Desalination 212 (2007)
328 343
An experimental study on the drying kinetics of quince
Ahmet Kaya, Orhan Aydin*, Cevdet Demirtas, Mithat Akg�n
Karadeniz Technical University, Department of Mechanical Engineering, 61080 Trabzon, Turkey
Tel. [phone]; Fax [phone]; email: [e-mail]
Received 18 September 2006; accepted 19 October 2006
Abstract
In this experimental study, drying kinetics of quince slices was investigated as a function of drying conditions.
Experiments were conducted using air temperatures of 35, 45 and 55�C, mean velocities of 0.2, 0.4 and 0.6 m/s and,
relative humidity values of 40, 55 and 70%. The experimental moisture data were fitted to some models (namely
Henderson and Pabis, Lewis and two-term exponential models) available in the literature, and a good agreement
was observed. In the ranges covered, the values of the effective moisture diffusivity, Deff were obtained between
0.65�10 10 and 6.92�10 10 m2/s from the Fick s diffusion model. Using Deff, the value of activation energy (Ea) was
determined assuming the Arrhenius-type temperature relationship, which varied from 33.83 to 41.52 kJ/mol. Finally,
the sorption isotherms of the dried quince slices were determined.
Keywords: Convective drying; Quince; Experimental; Drying kinetics; Drying rate; Effective diffusivity; Moisture
content; Moisture ratio
1. Introduction ity and relative humidity of the drying medium
(air), while internal parameters include density,
Drying is used in order to preserve and store
permeability, porosity, sorption desorption char-
agricultural products for longer periods by remov-
acteristics and thermophysical properties of the
ing some of their moisture content. It is a compli-
material being dried.
cated process involving simultaneous heat and
Many studies have existed in the literature to
mass transfer under transient conditions. Under-
investigate the effects of the above mentioned pa-
standing the heat and mass transfer in the product
rameters on the drying process of different fruits
will help to improve drying process parameters
and vegetables. For the brevity, we cover only a
and hence the quality. A number of internal and
few of them: apple by Sacilik and Elicin [1] and
external parameters influence drying behavior.
Velic et al. [2]; tropical fruits by Karim and Haw-
External parameters include temperature, veloc-
lader [3]; kiwi by Simal et al. [4]; potato and car-
rot by Srikiatden and Roberts [5], some vegetables
*Corresponding author.
0011-9164/07/$ See front matter � 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.desal.2006.10.017
A. Kaya et al. / Desalination 212 (2007) 328 343 329
by Krokida et al. [6]; prickly pear by Lahsasni et unit, air-conditioned room and test section. The
al. [7]; fig by Babalis and Belessiotis [8]; chesnut air conditioning unit acclimatizes and, therefore,
by Guine and Fernandes [9]; pistachio nuts by supplies the external air to the room from where
Kashaninejad et al. [10]. the conditioned air is driven into the test section
Quince is a very ancient and delicious fruit. keeping the products to be dried. In the air-condi-
Turkey is the leading grower of quince in the tioned room with a volume of 3 m � 3 m � 3 m,
world. The purpose of this study is to experimen- the conditioned drying air is brought up to the
tally investigate the drying kinetics of quince as a thermal equilibrium. Three different channels (i.e.,
function of drying conditions and to evaluate the the test section) are connected to the room sup-
diffusion coefficient. The effects of the tempera- plying the conditioned air with desired tempera-
ture, velocity and relative humidity of the drying ture, velocity and relative humidity. Three differ-
air on the drying kinetics will be determined. ent cases can be simultaneously tested in these
channels. The mass flow rate of the drying air is
regulated by a fan driven by a variable speed
2. Materials and methods motor. This regulation ensured mean velocities
in the range from 0.2 to 0.6 m/s at the entrance of
2.1. Experimental setup and procedure
the channels, which is proven to be high enough
The experimental apparatus, designed and to eliminate possible velocity effects on the wet-
manufactured to study drying behaviors and char- ting rates on the surfaces of the product to be dried.
acteristics of different fruits and vegetables, is The channels, i.e. the drying units, have square
shown in Fig. 1. As it is seen from the figure, it cross sections (35 cm � 35 cm). Wire-mesh-bot-
mainly consists of three units: air conditioning tomed trays with a holding area of 25 cm � 15 cm
Air Suction Channel
Data
Acquisition
Air Blowing Channel
Loadcell
Product
Variable
Speed Motor
Fig. 1. The schematic of the experimental setup.
Air Conditioner
Thermocouple
Air Conditioned Room
Drying Channel
330 A. Kaya et al. / Desalination 212 (2007) 328 343
are included in the channels. In order to prevent tion between the water activity in the product and
the heat loss to the environment, the channels are its moisture content. It is of particular importance
well insulated. in the design of a food dehydration process, espe-
The samples of the quince slices weighing cially in the determination of a drying end point
about 100 g with a thickness of 4 mm are placed which ensures economic viability and microbio-
in trays of each drying unit. The initial moisture logical safety [11,12].
content of quince slices is determined using the The water activity of a food product can be
OHAUS MB45 infrared moisture analyzer. Dur- defined as:
ing the experiments, the temperature changes and
the sample weight were recorded every 5 min us- pf Ćeq
aw = =
(1)
ing copper-constantan thermocouples (0 200
p0 100
ą 0.5�C) and Lama type load cells (10000 ą 0.01 g),
respectively. Furthermore, the velocity in the dry-
where aw is the water activity, pf is the vapor pres-
ing channel was measured with an anemometer
sure of the water in the product, p0 is the vapor
(Lutron HT-3006HA model with the accuracy of
pressure of pure water and Ćeq is the equilibrium
0.2 20.0 ą 0.05 m/s), while the relative humidity
relative humidity of the salt solutions [11].
in the conditioning room was measured using a
A static gravimetric method [13] is used to
humidity/temperature meter (Lutron AM-4204
determine sorption isotherms of quince at 25, 35,
HA model with the accuracy of 10 95 ą 1%). Five
45 and 55�C. Nine different saturated salt solu-
experiments were performed with different val-
tions and distilled water, whose relative humidity
ues of the drying parameters shown in Table 1.
values varied between 12% and 100%, were used
(Table 2). Each solution was placed into a sepa-
2.2. Sorption isotherm
rate glass jar, i.e. desiccators, and the samples were
placed as seen in Fig. 2. Each salt solution pro-
The sorption isotherm represents water activ-
duced and maintained a specific relative humid-
ity of a product, suggesting the equilibrium rela-
ity as seen in Table 2. The glass jars which were
tightly closed were then kept in an oven having a
Table 1
nearly isothermal condition at 25, 35, 45 and 55�C.
Air drying conditions and parameters of the product used
The dried samples equilibrate with the environ-
in the experimental tests
ment inside the jar until no discernible weight
T (�C) Me (db) U (m/s) Time (s)
Ć (%)
change was observed, when it was assumed that
the equilibrium moisture was reached. It was ob-
35 40 0.092 0.2 28,479
0.4 25,405
served from the measurements using the CHYO-
0.6 23,106
MP300 digital balance (with a measurement range
45 0.084 0.2 18,135
of 0 300 g and an accuracy of ą0.001 g) that the
0.4 15,472
equilibrium condition was usually reached in 32 d.
0.6 12,817
Finally, in the equilibrium condition, the equilib-
55 0.062 0.2 12,822
rium moisture content was measured using the
0.4 10,550
0.6 8,284
infrared moisture analyzer (OHAUS MB45).
35 55 0.10 0.2 43,126
0.4 37,189
2.3. Data analysis
0.6 31,683
70 0.17 0.2 79,897
Drying process is proven to mostly occur in
0.4 72,716
the falling rate period, and moisture transfer dur-
0.6 65,211
ing drying is controlled by internal diffusion. The
A. Kaya et al. / Desalination 212 (2007) 328 343 331
Table 2
distributions, long drying times and negligible
Water activities of the saturated salt solutions used in the
external resistance, the solution is as follows:
experimental study
Salt aw M - Me
�=
LiCl 0.12 M0 - Me
(3)
CH3COOK 0.28
2
"
Ą#ń#
Ą2 2n +1
K2CO3 0.38
= f
"(2n1 ) exp ó#- ( 4L2 ) DefftĄ#
MgCl2 0.42 2
n=1 +1
ó#Ą#
0
Ł#Ś#
Mg(NO3)2 0.57
NaNO3 0.63
SrCl2 0.70
where � is the moisture ratio and f is the shape
NaCl 0.75
factor depending on the geometry of the material.
(NH4)2SO4 0.80
The value of f is 8/Ą2 for a semi-infinite slab, 4/Ą2
Distilled H2O 1.0
for a cylinder and 6/Ą2 for a sphere. In addition,
M is the moisture content at t, Me is the equilib-
rium moisture content determined from Fig. 3, M0
is the initial moisture content and L0 is the char-
acteristics dimension (which equals L/2 for a semi-
Sample
Aluminum cover
infinite slab), Deff is the effective moisture diffusi-
vity and t is the drying time. When the drying
curve and equilibrium moisture content is experi-
Glass
mentally obtained, Deff can be easily predicted
Jar
using the non-linear regression analyses tech-
nique.
Salt solution
As can be seen, the above general solution has
an exponential form. There are many statistically-
based expressions correlating experimentally ob-
Fig. 2. The unit used to determine the sorption isotherm.
tained � values in terms of t in the existing litera-
ture. Generally, these correlations remain case-
dependent, each suggesting coefficients varying
from product to product. Therefore, they cannot
Fick s second law of unsteady state diffusion has
be generalized. Moreover, many of these expres-
been widely used to describe the drying process
in the falling rate period for most biological ma- sions just fitting curves for � vs. t have a form not
consistent with the analytical solution of the prob-
terials [14].
lem. Therefore, we only consider the expressions
consistent with the nature of the problem. If only
"M
="Ą#Deff "M ń#
( )Ś#
(2)
Ł# the first term of the series is considered, Eq. (2)
"t
takes the following form:
where Deff is the effective moisture diffusivity,
which is a mass diffusion property of the prod- �= Ae-kt (4)
uct. Analytical solutions to the above equation
under various initial and boundary conditions for which is called a single-exponential model or the
different geometries can be found in textbook by Henderson and Pabis model [15] in the existing
Crank [14]. Assuming uniform internal moisture literature. The Lewis model [16] assumes 1 for A.
332 A. Kaya et al. / Desalination 212 (2007) 328 343
2.2
2.0
T=25OC
T=35OC
1.8
T=45OC
1.6
T=55OC
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
aw
Fig. 3. Sorption isotherms of quince at 25, 35, 45 and 55�C.
When the first two terms of the series considered, thermal assumption has been applied in determin-
Eq. (2) takes the form ing the activation energy [5].
(5)
�= Ae-kt + Be-lt
2.4. Uncertainty analysis
Experimental studies are not free of errors and
which is called a two-term exponential model in
uncertainties originating from measuring instru-
the existing literature [17].
ments, environment, observer, friction and oscil-
The dependence of Deff on temperature can be
lations during the running of the system. There-
determined by a simple Arrhenius expression:
fore, in order to indicate the quality of the mea-
surements carried out, an uncertainty analysis has
�# ś#
Ea
Deff = D0 expś# -
been performed by following the method de-
ź#
(6)
TabsR
�# #
scribed by Holman [18]. The uncertainties in cal-
culating the moisture content and temperature
where Ea is the activation energy of the moisture
were obtained to be ą0.1% and 0.2%, respectively
diffusion (kJ/mol), D0 is the diffusivity value for
(Table 3).
an infinite moisture content, R represents the uni-
versal gas constant and Tabs is the absolute tem-
perature. By plotting ln (Deff) vs. 1/Tabs diagram,
3. Results and discussion
Ea and D0 coefficients can be subsequently related
to drying air conditions via non-linear regression The initial moisture content of quince slices
analysis techniques. The temperature used in the was measured to be around 82.5% w.b. (4.71 d.b.).
Arrhenius analysis is the ambient temperature of Prior to the drying experiments, the equipment
the material being dried is also that of the sur- was run for about an hour to achieve steady state
rounding drying environment. Therefore, the iso- conditions for the desired temperature and rela-
2
Equilibrium Moisture Content (gH
O/g dry matter)
A. Kaya et al. / Desalination 212 (2007) 328 343 333
tive humidity levels of the drying air. Experiments as a result of increasing convective heat and mass
were conducted for the following ranges of the transfer coefficients between the drying air and
governing parameters of the drying air: tempera- the product. The convective heat and mass coef-
tures at 35, 45 and 55�C; mean velocities at 0.2, ficients are used to determine the heat transfer
0.4 and 0.6 m/s; relative humidity values at 40, from the drying air to the product and the mass
55 and 70%. Drying was continued until the equi- transfer from the product to the drying air, respec-
librium moisture content was reached. Experi- tively. As is seen from Fig. 4a, increasing U from
ments were repeated at least three times for any 0.2 m/s to 0.4 m/s decreased the total drying time
studying range in order to validate the results ob- from about 28,479 s to about 25,405 s (a decrease
tained. of 10.8%). Similarly, a further increase in U to
At first, the sorption isotherm representing the 0.6 m/s decreased the total drying time to about
variation of the moisture content with the water 23,106 s, which indicates a decrease of 9.05% and
activity, aw, is plotted in Fig. 3. As can be seen 18.9% according to those at U = 0.2 m/s and
from Fig. 3, at a constant water activity, equilib- 0.4 m/s, respectively. As expected, increasing the
rium moisture contents increases with decreasing temperature of the drying air decreased the total
temperature. Similar characteristics were reported drying time since heat transfer was increased due
by Palipane and Driscoll [19], Litchfield and Okos to the increasing temperature difference which is
[20], Timoumi and Zagrouba [21] and McLaugh- the driving potential of the heat transfer (Fig. 4b,c).
lin and Magee [11]. This trend may be explained The influence of T on the drying behavior can be
by considering excitation states of molecules. At better seen from Fig. 5. For constant values of the
increased temperatures molecules are in an in- velocity and the relative humidity of the drying
creased state of excitation, thus increasing their air, at Ć = 40% and U = 0.2 m/s, increasing the
distance apart and decreasing the attractive forces temperature of the drying air from T = 35�C to
between them. This leads to a decrease in the de- 45�C decreased the total drying time about 36%.
gree of water sorption at a given relative humid- A further increase in T to 55�C decreased the total
ity with increasing temperature. It is also shown drying time to about 29.3% and about 55% ac-
that equilibrium moisture content increases with cording to those at T = 45�C and T = 35�C, re-
increasing water activity at constant temperature. spectively.
These changes in equilibrium moisture content are Fig. 6 shows effect of Ć on the moisture con-
due to an inability of the foodstuff to maintain tent � t variation. A decrease in Ć decreases the
vapor pressure at unity with decreasing moisture total drying time due to the increasing mass trans-
content. As moisture content decreases, moisture fer. Decreasing Ć increases the difference between
in the food tends to show a lower vapor pressure, the concentrations of water in the drying air and
acting as if in solution, changing with atmospheric the product. The experimental results and effects
humidity [11]. of the above drying air parameters considered on
Variations of the moisture content with the the drying kinetics are found to be in consistent
drying time, t, for varying values of the govern- with those given for some other products in the
ing parameters (mainly, the temperature, T, the existing literature. For constant values of the tem-
velocity, U, and the relative humidity, Ć, of the perature and the velocity of the drying air, at T =
drying air) were determined. Fig. 4 shows the in- 35�C and U = 0.2 m/s, decreasing the relative
fluence of U on the moisture content � t variation humidity of the drying air from 70% to 55% de-
at Ć = 40% for T = 35�C (a), 45�C (b) and 55�C creased the total drying time about 46%. A fur-
(c). As can be seen, an increase in the velocity of ther decrease in Ć to 40% decreased the total dry-
the drying air results in decreasing drying times ing time to about 34% and about 64.4% accord-
334 A. Kaya et al. / Desalination 212 (2007) 328 343
Fig. 4. The variation of moisture content with t
for various U at Ć = 40% for T = 35�C (a), 45�C
(b) and 55�C (c).
A. Kaya et al. / Desalination 212 (2007) 328 343 335
5.0
T=35OC
4.5
U=0.2 m/s
T=45OC
Ć=40%
4.0
T=55OC
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 6000 12000 18000 24000 30000
Time, sec
Fig. 5. The variation of moisture content with t for various T at Ć = 40% and U = 0.2 m/s.
5.0
Ć=70%
4.5 U=0.2 m/s
Ć=55%
T=45OC
Ć=40%
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 15000 30000 45000 60000 75000 90000
Time, sec
Fig. 6. The variation of moisture content with t for various Ć at T = 35�C and U = 0.2 m/s.
2
Moisture Content (gH
O/g dry matter)
2
Moisture Content (g H
O/g dry matter)
336 A. Kaya et al. / Desalination 212 (2007) 328 343
ing to those at Ć = 55% and Ć = 70%, respec- occur with an increase in the temperature of the
tively. drying air, since there is a negligible amount of
In order to gain a deeper insight into the dry- water to evaporate. In Fig. 8, we observe similar
ing behavior, the variations of the drying rate with behaviors for the effect of the temperature of the
the drying time, t (a) and the moisture content (b) drying fluid. For higher values of the moisture
are shown in Figs. 7 9 for varying velocity, tem- content, increasing drying temperature results in
perature and relative humidity of the drying air, increasing the drying rate and therefore decreas-
respectively. Due to the moisture diffusion pro- ing the drying time. This can be explained by the
cess, the drying rate decreases with time. increasing the temperature difference between the
The period of constant drying rate, as is typi- drying air and the product and resulting in accel-
cally the case for fruits, is either very small or erating water migration. Fig. 9 shows that rela-
does not exist at all, for all values of the process tive humidity has a considerable influence on the
variables tested. The value of the moisture ratio variation of the drying rate with moisture content
decreases rapidly, with a consequent increase of or the drying time. As expected, decreasing the
the drying rate, when air temperature increases. relative humidity intensifies the drying rate change
The initial value of drying rate almost doubled by moisture content or the drying time. The varia-
when the air temperature was increased from 35 tion of ln(Deff) with 1/Tabs is plotted in Fig. 10,
to 55�C. from which Ea and D0 coefficients are predicted.
The drying rate is another common parameter In the following, the experimental results are
used in the drying analysis, which equals (Mt  fit to the expression given in Eqs. (4) and (5) us-
Mt + "t)/"t. At the first stages of the drying pro- ing STATISTICA and the results are listed in
cess, the variation of the drying rate with time is Table 4. Readers are referred to McMinn [22] in
very strong, which then becomes nearly constant order to have detailed information on the statisti-
(Figs. 7a, 8a and 9a). From Fig. 7a, initially, it is cal parameters defined. Coefficients used in the
very clear that the higher the air velocity, the models considered are determined and shown in
higher the drying rate. At lower moisture ratios, Table 4. As shown, for all the cases studied, the
the effect of the drying air velocity on the drying models considered predict the experimental re-
rate is nearly negligible (Fig. 7b). However, es- sults with a satisfactory and reasonable agreement
pecially for higher values of moisture content, an (R > 0.99).
increase in U increases the drying rate. This can Using the experimental results obtained, the
be explained as follows: lower values of mois- effective moisture diffusivity Deff is predicted from
ture content represent lower values of the water Eq. (3) and given in Table 5. As can be seen, an
content inside the product. Therefore, for the lower increase in either U or T, or a decrease in Ć in-
values of moisture content, no significant changes creases Deff. As can be seen from Table 4, the ef-
Table 3
Uncertainties in measurement of parameters during drying of quince
Instrument Range Estimated uncertainty
Load cell, g 0 10,000 ą 0.01 (based on manufacturer s specification and calibration data)
Thermocouples 0 200 ą 0.2 (based on manufacturer s specification and calibration data )
(copper + constantan), �C
Hygrometer, % 5 90 ą 1 (based on manufacturer s specification)
Anemometer, m/s 0.2 20 ą 0.05 (based on manufacturer s specification)
A. Kaya et al. / Desalination 212 (2007) 328 343 337
1.2E-03
U=0.2 m/s (a)
T=45OC
U=0.4 m/s
Ć=40%
U=0.6 m/s
8.0E-04
4.0E-04
0.0E-01
0 4000 8000 12000 16000 20000
Time, sec
1.2E-03
U=0.2 m/s
T=45OC
U=0.4 m/s
Ć=40%
U=0.6 m/s
8.0E-04
4.0E-04
(b)
0.0E-01
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Moisture Content (g H O/g dry matter)
2
Fig. 7. The influence of U on the variation of the drying rate with t (a) and moisture content (b) at Ć = 40% and T = 45�C.
2
Drying Rate (g H
O/g dry matter sec)
2
Drying Rate (g H
O/g dry matter sec)
338 A. Kaya et al. / Desalination 212 (2007) 328 343
1.6E-03
(a)
T=35OC
U=0.2 m/s
T=45OC
Ć=40%
T=55OC
1.2E-03
8.0E-04
4.0E-04
0.0E-01
0 5000 10000 15000 20000 25000 30000
Time, sec
1.6E-03
(b)
T=35OC
U=0.2 m/s
T=45OC Ć=40%
T=55OC
1.2E-03
8.0E-04
4.0E-04
0.0E-01
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Moisture Content (g H O/g dry matter)
2
Fig. 8. The influence of T on the variation of the drying rate with t (a) and moisture content (b) at Ć = 40% and U = 0.2 m/s.
2
Moisture Content (g H
O/g dry matter sec)
2
Drying Rate (g H
O/g dry matter sec)
A. Kaya et al. / Desalination 212 (2007) 328 343 339
1.2E-03
(a)
Ć=70%
U=0.2 m/s
Ć=55%
T=35OC
Ć=40%
8.0E-04
4.0E-04
0.0E-01
0 15000 30000 45000 60000 75000 90000
Time, sec
(b)
1.2E-03
Ć=70%
U=0.2 m/s
Ć=55%
T=35OC
Ć=40%
8.0E-04
4.0E-04
0.0E-01
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Moisture Content (g H O/g dry matter)
2
Fig. 9. The influence of Ć on the variation of the drying rate with t (a) and moisture content (b) at T = 35�C and U = 0.2 m/s.
2
Drying Rate (g H
O/g dry matter sec)
2
Drying Rate (g H O/g dry matter sec)
340 A. Kaya et al. / Desalination 212 (2007) 328 343
Table 4
Prediction of the model coefficients
Two-term exponential model
U = 0.2 m/s R U = 0.4 m/s R U = 0.6 m/s R
Ć = 40%
T = 35�C A 0.5442 0.998 0.5121 0.999 0.5172 0.999
B 0.5090 0.5122 0.4848
k �104 (s 1) 1.1988 1.3093 1.4667
l �104 (s 1) 1.1988 1.3093 1.4833
T = 45�C A 0.5019 0.999 0.0855 0.999 0.0944 0.998
B 0.5029 0.9245 0.9133
k �104 (s 1) 1.8511 10.4131 15.8833
l �104 (s 1) 2.0667 2.1667 2.6501
T = 55�C A 0.9687 0.999 0.9245 0.999 0.9514 0.999
B 0.0617 0.1092 0.0711
k �104 (s 1) 2.9103 3.3021 4.2667
l �104 (s 1) 7.8666 8.9833 1.1466
Henderson and Papis model
T = 35�C A 1.0533 0.998 1.0244 0.999 1.0021 0.998
k �104 (s 1) 1.2031 1.3167 1.4667
T = 45�C A 1.0042 0.998 0.9804 0.999 0.9697 0.998
k �104 (s 1) 1.9503 2.2833 2.7833
T = 55�C A 1.0203 0.998 1.0171 0.999 1.0127 0.999
k �104 (s 1) 3.0342 3.5167 4.4534
Lewis model
T = 35�C k �104 (s 1) 1.1333 0.997 1.2833 0.998 1.4667 0.999
T = 45�C k �104 (s 1) 1.9483 0.999 2.3333 0.999 2.8883 0.998
T = 55�C k �104 (s 1) 2.9534 0.998 3.4523 0.998 4.3833 0.998
Two-term exponential model
U = 0.2 m/s R U = 0.4 m/s R U = 0.6 m/s R
T = 35�C
A 0.5442 0.998 0.5121 0.999 0.5172 0.999
Ć = 40%
B 0.5090 0.5122 0.4848
k �104 (s 1) 1.1988 1.3093 1.4667
l�104 (s 1) 1.1988 1.3093 1.4833
A 0.5218 0.999 0.5077 0.999 0.5113 0.999
Ć = 55%
B 0.5269 0.5252 0.5132
k �104 (s 1) 0.8231 0.9333 1.1023
l �104 (s 1) 0.8231 0.9333 1.1023
A 0.5336 0.998 0.5406 0.998 0.4457 0.998
Ć = 70%
B 0.5541 0.5407 0.6390
k �104 (s 1) 0.3833 0.4167 0.4667
l �104 (s 1) 0.3833 0.4167 0.4667
Henderson and Papis model
A 1.0533 0.998 1.0244 0.999 1.0021 0.994
Ć = 40%
k �104 (s 1) 1.2031 1.3167 1.4667
A 1.0488 0.999 1.0329 0.999 1.0246 0.999
Ć = 55%
k �104 (s 1) 0.8032 0.9333 1.1023
A 1.0879 0.998 1.0835 0.998 1.0846 0.999
Ć = 70%
k �104 (s 1) 0.3833 0.4333 0.4833
Lewis model
k �104 (s 1) 1.1333 0.997 1.2833 0.998 1.4667 0.999
Ć = 40%
k �104 (s 1) 0.7667 0.997 0.9012 0.998 1.0833 0.999
Ć = 55%
k �104 (s-1) 0.3667 0.994 0.4002 0.994 0.4502 0.994
Ć = 70%
A. Kaya et al. / Desalination 212 (2007) 328 343 341
-20.8
-21
U=0.2 m/s
U=0.4 m/s
-21.2
U=0.6 m/s
-21.4
-21.6
-21.8
-22
-22.2
-22.4
-22.6
3.02 3.06 3.10 3.14 3.18 3.22 3.26
1/T (x1000)
Fig. 10. Arrhenius-type relationship between effective moisture diffusivity and temperature.
fective diffusivity values varied from 0.65�10 10 On the quality of the dried products, observa-
and 6.92�10 10 m2/s. These values are in fact con- tions of the color have been made before and af-
sistent with those existing in the literature, e.g. ter drying. Especially for higher values of the rela-
1 3�10 11 m2/s for air drying of apricots [23], tive humidity (e"70%) color changes have been
10.4 9.9�10 11 m2/s for sun drying of differently observed, which, in turn, affected the taste of the
treated grapes [24], 4.28�10 10 6.8�10 9 m2/s for product.
hot air drying of okra [25], 2.32�10 10 2.76
�10 9 m2/s for hot air drying of mulberry [26] and
4. Conclusions
8.33�10 10 m2/s hot air drying of banana slices
[27]. In this experimental study, drying kinetics of
In the following, the value of Deff is used to quince slices was investigated as a function of
predict the activation energy of the moisture dif- drying conditions. Experiments were carried out
fusion, Ea using the Arrhenius equation given in for several values of the air temperature, the mean
Eq. (6), which is tabulated in Table 6. An increase velocity and the relative humidity. The following
in U increases Ea and D0. As seen, the activation conclusions can be drawn from the study:
energy for diffusion, calculated from Eq. (6), i) At a constant water activity, equilibrium
ranged between 33.832 kJ/mol and 41.515, as moisture content decreases with increasing
similar to those given in the literature for drying temperature.
of different foods: 26.2 kJ/mol for broccoli dry- ii) At a constant temperature, equilibrium mois-
ing [28]; between 49 54 kJ/mol in drying of ture content increases with increasing water
grapes [29]; 12.3 39.5 kJ/mol for potato and bean activity.
drying, respectively [30]. iii) Increasing the temperature or the velocity of
eff
ln (D
)
342 A. Kaya et al. / Desalination 212 (2007) 328 343
Table 5
Diffusion coefficient, Deff
U = 0.2 m/s R U = 0.4 m/s R U = 0.6 m/s R
Ć = 40%
Deff �1010 m2/s
T = 35�C 1.96 0.996 2.09 0.995 2.43 0.999
T = 45�C 3.71 0.994 4.15 0.997 4.54 0.995
T = 55�C 4.84 0.998 5.69 0.998 6.92 0.997
T = 35�C
1.96 0.996 2.09 0.995 2.43 0.999
Ć = 40%
1.38 0.997 1.42 0.998 1.72 0.996
Ć = 55%
0.65 0.996 0.73 0.999 0.82 0.997
Ć = 70%
Table 6
Energy of activation and coefficient D0
U = 0.2 m/s R U = 0.4 m/s R U = 0.6 m/s R
Ea (kj/mol) 33.832 0.997 37.532 0.998 41.515 0.997
D0 (m2/s) 1.21�10 04 5.52�10 04 2.86�10 03
the drying air decreases the total drying time, Acknowledgements
while decreasing the relative humidity de-
The authors acknowledge the financial sup-
creases it. At T = 35�C and Ć = 40%, increas-
port provided by Karadeniz Technical University
ing U from 0.2 m/s to 0.6 m/s has lead to a
Research Fund under Grant No 2004.112.003.01.
decrease of 18.9% in the total drying time.
At U = 0.2 m/s and Ć = 40%, an increase in T
from 35�C to 55�C decreased the total drying Symbols
time 55%. At T = 35�C and U = 0.2 m/s, a
aw  Water activity
decrease in Ć from 70% to 40% decreased
Deff  Effective diffusivity coefficient, m2/s
the total drying time 64.4%.
D0  Arrhenius factor, m2/s
iv) The forms of the single-exponential model
Ea  Energy of activation, kJ/mol
or the Henderson and Pabis model, the Lewis
f  Shape factor
model and the two-term exponential model
L0  Characteristics dimension, m
are consistent with the analytical solution of
M  Moisture content at t, g H2O/g dry
the mass diffusion equation. All these three
matter
models have been shown to correspond very
Me  Equilibrium moisture content, g H2O/g
well with the experimental data.
dry matter
v) An increase either in U or T, or a decrease in
M0  Initial moisture content, g H2O/g dry
Ć increases Deff.
matter
vi) An increase in U increases Ea. pf  Vapor pressure of the water in the
vii) An uncertainty analysis was made, which product, Pa
yielded uncertainty values lower than 0.2% p0  Vapor pressure of pure water, Pa
R  Universal gas content, kJ/mol.oK
for temperature and moisture measurements.
A. Kaya et al. / Desalination 212 (2007) 328 343 343
Press, Oxford, 1972.
T  Temperature, oC
[14] J. Crank, The Mathematics of Diffusion. Oxford Uni-
Tabs  Absolute temperature, oK
versity Press, London, 1975.
t  Time, s
[15] S.M. Henderson and S. Pabis, Grain drying theory. II.
U  Velocity, m/s
Temperature effects on drying coefficients, J. Agric.
�  Dimensionless moisture content
Eng. Res., 6 (1961) 169 174.
Ć  Relative humidity
[16] W.K. Lewis, The rate of drying of solid materials, J.
Ćeq  Equilibrium relative humidity of the salt Ind. Eng. Chem., 13(5) (1921) 427 432.
[17] Y.I. Sharaf-Eldeen, J.L. Blaisdell and M.Y. Hamdy, A
solution
model for ear corn drying, Trans. ASEA, 23 (1980)
1261 1271.
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