used in the experiment by Kiranoudis et al.
(1997) were spherical particles with 30 mm in diameter,
therefore, the drying rate was controlled by moisture
diﬀusion and aﬀected by the vacuum level with lower
vacuum pressure leading to higher drying rate.

5. Conclusions

In this paper, a theoretical model for microwave–

vacuum drying of carrot slices was developed and
modiﬁed for the later stages of drying. The model and
experimental data reveal that the drying rate is a con-
stant one until the moisture content is about 2 dry-basis
and remains essentially unchanged for most of sliced
vegetables and fruits in this period due to the initial high
moisture content of the samples, and then the drying
rate declines. As X

2, the correction coeﬃcient, u

must be introduced as a function of X

. In the earlier

period of the drying (high moisture content, X

2), the

drying rate can be estimated to range from 1474 to 1498
g water/kW h at the vacuum pressure from 30 to 70
mbar.

The model and experimental data also show that the

microwave power and vacuum pressure aﬀect the drying

Drying time t (min)

Moisture content X

(kg/kg db)

336.3w

267.5W

162.8W

Drying time t (min)

Moisture content X

(kg/kg db)

336.5W

267.5W

162.8W

Drying time t (min)

Moisture content X

(kg/kg db)

336.5W
267.5W
162.8W

(a)

(b)

(c)

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;

¼ 71 mbar.

Drying time t (min)

Moisture content X

(kg/kg db)

30 mbar
51 mbar
71 mbar

Drying time t (min)

Moisture content X

(kg/kg db)

Moisture content X

(kg/kg db)

30 mbar
51 mbar
71 mbar

Drying time t (min)

30 mbar

51 mbar

71 mbar

(c)

(b)

(a)

Fig. 7. Eﬀect of vacuum pressure on experimental drying curves:
initial sample weight

¼ 220 g. (a) Q ¼ 336:5 W; (b) Q ¼ 267:5 W;

¼ 162:8 W.

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

163

rate. For constant vacuum pressure levels, the drying
rate is the ﬁrst order of microwave power output, and
inversely proportional to the ﬁrst order of r

at vacuum

pressure, P . Because the vacuum pressure usually ranges
from 20 to 70 mbar, the value of r

varies a little and the

drying rate is strongly aﬀected by microwave power
output but slightly aﬀected by vacuum pressure.

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Microwave-vacuum drying kinetics of carrot slices

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