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Original article
Modelling of the drying of eggplants in thin-layers
Ebru Kavak Akpinar* & Yasar Bicer
Mechanical Engineering Department, Firat University, 23279, Elazig, Turkey
(Received 16 February 2004; Accepted in revised form 27 May 2004)
Summary In this paper, the thin-layer drying behaviour of eggplant slices (6 mm thick layers) in a
convective-type cyclone dryer is reported. Thin-layer drying experiments were conducted at
drying air temperatures of 55, 65 and 75 C and dry air velocities of 1 and 1.5 ms)1
. Data
on sample mass, temperature and velocity of the dry air were recorded continuously during
each test. In order to estimate and select a suitable form of the drying curve, eight different
semi-theoretical and/or empirical models were fitted to the experimental data and
comparisons made of their coefficients of determination as predicted by non-linear
regression analysis. The Page model best described the drying curve of eggplant, with a
correlation coefficient, r ¼ 0.9999.
Keywords Drying models, mathematical modelling, moisture ratio, non-linear regression.
Introduction
Dehydration is an important operation in the
chemical and food processing industries. The
objective dehydration is the removal of water to
the level at which microbial spoilage and deteri-
oration reactions are greatly minimized. The wide
variety of dehydrated foods available to the
consumer (snacks, dry mixes and soups, dried
fruits, etc.) and the importance of meeting quality
specifications and conserving energy, emphasize
the need for a thorough understanding of the
drying process.
Thin-layer drying models that describe the
drying phenomenon of agricultural products fall
mainly into three categories, namely theoretical,
semi-theoretical and empirical (Panchariya et al.,
2002). The theoretical approach is concerned
with diffusion or simultaneous heat and mass
transfer equations. The semi-theoretical ap-
proach is concerned with approximated theoret-
ical equations. Empirical equations are easily
applied to drying simulation as they depend only
on experimental data (Afzal  Abe, 2000).
Theoretical approaches take into account the
internal resistance to moisture transfer, while
semi-theoretical and empirical approaches con-
sider only the external resistance to moisture
transfer between the product and air (Hender-
son, 1974).
To design and control a dryer and to define
optimum drying conditions, it is necessary to
model the actual process of drying in terms of
mathematical relations. Although, in the past,
many theoretical and empirical models have been
developed for various foods and agro-based
products (Diamante  Munro, 1991; Sarsavadia
et al., 1999; Özdemir  Devres, 1999; Afzal 
Abe, 2000; Yaldiz et al., 2001; Yaldiz  Ertekin,
2001; Panchariya et al., 2002; Midilli  Kucuk,
2003), no investigations on the thin-layer drying
of eggplant have been reported in the literature.
Eggplant is of particular interest in the prepara-
tion of dry mixtures used for soups etc. Therefore,
the main objectives of this study were to
determine the effect of the drying air temperature
and air velocity on the drying kinetics of eggplant
slices in a convective-type cyclone dryer, and to
select the best mathematical model for the drying
curves.
*Correspondent: Fax: +90 424 241 5526;
e-mail: eakpinar@firat.edu.tr
International Journal of Food Science and Technology 2005, 40, 273–281 273
doi:10.1111/j.1365-2621.2004.00886.x
 2005 Institute of Food Science and Technology Trust Fund
Materials and methods
Experimental set-up
Figure 1 shows a schematic diagram of the cyclone
type dryer developed for the experimental work
(Akpinar, 2002). It consists of a fan (12), resist-
ance and heating control systems (7, 10, 11), air-
duct (15), cyclone-type drying chamber (1), and
measurement instruments (3, 5, 8, 9, 13). The
airflow was adjusted by means of a variable speed
blower and a manually operated adjustable flap
(14) in the entrance. Airflow rate was measured
with an anemometer (Lutron AM-4201, Taipei,
Taiwan). The heating system consisted of an
electric 4000 W heater (11) placed inside the duct.
A rheostat (10) was used to adjust the drying
chamber temperature. The rectangular duct (15),
containing the air fan and heater, constructed
from sheet iron, was 100 cm long, 20 cm wide and
25 cm high. The cylindrical drying chamber (1),
constructed from sheet iron, had a diameter of
60 cm and a height of 80 cm. The inside and
outside surfaces of the drying chamber were
painted with a spray dye to prevent rusting of
the sheet iron surface. The drying chamber was
constructed in concentric form with a 3 cm annu-
lus insulated with polystyrene. Both the top and
bottom ends of the drying chamber were closed
with steel covers insulated with polystyrene. The
top cover was used to load or unload the chamber.
In the cyclone type dryer, samples are dried by a
swirling flow of drying air instead of an axial
airflow. Air entering across the bottom part of the
drying chamber produces the swirling flow. The
samples were dried in a tray manufactured from a
nylon sieve, which allowed the airflow to pass
through the trays. The flow diagram of the thin-
layer drying process is presented in Fig. 2.
In the measurements of temperatures, J type
iron-constant thermocouples were used with a
manually controlled 20-channel automatic digital
thermometer (Elimko 6400, Ankara, Turkey),
with an accuracy of ±0.1 C. A thermo hygrom-
eter (Extech 444731, Shenzhen, China) was used to
measure humidity levels at various locations in the
system. Moisture loss was recorded at 20-min
intervals during drying by means of a digital
balance (Bel, Mark 3100, Monza, Italy) with an
accuracy of ±0.01 g (Fig. 1).
13
3
4
2
3
6
5
1
7
9
8
13
11
15
12
10
14
Figure 1 Experimental set-up (1, drying chamber; 2, tray; 3, digital balance; 4, observation windows; 5, digital thermometer; 6,
the balance suspension bar; 7, control panel; 8, thermocouples; 9, digital thermometer and channel selector; 10, rheostat; 11,
heater; 12, fan; 13, wet and dry thermometers; 14, adjustable flap; 15, duct).
Thin-layer modelling E. K. Akpinar and Y. Bicer
274
International Journal of Food Science and Technology 2005, 40, 273–281  2005 Institute of Food Science and Technology Trust Fund
Procedure
Fresh eggplant slices were used in the experi-
ments. Before the drying process, the eggplants
were cut into slices of 6 mm thickness and 30 mm
diameter with a mechanical cutter. After the
dryer had reached steady state temperature con-
ditions for operation, 500 g of eggplant slices
were put on the tray of the dryer and dried there.
The initial and final moisture contents of the
eggplant slices were determined at 80 C using an
infrared moisture analyser (Mettler LJ16, Grei-
fensee, Switzerland).
Drying experiments were done at 55, 65, and
75 C drying air temperatures and 1 and 1.5 m s)1
air velocities. The ranges of the air temperature
and velocity were set to the values largely used in
actual industrial air drying applications and the
thin-layer drying of vegetables and fruits by many
researchers (Chiang  Petersen, 1985; Diamante 
Munro, 1991; Karathanos  Belessiotis, 1997;
Yaldiz  Ertekin, 2001; Yaldiz et al., 2001;
Akpinar et al., 2003a,b). The relative humidity of
the drying air was determined as 15% at 55 C,
9% at 65 C and 5% at 75 C. Drying was
continued until the final moisture content of the
samples reached approximately 0.04 g water g)1
dry matter. During the experiments, ambient
temperature and relative humidity, and the inlet
and outlet temperatures of the drying air in the
dryer chamber were recorded.
Mathematical modelling of drying curves
The moisture ratio (MR) of the eggplant slices
during the thin-layer drying experiments was
calculated using the following equation:
MR ¼
M  Me
Mo  Me
ð1Þ
where M0 and Me are the initial and equilibrium
moisture contents (% dry basis) respectively.
For mathematical modelling, the thin-layer
drying equations in Table 1 were tested to select
the best model for describing the experimental
drying curves of the eggplant slices during drying
in the convective type-cyclone dryer. Regression
analysis was performed by using the Statistica
computer program (StatSoft Inc., 1993, Tulsa,
OK, USA). The correlation coefficient (r) was the
primary criterion for selecting the best equation to
describe the drying curves (Guarte, 1996). In
addition to r, the reduced chi-squared (v2
) and
root mean square error (RMSE) analyses were
used to determine the best fit. These parameters
are calculated as follows:
v2
¼
P
n
i¼1
ðMRexp;i  MRpre;iÞ2
N  n
ð2Þ
RMSE ¼
1
N
X
N
i¼1
ðMRpre;i  MRexp;iÞ2
 #1=2
ð3Þ
Fresh air Fan Heaters
Tray
Sample
weighing
Drying air
inlet
Drying air
outlet
Drying chamber
Velocity
measurement
Velocity
measurement
Airflow rate
setting
Temperature
measurement
Temperature
velocity
measurement
Temperature
measurement
Temperature
measurement
Figure 2 Flow diagram of the thin-layer drying process of eggplant slices.
Thin-layer modelling E. K. Akpinar and Y. Bicer 275
 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 273–281
where MRexp,i is the ith experimentally observed
moisture ratio, MRpre,i the ith predicted moisture
ratio, N the number of observations and n is the
number of constants (Sarsavadia et al., 1999;
Yaldiz et al., 2001).
The effects of parameters related to the product
or drying conditions, such as slice thickness,
drying air temperature, relative humidity, etc.,
have been investigated by many researchers
(Henderson, 1974; Özdemir  Devres, 1999;
Yaldiz  Ertekin, 2001). Modelling the drying
behaviour of different agricultural products often
requires the statistical methods of regression and
correlation analysis. Linear and non-linear regres-
sion models are important tools to use find the
relationship between different variables, especially
those for which no established empirical relation-
ship exists. In this study, the constants and
coefficients of the best fitting model were
determined, involving drying variables such as
air temperature and velocity. The effects of these
variables on the constants and coefficients of the
drying expression were also investigated by multi-
ple linear regression analysis.
Results and discussion
Eggplant slices of 10.63 g water g)1
dry matter
average initial moisture content were dried to
0.04 g water g)1
dry matter using different air
temperatures (55, 65 and 75 C) and different air
velocities (1 and 1.5 m s)1
). The final moisture
contents represent the moisture equilibrium
between the sample and the drying air, under the
conditions in the dryer, beyond which any changes
in the mass of the sample could not occur.
The changes in the moisture contents (dry basis)
of the eggplant slices with drying time at different
air temperatures and velocities are shown in
Fig. 3. This Figure demonstrates the influence of
the air temperature and velocity on the change in
the moisture content of the eggplant slices over
time, and shows that air temperature had a
significant effect while air velocity had a small
effect. A number of previous researchers have
neglected the effect of air velocity in the analysis of
their thin-layer drying data by citing the conclu-
sion of Henderson  Pabis (1962) that the
resistance to moisture movement at the surface is
negligible compared with the internal resistance
for turbulent flow, which occurs in most driers.
However, Islam  Flink (1982) pointed out that at
air velocities of 2.5 m s)1
or less, the external mass
transport resistance is significant and needs to be
considered in the analysis of the drying data. This
study has shown this to be the case for air velocity
in the range 1–1.5 m s)1
. The time to reach
0.04 g water g)1
dry matter moisture content from
the initial moisture content, at the various drying
air temperatures and velocities, was between 180
and 340 min. In order to normalize the drying
curves, the dry basis moisture content data were
transformed to a dimensionless moisture ratio
parameter (Fig. 4), The changes in the drying rates
with drying time are shown in Fig. 5. It is
apparent that drying rate decreases continuously
with drying time. There is no constant-rate drying
period in these curves and all the drying opera-
tions are seen to occur in the falling rate period.
These results are in agreement with the earlier
observations of Chiang  Petersen (1985) and
Maskan (2001).
Table 1 Thin-layer drying curve
models for the variation of mois-
ture ratio (MR) with time (t)
Model
no
Model
name Model References
1 Newton MR ¼ exp()kt) Mujumdar  Menon, 1995
2 Page MR ¼ exp()ktn
) Diamante  Munro, 1993
3 Modified Page MR ¼ exp()kt)n
Overhults et al., 1973
4 Henderson and Pabis MR ¼ aexp()kt) Zhang  Litchfield, 1991
5 Logarithmic MR ¼ aexp()kt) + c Yagcioglu et al., 1999
6 Two term MR ¼ aexp()k0t) +
bexp()k1t)
Henderson, 1974
7 Two-term exponential MR ¼ a exp()kt) +
(1 ) a) exp()kat)
Sharaf-Eldeen et al., 1980
8 Wang and Singh MR ¼ 1 + at + bt2
Wang  Singh, 1978
Thin-layer modelling E. K. Akpinar and Y. Bicer
276
International Journal of Food Science and Technology 2005, 40, 273–281  2005 Institute of Food Science and Technology Trust Fund
The moisture content data at the different drying
air temperatures and velocities were converted to
the more useful moisture ratio expression and then
curve fitting computations with the drying time
were done by using the 8 drying models in Table 1.
The results of statistical analyses undertaken on
these models are given in Table 2. The r-values
varied between 0.9696 and 0.9784, the Page model
giving the highest values of r and the lowest values
of RMSE and chi-squared. Thus, the Page model
was selected as best representing the thin-layer
drying behaviour of eggplant:
MR ¼ expðktn
Þ
The Page model is a modification of the Newton
model and overcomes the shortcomings of the
latter (Panchariya et al., 2002). Several investiga-
tors (Guarte, 1996; Afzal  Abe, 1999; Karath-
anos  Belessiotis, 1999; Hossain  Bala, 2002)
have reported that the Page model adequately
predicts the thin-layer drying of a wide variety of
crops such as copra, potato, currant, sultanas, figs,
plums and chilli.
Although this model could be used to model
the drying behaviour of eggplants, it did not
indicate the effect of drying air temperature and
velocity. To account for the effect of these
drying variables on the Page model’s constant
k (min)1
) and coefficient n (dimensionless), the
values of k and n were regressed against drying
air temperature and velocity using multiple
regression analysis. All possible combinations
of the variables were tested and included in the
multiple regression analysis. The multiple com-
binations of the parameters that gave the highest
r-values were eventually included in the final
model.
Based on the multiple regression analysis, the
Page model constants and coefficients were
expressed in terms of the drying air temperature,
T (C) and velocity, V (m s)1
) as;
k ¼ 0:000312T0:5817
V1:1711
r ¼ 0:9639
n ¼ 0:4829T0:2310
V0:1183
r ¼ 0:9618
These expressions can be used to estimate the
moisture ratio of eggplant at any time during
the drying process, with a high accuracy in the
measurement ranges of T ¼ 55–75 C and V ¼
l–1.5 m s)1
. The model and its incorporated rela-
tionships between the coefficients and the drying
air temperature and velocity is consistent with the
experimental data as evidenced by the good
correlation values of:
r ¼ 0:9999 v2
¼ 4:27  104
RMSE ¼ 0:0204
The accuracy of the established model was
evaluated by comparing the computed moisture
ratios with the observed values in Fig. 6. The
closeness of the plotted data to the straight line
Figure 3 Variation of moisture
content with drying time at differ-
ent air temperatures (T) and
velocities (V).
Thin-layer modelling E. K. Akpinar and Y. Bicer 277
 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 273–281
representing equality between the experimental
and predicted values illustrates the suitability of
the Page model for describing the drying beha-
viour of eggplant.
Conclusions
In this study of the thin-layer drying of egg-
plant, no constant drying rate period was
observed under any of the test conditions. The
eggplant drying process occurred in the falling
rate. The drying time to reach 0.04 g water g)1
dry matter moisture content from the initial
moisture content, at the various drying air
temperatures and velocities, was found to be
between 180 and 340 min. The influence of air
temperature on the drying behaviour of the egg-
plant was more significant than that of the air
velocity.
Of the eight thin-layer drying models, com-
paratively tested according to their coefficients of
correlation and reduced chi-squared and RMSE
values, the Page model best described the drying
behaviour of the eggplant slices. When the
effects of the drying air temperature and velocity
on the constant and coefficients of the Page
Figure 4 Variation of moisture
ratio (MR) with drying time at
different air temperatures (T) and
velocities (V).
Thin-layer modelling E. K. Akpinar and Y. Bicer
278
International Journal of Food Science and Technology 2005, 40, 273–281  2005 Institute of Food Science and Technology Trust Fund
Figure 5 Variation of drying rate
with drying time at different air
temperatures (T) and velocities (V).
Table 2 Modelling of moisture
ratio according to the drying time Model no Model constants r RMSE v2
1 k ¼ 0.0127 0.9758 0.0688 4.798 · 10)3
2 k ¼ 0.006165; n ¼ 1.160 0.9784 0.0650 4.335 · 10)3
3 k ¼ 0.1128; n ¼ 0.1128 0.9758 0.0688 4.857 · 10)3
4 a ¼ 1.031; k ¼ 0.01311 0.9764 0.0680 4.743 · 10)3
5 a ¼ 1.063; k ¼ 0.01164;
c ¼ 0.04650
0.9779 0.0658 4.505 · 10)3
6 a ¼ 0.5471; k0 ¼ 0.01311;
b ¼ 0.4842; k1 ¼ 0.01311
0.9764 0.0680 4.863 · 10)3
7 a ¼ 0.003166; k ¼ 4.008 0.9757 0.06901 4.880 · 10)3
8 a ¼ )0.008557; b ¼ 0.000018 0.9696 0.0770 6.081 · 10)3
Thin-layer modelling E. K. Akpinar and Y. Bicer 279
 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 273–281
model were taken into account, the resulting
model gave a good fit (r ¼ 0.9999, v2
¼
4.27 · 10)4
, RMSE ¼ 0.0204) to the observed
drying behaviour of eggplant slices dried at air
temperatures of 55–75 C and velocities of
1–1.5 m s)1
.
Acknowledgment
Authors wish to thank the Firat University
Research Foundation (FUNAF) for financial
support, under project number 357.
Nomenclature
a, b, c, n empirical constants in the drying
models
k, k0, k1 empirical coefficients in the drying
models, min)1
n number of constants
N number of observations
MR moisture ratio
MRexp experimental moisture ratio
MRpre predicted moisture ratio
M moisture content, %dry basis
(g water g)1
dry matter)
Me equilibrium moisture content, %dry
basis
M0 initial moisture content, %dry basis
r correlation coefficient
RMSE root mean square error
t time, min
T temperature, C
V velocity, m s)1
v2
chi-squared
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j.1365-2621.2004.00886.x.pdf

  • 1. Original article Modelling of the drying of eggplants in thin-layers Ebru Kavak Akpinar* & Yasar Bicer Mechanical Engineering Department, Firat University, 23279, Elazig, Turkey (Received 16 February 2004; Accepted in revised form 27 May 2004) Summary In this paper, the thin-layer drying behaviour of eggplant slices (6 mm thick layers) in a convective-type cyclone dryer is reported. Thin-layer drying experiments were conducted at drying air temperatures of 55, 65 and 75 C and dry air velocities of 1 and 1.5 ms)1 . Data on sample mass, temperature and velocity of the dry air were recorded continuously during each test. In order to estimate and select a suitable form of the drying curve, eight different semi-theoretical and/or empirical models were fitted to the experimental data and comparisons made of their coefficients of determination as predicted by non-linear regression analysis. The Page model best described the drying curve of eggplant, with a correlation coefficient, r ¼ 0.9999. Keywords Drying models, mathematical modelling, moisture ratio, non-linear regression. Introduction Dehydration is an important operation in the chemical and food processing industries. The objective dehydration is the removal of water to the level at which microbial spoilage and deteri- oration reactions are greatly minimized. The wide variety of dehydrated foods available to the consumer (snacks, dry mixes and soups, dried fruits, etc.) and the importance of meeting quality specifications and conserving energy, emphasize the need for a thorough understanding of the drying process. Thin-layer drying models that describe the drying phenomenon of agricultural products fall mainly into three categories, namely theoretical, semi-theoretical and empirical (Panchariya et al., 2002). The theoretical approach is concerned with diffusion or simultaneous heat and mass transfer equations. The semi-theoretical ap- proach is concerned with approximated theoret- ical equations. Empirical equations are easily applied to drying simulation as they depend only on experimental data (Afzal Abe, 2000). Theoretical approaches take into account the internal resistance to moisture transfer, while semi-theoretical and empirical approaches con- sider only the external resistance to moisture transfer between the product and air (Hender- son, 1974). To design and control a dryer and to define optimum drying conditions, it is necessary to model the actual process of drying in terms of mathematical relations. Although, in the past, many theoretical and empirical models have been developed for various foods and agro-based products (Diamante Munro, 1991; Sarsavadia et al., 1999; Özdemir Devres, 1999; Afzal Abe, 2000; Yaldiz et al., 2001; Yaldiz Ertekin, 2001; Panchariya et al., 2002; Midilli Kucuk, 2003), no investigations on the thin-layer drying of eggplant have been reported in the literature. Eggplant is of particular interest in the prepara- tion of dry mixtures used for soups etc. Therefore, the main objectives of this study were to determine the effect of the drying air temperature and air velocity on the drying kinetics of eggplant slices in a convective-type cyclone dryer, and to select the best mathematical model for the drying curves. *Correspondent: Fax: +90 424 241 5526; e-mail: eakpinar@firat.edu.tr International Journal of Food Science and Technology 2005, 40, 273–281 273 doi:10.1111/j.1365-2621.2004.00886.x 2005 Institute of Food Science and Technology Trust Fund
  • 2. Materials and methods Experimental set-up Figure 1 shows a schematic diagram of the cyclone type dryer developed for the experimental work (Akpinar, 2002). It consists of a fan (12), resist- ance and heating control systems (7, 10, 11), air- duct (15), cyclone-type drying chamber (1), and measurement instruments (3, 5, 8, 9, 13). The airflow was adjusted by means of a variable speed blower and a manually operated adjustable flap (14) in the entrance. Airflow rate was measured with an anemometer (Lutron AM-4201, Taipei, Taiwan). The heating system consisted of an electric 4000 W heater (11) placed inside the duct. A rheostat (10) was used to adjust the drying chamber temperature. The rectangular duct (15), containing the air fan and heater, constructed from sheet iron, was 100 cm long, 20 cm wide and 25 cm high. The cylindrical drying chamber (1), constructed from sheet iron, had a diameter of 60 cm and a height of 80 cm. The inside and outside surfaces of the drying chamber were painted with a spray dye to prevent rusting of the sheet iron surface. The drying chamber was constructed in concentric form with a 3 cm annu- lus insulated with polystyrene. Both the top and bottom ends of the drying chamber were closed with steel covers insulated with polystyrene. The top cover was used to load or unload the chamber. In the cyclone type dryer, samples are dried by a swirling flow of drying air instead of an axial airflow. Air entering across the bottom part of the drying chamber produces the swirling flow. The samples were dried in a tray manufactured from a nylon sieve, which allowed the airflow to pass through the trays. The flow diagram of the thin- layer drying process is presented in Fig. 2. In the measurements of temperatures, J type iron-constant thermocouples were used with a manually controlled 20-channel automatic digital thermometer (Elimko 6400, Ankara, Turkey), with an accuracy of ±0.1 C. A thermo hygrom- eter (Extech 444731, Shenzhen, China) was used to measure humidity levels at various locations in the system. Moisture loss was recorded at 20-min intervals during drying by means of a digital balance (Bel, Mark 3100, Monza, Italy) with an accuracy of ±0.01 g (Fig. 1). 13 3 4 2 3 6 5 1 7 9 8 13 11 15 12 10 14 Figure 1 Experimental set-up (1, drying chamber; 2, tray; 3, digital balance; 4, observation windows; 5, digital thermometer; 6, the balance suspension bar; 7, control panel; 8, thermocouples; 9, digital thermometer and channel selector; 10, rheostat; 11, heater; 12, fan; 13, wet and dry thermometers; 14, adjustable flap; 15, duct). Thin-layer modelling E. K. Akpinar and Y. Bicer 274 International Journal of Food Science and Technology 2005, 40, 273–281 2005 Institute of Food Science and Technology Trust Fund
  • 3. Procedure Fresh eggplant slices were used in the experi- ments. Before the drying process, the eggplants were cut into slices of 6 mm thickness and 30 mm diameter with a mechanical cutter. After the dryer had reached steady state temperature con- ditions for operation, 500 g of eggplant slices were put on the tray of the dryer and dried there. The initial and final moisture contents of the eggplant slices were determined at 80 C using an infrared moisture analyser (Mettler LJ16, Grei- fensee, Switzerland). Drying experiments were done at 55, 65, and 75 C drying air temperatures and 1 and 1.5 m s)1 air velocities. The ranges of the air temperature and velocity were set to the values largely used in actual industrial air drying applications and the thin-layer drying of vegetables and fruits by many researchers (Chiang Petersen, 1985; Diamante Munro, 1991; Karathanos Belessiotis, 1997; Yaldiz Ertekin, 2001; Yaldiz et al., 2001; Akpinar et al., 2003a,b). The relative humidity of the drying air was determined as 15% at 55 C, 9% at 65 C and 5% at 75 C. Drying was continued until the final moisture content of the samples reached approximately 0.04 g water g)1 dry matter. During the experiments, ambient temperature and relative humidity, and the inlet and outlet temperatures of the drying air in the dryer chamber were recorded. Mathematical modelling of drying curves The moisture ratio (MR) of the eggplant slices during the thin-layer drying experiments was calculated using the following equation: MR ¼ M Me Mo Me ð1Þ where M0 and Me are the initial and equilibrium moisture contents (% dry basis) respectively. For mathematical modelling, the thin-layer drying equations in Table 1 were tested to select the best model for describing the experimental drying curves of the eggplant slices during drying in the convective type-cyclone dryer. Regression analysis was performed by using the Statistica computer program (StatSoft Inc., 1993, Tulsa, OK, USA). The correlation coefficient (r) was the primary criterion for selecting the best equation to describe the drying curves (Guarte, 1996). In addition to r, the reduced chi-squared (v2 ) and root mean square error (RMSE) analyses were used to determine the best fit. These parameters are calculated as follows: v2 ¼ P n i¼1 ðMRexp;i MRpre;iÞ2 N n ð2Þ RMSE ¼ 1 N X N i¼1 ðMRpre;i MRexp;iÞ2 #1=2 ð3Þ Fresh air Fan Heaters Tray Sample weighing Drying air inlet Drying air outlet Drying chamber Velocity measurement Velocity measurement Airflow rate setting Temperature measurement Temperature velocity measurement Temperature measurement Temperature measurement Figure 2 Flow diagram of the thin-layer drying process of eggplant slices. Thin-layer modelling E. K. Akpinar and Y. Bicer 275 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 273–281
  • 4. where MRexp,i is the ith experimentally observed moisture ratio, MRpre,i the ith predicted moisture ratio, N the number of observations and n is the number of constants (Sarsavadia et al., 1999; Yaldiz et al., 2001). The effects of parameters related to the product or drying conditions, such as slice thickness, drying air temperature, relative humidity, etc., have been investigated by many researchers (Henderson, 1974; Özdemir Devres, 1999; Yaldiz Ertekin, 2001). Modelling the drying behaviour of different agricultural products often requires the statistical methods of regression and correlation analysis. Linear and non-linear regres- sion models are important tools to use find the relationship between different variables, especially those for which no established empirical relation- ship exists. In this study, the constants and coefficients of the best fitting model were determined, involving drying variables such as air temperature and velocity. The effects of these variables on the constants and coefficients of the drying expression were also investigated by multi- ple linear regression analysis. Results and discussion Eggplant slices of 10.63 g water g)1 dry matter average initial moisture content were dried to 0.04 g water g)1 dry matter using different air temperatures (55, 65 and 75 C) and different air velocities (1 and 1.5 m s)1 ). The final moisture contents represent the moisture equilibrium between the sample and the drying air, under the conditions in the dryer, beyond which any changes in the mass of the sample could not occur. The changes in the moisture contents (dry basis) of the eggplant slices with drying time at different air temperatures and velocities are shown in Fig. 3. This Figure demonstrates the influence of the air temperature and velocity on the change in the moisture content of the eggplant slices over time, and shows that air temperature had a significant effect while air velocity had a small effect. A number of previous researchers have neglected the effect of air velocity in the analysis of their thin-layer drying data by citing the conclu- sion of Henderson Pabis (1962) that the resistance to moisture movement at the surface is negligible compared with the internal resistance for turbulent flow, which occurs in most driers. However, Islam Flink (1982) pointed out that at air velocities of 2.5 m s)1 or less, the external mass transport resistance is significant and needs to be considered in the analysis of the drying data. This study has shown this to be the case for air velocity in the range 1–1.5 m s)1 . The time to reach 0.04 g water g)1 dry matter moisture content from the initial moisture content, at the various drying air temperatures and velocities, was between 180 and 340 min. In order to normalize the drying curves, the dry basis moisture content data were transformed to a dimensionless moisture ratio parameter (Fig. 4), The changes in the drying rates with drying time are shown in Fig. 5. It is apparent that drying rate decreases continuously with drying time. There is no constant-rate drying period in these curves and all the drying opera- tions are seen to occur in the falling rate period. These results are in agreement with the earlier observations of Chiang Petersen (1985) and Maskan (2001). Table 1 Thin-layer drying curve models for the variation of mois- ture ratio (MR) with time (t) Model no Model name Model References 1 Newton MR ¼ exp()kt) Mujumdar Menon, 1995 2 Page MR ¼ exp()ktn ) Diamante Munro, 1993 3 Modified Page MR ¼ exp()kt)n Overhults et al., 1973 4 Henderson and Pabis MR ¼ aexp()kt) Zhang Litchfield, 1991 5 Logarithmic MR ¼ aexp()kt) + c Yagcioglu et al., 1999 6 Two term MR ¼ aexp()k0t) + bexp()k1t) Henderson, 1974 7 Two-term exponential MR ¼ a exp()kt) + (1 ) a) exp()kat) Sharaf-Eldeen et al., 1980 8 Wang and Singh MR ¼ 1 + at + bt2 Wang Singh, 1978 Thin-layer modelling E. K. Akpinar and Y. Bicer 276 International Journal of Food Science and Technology 2005, 40, 273–281 2005 Institute of Food Science and Technology Trust Fund
  • 5. The moisture content data at the different drying air temperatures and velocities were converted to the more useful moisture ratio expression and then curve fitting computations with the drying time were done by using the 8 drying models in Table 1. The results of statistical analyses undertaken on these models are given in Table 2. The r-values varied between 0.9696 and 0.9784, the Page model giving the highest values of r and the lowest values of RMSE and chi-squared. Thus, the Page model was selected as best representing the thin-layer drying behaviour of eggplant: MR ¼ expðktn Þ The Page model is a modification of the Newton model and overcomes the shortcomings of the latter (Panchariya et al., 2002). Several investiga- tors (Guarte, 1996; Afzal Abe, 1999; Karath- anos Belessiotis, 1999; Hossain Bala, 2002) have reported that the Page model adequately predicts the thin-layer drying of a wide variety of crops such as copra, potato, currant, sultanas, figs, plums and chilli. Although this model could be used to model the drying behaviour of eggplants, it did not indicate the effect of drying air temperature and velocity. To account for the effect of these drying variables on the Page model’s constant k (min)1 ) and coefficient n (dimensionless), the values of k and n were regressed against drying air temperature and velocity using multiple regression analysis. All possible combinations of the variables were tested and included in the multiple regression analysis. The multiple com- binations of the parameters that gave the highest r-values were eventually included in the final model. Based on the multiple regression analysis, the Page model constants and coefficients were expressed in terms of the drying air temperature, T (C) and velocity, V (m s)1 ) as; k ¼ 0:000312T0:5817 V1:1711 r ¼ 0:9639 n ¼ 0:4829T0:2310 V0:1183 r ¼ 0:9618 These expressions can be used to estimate the moisture ratio of eggplant at any time during the drying process, with a high accuracy in the measurement ranges of T ¼ 55–75 C and V ¼ l–1.5 m s)1 . The model and its incorporated rela- tionships between the coefficients and the drying air temperature and velocity is consistent with the experimental data as evidenced by the good correlation values of: r ¼ 0:9999 v2 ¼ 4:27 104 RMSE ¼ 0:0204 The accuracy of the established model was evaluated by comparing the computed moisture ratios with the observed values in Fig. 6. The closeness of the plotted data to the straight line Figure 3 Variation of moisture content with drying time at differ- ent air temperatures (T) and velocities (V). Thin-layer modelling E. K. Akpinar and Y. Bicer 277 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 273–281
  • 6. representing equality between the experimental and predicted values illustrates the suitability of the Page model for describing the drying beha- viour of eggplant. Conclusions In this study of the thin-layer drying of egg- plant, no constant drying rate period was observed under any of the test conditions. The eggplant drying process occurred in the falling rate. The drying time to reach 0.04 g water g)1 dry matter moisture content from the initial moisture content, at the various drying air temperatures and velocities, was found to be between 180 and 340 min. The influence of air temperature on the drying behaviour of the egg- plant was more significant than that of the air velocity. Of the eight thin-layer drying models, com- paratively tested according to their coefficients of correlation and reduced chi-squared and RMSE values, the Page model best described the drying behaviour of the eggplant slices. When the effects of the drying air temperature and velocity on the constant and coefficients of the Page Figure 4 Variation of moisture ratio (MR) with drying time at different air temperatures (T) and velocities (V). Thin-layer modelling E. K. Akpinar and Y. Bicer 278 International Journal of Food Science and Technology 2005, 40, 273–281 2005 Institute of Food Science and Technology Trust Fund
  • 7. Figure 5 Variation of drying rate with drying time at different air temperatures (T) and velocities (V). Table 2 Modelling of moisture ratio according to the drying time Model no Model constants r RMSE v2 1 k ¼ 0.0127 0.9758 0.0688 4.798 · 10)3 2 k ¼ 0.006165; n ¼ 1.160 0.9784 0.0650 4.335 · 10)3 3 k ¼ 0.1128; n ¼ 0.1128 0.9758 0.0688 4.857 · 10)3 4 a ¼ 1.031; k ¼ 0.01311 0.9764 0.0680 4.743 · 10)3 5 a ¼ 1.063; k ¼ 0.01164; c ¼ 0.04650 0.9779 0.0658 4.505 · 10)3 6 a ¼ 0.5471; k0 ¼ 0.01311; b ¼ 0.4842; k1 ¼ 0.01311 0.9764 0.0680 4.863 · 10)3 7 a ¼ 0.003166; k ¼ 4.008 0.9757 0.06901 4.880 · 10)3 8 a ¼ )0.008557; b ¼ 0.000018 0.9696 0.0770 6.081 · 10)3 Thin-layer modelling E. K. Akpinar and Y. Bicer 279 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 273–281
  • 8. model were taken into account, the resulting model gave a good fit (r ¼ 0.9999, v2 ¼ 4.27 · 10)4 , RMSE ¼ 0.0204) to the observed drying behaviour of eggplant slices dried at air temperatures of 55–75 C and velocities of 1–1.5 m s)1 . Acknowledgment Authors wish to thank the Firat University Research Foundation (FUNAF) for financial support, under project number 357. Nomenclature a, b, c, n empirical constants in the drying models k, k0, k1 empirical coefficients in the drying models, min)1 n number of constants N number of observations MR moisture ratio MRexp experimental moisture ratio MRpre predicted moisture ratio M moisture content, %dry basis (g water g)1 dry matter) Me equilibrium moisture content, %dry basis M0 initial moisture content, %dry basis r correlation coefficient RMSE root mean square error t time, min T temperature, C V velocity, m s)1 v2 chi-squared References Afzal, T.M. Abe, T. (1999). Some fundamental attributes of far infrared radiation drying of potato. Drying Technology, 17, 137–155. Afzal, T.M. Abe, T. (2000). Simulation of moisture changes in barley during far infrared radiation drying. Computational Electronic and Agricultural 26, 137–145. Akpinar, E.K. (2002), The Development of a Cyclone Type Dryer for Agricultural Products. PhD Thesis. Elazig, Turkey: Firat University. Akpinar, E.K., Midilli, A. Bicer, Y. (2003a). Single layer drying behavior of potato slices in a convective cyclone dryer and mathematical modeling. Energy Conversion and Management, 44, 1689–1705. Akpinar, E.K., Bicer, Y. Yildiz, C. (2003b). Thin layer drying of red pepper. Journal of Food Engineering, 59, 99–104. Chiang, W.C. Petersen, J.N. (1985). Thin layer air drying of French fried potatoes. Journal of Food Technology, 20, 67–78. Diamante, L.M. Munro, P.A. (1991). Mathematical modelling of hot air drying of sweet potato slices. International Journal of Food Science and Technology, 26, 99–109. Diamante, L.M. Munro, P.A. (1993). Mathematical modelling of the thin layer solar drying of sweet potato slices. Solar Energy, 51, 271–276. Guarte, R.C. (1996). Modelling the Drying Behaviour of Copra and Development of a Natural Convection Dryer for Production of High Quality Copra in the Philippines. PhD Dissertation. Stuttgart, Germany: Hohenheim University. Figure 6 Comparison of experimental (u, s) moisture ratios with those predicted from the Page model (continuous line). Thin-layer modelling E. K. Akpinar and Y. Bicer 280 International Journal of Food Science and Technology 2005, 40, 273–281 2005 Institute of Food Science and Technology Trust Fund
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