Journal of Agricultural Sciences
Dergi web sayfası:
www.agri.ankara.edu.tr/dergi
Journal homepage:
www.agri.ankara.edu.tr/journal
Tar. Bil. Der.
Mathematical Modelling of Convection Drying Characteristics of
Artichoke (Cynara scolymus L.) Leaves
Tuncay GÜNHANa, Vedat DEMİRa, Abdülkadir YAĞCIOĞLUa
a
Ege University, Faculty of Agriculture, Department of Agricultural Machinery, 35100, Bornova, Izmir, TURKEY
ARTICLE INFO
Research Article
Corresponding Author: Tuncay GÜNHAN, E-mail: [email protected], Tel: +90 (232) 311 26 62
Received: 11 February 2014, Received in Revised Form: 17 March 2014, Accepted: 18 March 2014
ABSTRACT
This paper presents the results of a study on mathematical modelling of convection drying of artichoke (Cynara scolymus
L.) leaves. Artichoke leaves used for drying experiments were picked from the agricultural faculty experimentation fields
on the campus area of Ege University. Chopped artichoke leaves were then used in the drying experiments performed
in the laboratory at different air temperatures (40, 50, 60 and 70 °C) and airflow velocities (0.6, 0.9 and 1.2 m s-1)
at constant relative humidity of 15±2%. Drying of artichoke leaves down to 10% wet based moisture content at air
temperatures of 40, 50, 60 and 70 °C lasted about 4.08, 2.29, 1.32 and 0.98 h respectively at a constant drying air velocity
of 0.6 m s-1 while drying at an air velocity of 0.9 ms-1 took about 3.83, 1.60, 0.96 and 0.75 h. Increasing the drying air
velocity up to 1.2 m s-1 at air temperatures of 40, 50, 60 and 70 °C reduced the drying time down to 3.5, 1.54, 1.04 and
0.71 h respectively. Different mathematical drying models published in the literature were used to compare based on the
coefficient of multiple determination (R2), root mean square error (RMSE), reduced chi-square (χ2) and relative deviation
modulus (P). From the study conducted, it was concluded that the Midilli et al drying model could satisfactorily explain
convection drying of artichoke (Cynara scolymus L.) leaves under the conditions studied.
Keywords: Drying; Artichoke; Modelling
Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma
Karakteristiklerinin Matematiksel Modellenmesi
ESER BİLGİSİ
Araştırma Makalesi
Sorumlu Yazar: Tuncay GÜNHAN, E-posta: [email protected], Tel: +90 (232) 311 26 62
Geliş Tarihi: 11 Şubat 2014, Düzeltmelerin Gelişi: 17 Mart 2014, Kabul: 18 Mart 2014
ÖZET
Bu çalışmada enginar yapraklarının (Cynara scolymus L.) konveksiyonel kuruma karakteristiklerinin matematiksel
modellenmesi sunulmuştur. Denemelerde kullanılan enginar yaprakları Ege Üniversitesi yerleşke alanı içerisindeki
Ziraat Fakültesi deneme parsellerinden toplanmıştır. Doğranmış enginar yaprakları, laboratuvarda çeşitli sıcaklıklarda
(40, 50, 60 ve 70 °C) ve hava hızlarında (0.6, 0.9 ve 1.2 m s-1) sabit bağıl nem değerinde (% 15±2) kurutma denemelerinde
TARIM BİLİMLERİ DERGİSİ — JOURNAL OF AGRICULTURAL SCIENCES 20 (2014) 415-426
Tarım Bilimleri Dergisi
Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
kullanılmıştır. Enginar yapraklarının 40, 50, 60 ve 70 °C sıcaklıklarda % 10 nem içeriğine (yb) ulaşmaları 0.6 m s-1 sabit
hava hızında sırasıyla yaklaşık olarak 4.08, 2.29, 1.32 ve 0.98 h sürerken, 0.9 m s-1 sabit hava hızında yaklaşık olarak
3.83, 1.60, 0.96 ve 0.75 h sürmüştür. 40, 50, 60 ve 70 °C sıcaklıklarda kurutma havası hızını 1.2 m s-1’ye kadar artırmak
kuruma süresini sırasıyla 3.5, 1.54, 1.04 ve 0.71 h’e kadar düşürmüştür. Literatürde yer alan çeşitli kuruma modelleri,
belirtme katsayısı (R2), ortalama hata kareleri karekökü (RMSE), khi-kare (χ2) ve mutlak bağıl hata (P) değerleri
kullanılarak karşılaştırılmıştır. Yapılan çalışma sonunda denemelerin yapıldığı koşullar altında enginar yapraklarının
kurumasını en iyi Midilli vd. kuruma modelinin açıkladığı belirlenmiştir.
Anahtar Kelimeler: Kurutma; Enginar; Modelleme
© Ankara Üniversitesi Ziraat Fakültesi
1. Introduction
The artichoke (Cynara scolymus L.) is a perennial
vegetable that has a great production potential
in Europe and in the continent of America and it
received a great acceptance for the consumption in
recent years in Turkey. Italy, Egypt, Spain, Peru and
Argentina are the biggest artichoke producers in the
World respectively while Turkey is ranked the 13th
one and the production area of artichoke shows an
increasing trend in Turkey (FAO 2013).
Among the public, artichoke leaves are known
to be useful in eliminating hepatitis and disorders
related to hyperlipidemia. Artichoke leaf is also
known as an herbal medicine for a long time
and used for the treatment of hyperlipidemia and
hepatitis in EU traditional folk medicine. Different
studies about artichoke have demonstrated their
health-protective potential. The artichoke leaves
are characterized by the composition and high
content in bitter phenolic acids, whose choleretic,
hypocholerestemic and hepatoprotector activities
are attributed (Alonso et al 2006). Antioxidant,
hepatoprotective, anti-HIV, choleretic and
inhibiting cholesterol biosynthesis activities of
artichoke extracts are also reported by Zhu et al
(2005). Shimoda et al (2003) reported that the
methanolic extract of artichoke suppress the serum
triglyceride in mice. Zhu et al (2005) reported
that the artichoke leaves have a new potential
application in the treatment of fungal infections.
The composition of phytochemicals in artichoke
leaves were well documented in the literature and
medicinal values of artichoke leaves were found
higher than flowers (Sanchez-Rabaneda et al
416
2003; Bundy et al 2008). Moreover, anti-oxidant,
hepatoprotective, lowering blood cholesterol
effects were mostly studied in the literature.
Wang et al (2003) used three different
artichoke varieties in order to determine the
phenolic acid components. They dried the
artichoke leaves and tissues in an oven at 70
°C and also in a freeze drier. After the drying,
samples were kept in air tight bags at room
temperatures for further analysis. Researchers
determined the phenolic acid compounds and
amounts by HPLC analysis for mature leaves,
young and mature artichoke heads. According
to the results obtained by Wang et al (2003) it
was reported that the leaves have highest total
phenols content than young artichoke heads as
followed by mature artichoke heads. In terms of
the method they used, they concluded that freeze
drying and air assisted drying did not affect the
amount of phenolic acid in artichoke.
Fresh food materials cannot be stored for a
long time. Therefore, products must be dried for
a long-term storage. One of the most traditional
and extensive technique used for the production
of dehydrated fruits and vegetables is convection
drying (Nicoleti et al 2001). It allows to reduce
mass and volume, to store the products under
ambient temperature and to minimize packaging,
transportation and storage cost (Baysal et al
2003).
Mathematical modelling in drying studies is one
of the most significant step in drying technology and
allows engineers to select the most suitable drying
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al
conditions and to form a drying equipment at a
proper scale (Strumillo & Kudra 1986; Hawlader et
al 1997).
2. Material and Methods
Scientific studies on the drying process of
artichoke leaves in the literature is very limited and
the most of them focused on determination of the
chemical components of artichoke leaves and there
is no study published on the determination of the
drying characteristics of the artichoke leaves.
Drying experiments were performed in a laboratory
scale convective hot air dryer constructed in the
Department of Agricultural Machinery, Faculty
of Agriculture, Ege University, Izmir, Turkey.
A schematic diagram of the laboratory dryer is
illustrated in Figure 1. The drying system used in
this study has been described in details by Demir et
al (2007). The laboratory dryer includes; fan, cooler,
heater, humidifier, drying unit and automatic control
unit.
The aim of the study was to determine the drying
characteristics and to develop a mathematical model
for predicting the kinetics of convection drying of
artichoke leaves.
2.1. Experimental procedures
Figure 1- Schematic diagram of the drying unit: 1, centrifugal fan; 2, cooling and condensing tower; 3, cold
water tank and evaporator; 4,7,9, thermocouples (type T); 5, circulation pump; 6, cold water shower; 8,
electric heaters; 10, mixing chamber and air channels; 11, steam tank; 12, solenoid valve; 13, temperature
& humidity sensor; 14, balance; 15, computer with data acquisition and control cards; 16, artichoke leaves;
17, anemometer; 18, frequency converter
Şekil 1- Kurutma ünitesinin şematik çizimi; 1, santrifüj fan; 2, soğutma ve yoğuşturma kulesi; 3, soğuk su tankı
ve evaparatör; 4,7,9, termokupl (T tipi); 5, sirkülasyon pompası; 6, soğuk su duşu; 8, elektrikli ısıtıcı; 10, karışım
odası ve hava kanalları; 11, buhar tankı; 12, solenoid valf; 13, sıcaklık ve nem sensörü; 14, terazi; 15, veri akış
ve kontrol kartlı bilgisayar; 16, enginar yaprakları; 17, anemometre; 18, frekans dönüştürücü
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
417
Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
A personal computer equipped with A/D
converters cards and data acquisition & control
software called VisiDAQ (Advantech Automation
Corp., USA) was used to control the drying
temperature, relative humidity and the automation
of the drying system.
The artichoke leaves for the drying experiments
were picked from the middle branches of the
artichoke plants as they are located on the campus
area of Ege University, between 8:30 and 9:00
a.m. During the experiments, the fresh leaves were
collected daily in early-morning and unblemished
ones were picked and used in the drying experiments.
Some preliminary tests were carried out to
examine the drying conditions from the point of
test stand and some expected changes in artichoke
leaves. In these tests, a homogeneous drying of the
whole leaves was not obtained, especially the main
vein of the leaves was found to be the last part that
dried. In this situation, the tissues in the thinner
part of the leaves were subjected to over drying and
drying time significantly increased. For this reason,
the leaves were divided into two parts along the
main vein and then sliced perpendicularly to the
main vein. The 4 or 5 mm wide slices were then
used for the drying process.
The experiments conducted in the lab had the
objective to determine the effect of air temperature
and drying airflow velocity on the drying constant
were achieved at temperatures of 40, 50, 60 and
70 °C, and at velocity of 0.6, 0.9 and 1.2 m s-1
respectively. During the experiments, the relative
humidity was maintained at 15 ± 2%. The drying
system was run for at least one hour to maintain
steady-state conditions before the experiments.
Each drying experiment was performed with 20
g of leaves after steady state conditions of both
temperature and air velocity was achieved in
the dryer. The artichoke leaves were placed in a
vertical drying channel equipped with fine sieves
and weighed every three minutes in the first 15
minute drying process and then every 5 minutes
until the drying process is completed. The drying
experiments were ended when the mass of the
samples does not change.
The leaf samples were kept in an air-circulated
oven for 24 hours at 105 ±2 °C in order to determine
the initial moisture content. All of these experiments
mentioned above were triplicated.
2.2. Mathematical modelling of the drying curves
The experimental moisture ratio data of artichoke
leaves were fitted to semi-empirical models in Table
1 to define the convection drying kinetics. The
models in Table 1 were widely employed to describe
the convection drying kinetics of vegetables.
Table 1- Mathematical models widely used to describe the convection drying kinetics
Çizelge 1- Konveksiyonla kuruma kinetiklerini belirlemede yaygın olarak kullanılan matematiksel modeler
Model name
Model equation
References
Lewis
MR= exp(-kt)
Yaldız & Ertekin (2001)
Page
MR= exp(-ktn)
Modified Page
MR= exp[-(kt) ]
Artnaseaw et al (2010)
Henderson and pabis
MR= a exp(-kt)
Figiel (2010)
Logarithmic
MR= a exp(-kt)+c
Doymaz (2013)
Midilli et al
MR= a exp(-kt )+bt
Silva et al (2011)
Demir et al
MR= a exp[-(kt) ]+b
Demir et al (2007)
Alibaş (2012)
n
n
n
MR, moisture ratio; a, b, c coefficients; n, drying exponent specific to each equation; k, drying coefficients specific to each equation;
t, time
418
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
The experimental moisture ratio data of artichoke leaves were fitted tosemi-empirical models in Table 1
Lewis
MR= exp(-kt)
Yaldız&Ertekin (2001)
to define the convection drying kinetics.
The models in Table 1 were widely employed to describe the
Page
MR= exp(-ktn)
Alibaş (2012)
convection drying kinetics of vegetables. n
Artnaseaw et al (2010)
Modified Page
MR= exp[-(kt) ]
Henderson
and
Pabis
MR=
a
exp(-kt)
(2010) drying kinetics
Table 1- Mathematical models widely used to describe theFigiel
convection
Logarithmic
MR= a exp(-kt)+c
Doymaz (2013)
modeler
Çizelge 1- Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel
Midilli et al
MR= a exp(-ktn)+bt
Silva et al (2011)
The
leave
samples
were
kept
an
oven
for
at
order
n
The
leave Enginar
samplesYapraklarının
were Model
kept(Cynara
inequation
an air-circulated
air-circulated
oven References
for 24
24
hours
at 105
105 ±2
±2 C
C in
in Matematiksel
order to
to determine
determine
Model
name
Demir
et al
MR=
ain
exp[-(kt)
]+b L.) Konveksiyonel
Demir
ethours
al (2007)
scolymus
Kuruma
Karakteristiklerinin
Modellenmesi, Günhan et al
The
leave
samples
were
kept
in
an
air-circulated
oven
for
24
hours
at
105
±2
C
in
order
to determine
the
initial
moisture
content.
All
of
theseexperiments
mentioned
above
were
triplicated.
the initial
All n,
ofexp(-kt)
theseexperiments
above
were
triplicated.
MR,
moisturemoisture
ratio; a, b,content.
c coefficients;
drying
exponent specificmentioned
to each
equation;
k, drying
coefficients specific to each equation;
Lewis
MR=
Yaldız&Ertekin
(2001)
the
initial
moisture
content.
All
of
theseexperiments
mentioned
above
were
triplicated.
2.2.
Mathematical modelling
modelling of
of the
the drying
drying
curves
curves
n
t,2.2.
timeMathematical
Page
MR=
)
Alibaş (2012)
2.2. Mathematical modelling
of exp(-kt
the drying
curves
n of the equations
The
left
hand
side
iset al
a (2010) The better goodness of the fit means that the
Artnaseaw
Modified
Page
MR=
exp[-(kt)
]
TheThe
experimental
moisture
ratio
data of
of
artichoke
leavesnumber
were fitted
fitted
tosemi-empirical
models
in Table
Table
1
left hand
side
of the ratio
equations
isknown
aartichoke
dimensionless
known
asvalue
moisture
it
The
experimental
moisture
data
leaves
were
tosemi-empirical
in
1
2 MRand
of ratio
Rmodels
dimensionless
number
as
moisture
ratio
MR
should
becould
higher
while the value of
Henderson
and
Pabis
MR=
exp(-kt)
Figiel
The
experimental
moisture
ratio akinetics.
data
of artichoke
leaves
were (2010)
fitted
tosemi-empirical
models
in Table
1
to
the
convection
drying
The
in
11 were
widely
to
describe
the
be
written
as follows:
to define
define
the
convection
drying
kinetics.
The models
models
in Table
Table
were
widely employed
employed
to
describe
the
2
and
it
could
be
written
as
follows:
RMSE,
χ
and
P
should
be
lower.
Selection of
Logarithmic
MR=
a
exp(-kt)+c
Doymaz
(2013)
to define the
convection
kinetics. The models in Table 1 were widely employed to describe the
convection
drying
kineticsdrying
of vegetables.
vegetables.
convection
drying
kinetics
of
Midilli
et al drying kinetics of
MR=
a exp(-ktn)+bt
Silva et al (2011) the best suitable drying model was done using
convection
vegetables.
MMR=
Ma eexp[-(kt)
t -widely
Demir
et al (1)
(2007)
Tableet11-alMathematical
Mathematical
models
usedn]+b
to describe
describe the
theDemir
convection
drying
kinetics
used
this
criteria. The drying constants (k) of the
(1)
Table
widely
to
convection
drying
kinetics
MR models
Table
1-1models
used
to describe
drying
kineticsmodel
modeler
Çizelge
Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel
M 0 -widely
M
MR,
moisture
ratio; a, b, c coefficients;
n, drying
exponent
specific tothe
eachconvection
equation; k, drying
coefficients
specific
to
each equation;
modeler
Çizelge
1-Mathematical
Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel
e
chosen
were
then related
t,Çizelge
time 1- Konveksiyonlakurumakinetiklerinibelirlemedeyaygınolarakkullanılanmatematiksel modeler
to the multiple
The moisture ratio was calculated using equation combinations of the different equations as in the
Model name
name
Model equation
equation
References
Model
Model
References
(1),side
which
simplified
to equation number
(2)
by some
of ratio
linear,
polynomial,
logarithmic, power,
The
left hand
of thewas
equations
is a dimensionless
known asform
moisture
MRand
it could
Model
name
Model
equation
References
Lewis
MR=
exp(-kt)
Yaldız&Ertekin
Lewis
MR=
exp(-kt)
Yaldız&Ertekin (2001)
(2001)
M
investigators
(Menges
&
Ertekin,
2006;
Midilli
n
exponential
and
Arrhenius.
be
written
as
follows:
t
Lewis
Yaldız&Ertekin
Page
MR=
exp(-kt
Alibaş
(2)exp(-kt)
MR  MR=
Page
MR=
exp(-ktnn))
Alibaş (2012)
(2012) (2001)
& Kucuk 2003;
Sacilik) nn]& Elicin 2006;
Togrul
Page
MR=
exp(-kt
Alibaş
(2012)
Artnaseaw
et&al
al (2010)
(2010)
M
Modified
Page
MR=
exp[-(kt)
Artnaseaw
et
o
Modified Page
MR= exp[-(kt)n]
Artnaseaw
et al (2010)
Pehlivan
2003;
Yaldiz
et
al
2001)
because
of
the
M
M
Modified
Page
MR=
exp[-(kt)
]
Henderson and
and Pabis
Pabis
MR=
a eexp(-kt)
exp(-kt)
Figiel (2010)
(2010)
t
Henderson
MR=
a
Figiel
(1)
MR
 MR=small
3. Results and Discussion
is
relatively
comparedoftoFigiel
M0drying
and
the
M
Henderson
and Pabis
(2010)
MS Excel
software
was
usedaaa exp(-kt)
for when
the calculation
the
constants and coefficients of semiLogarithmic
MR=
exp(-kt)+c
Doymaz
(2013)
e
MMR=
Logarithmic
Doymaz
(2013)
0 -M
eexp(-kt)+c
2
n
Logarithmic
a
exp(-kt)+c
Doymaz
) was
considered
as leaves
the
empirical
models of
in MR=
Table
Then)+bt
coefficient
of the
multiple
deviation
the relative
humidity of
drying
air Drying
of the
artichoke
was performed in a
Midilli
et
MR=
a
exp(-kt
Silva
et
al
(2011)
Midilli
et al
al drying
MR=
a 1.
exp(-kt
)+bt
Silva
et determination(R
al(2013)
(2011)
n n
main
criteria
for
selecting
the
best
model
to
obtain
the
convection
drying
curves
of
artichoke
leaves.
Midilli
et
al
MR=
a
exp(-kt
)+bt
Silva
et
al
(2011)
n]+b
during
the
processes.
convective
drier
and
the
experiments
were carried
Demir
et
al
MR=
a
exp[-(kt)
Demir
et
al
(2007)
Demir et al
MR= a exp[-(kt) n]+b
Demir et al (2007)
other MR=
statistical
testswere
achieved
in equation;
order
evaluate
how
thespecific
developed
models
Besides
R2, some
Demir
et altheratio;
exp[-(kt)
]+bspecific
Demir
et altok,
(2007)
MR, moisture
moisture
ratio;
a, b,
b, cc coefficients;
coefficients;
n,adrying
drying
exponent
specific
to each
each
equation;
k,
dryingout
coefficients
specific
to each
each equation;
equation;
at
four
different
temperatures
(40,
50, 60 and
MR,
a,
n,
exponent
to
drying
coefficients
to
M t then, experiments.
fit
tomoisture
the data
from
root mean
square
error(RMSE)and
t, time
time
MR,
ratio;obtained
a, MR
b, c coefficients;
drying exponent Among
specific tothese,
each equation;
k, drying
coefficients
specific to eachreduced
equation;
t,
(2)
(2)

70
°C),
and
three
drying
air
velocities
(0.6, 0.9
t, time
et al 2002; -1Yaldiz&Ertekin
chi-square
(2)have a common
M o use in drying related studies (Krokidaand
1.2
m
s
)
and
constant
air
relative
humidity
The left
left hand
hand side
side 2003;
of the
the Akgun&Doymaz
equations is
is aa dimensionless
dimensionless
numbertoknown
known
as moisture
moisture
ratio
MRanddeviation
it could
could
2001;Midilli&Kucuk
2005).In addition
these methods,
mean
relative
The
of
equations
number
as
ratio
MRand
it
TheMRand
average
initial moisture content
The left
side
of
the
iswas
a dimensionless
known
moisture(Sacilik&Elicin
ratio
it 2006;
could
MS
Excel
software
used
thenumber
calculation
be written
written
ashand
follows:
modulus
(P)
value
was
alsoequations
used to evaluate
the for
goodness
of fit
of theas(15±2%).
models
be
as
follows:
MS Excel
software was used for the calculation of the drying constants and coefficients of semibe written
as follows:
of
the
drying
and
coefficients
of
semiÖzdemir&Devres
1999).
Theseconstants
test functions
used
to determine
the
best fit of
are the
given
below: leaves was 4.8964 kg water kg-1
2 artichoke
empirical drying models in Table 1. The coefficient of multiple determination(R ) was considered as the
dmcurves
and the
leaves was
dried to the average final
empirical
drying
in toTable
1. the
Theconvection
coefficientdrying
Mthe
Mmodels
tt - best
ee model
main criteria for
selecting
obtain
of artichoke
leaves.
MR  M
-1
(1) (R2) was considered as the
M
2of multiple
N (1)
moisture
content
of
0.0662
determination
t
e
other
testswere achieved in
order to evaluate how the developed models kg water kg dm until
Besides the R , some
1
Mstatistical
MR

2
0 -M ee (1)
0
RMSE
for
(MRthe
Among
MR
(3)
no changes
in the mass
of leaves were obtained.
criteria
selecting
model
the square
fit to the data main
obtained
from
theM
experiments.
root mean
error(RMSE)and
reduced
pre,ibest
exp,these,
i )to obtain
M
0 -N
e
i 1 in of
)have a common
use
drying
related
studies
(KrokidaThe
et alcharacteristic
2002; Yaldiz&Ertekin
chi-square (2convection
drying curves were constructed
drying curves
artichoke
leaves.
Besides
N Akgun&Doymaz 2005).In addition to these methods, mean relative deviation
2001;Midilli&Kucuk
the R2,2003;
some
other statistical 2tests were achieved from the experimental data and indicated that
M(MR
modulus (P) value
was
also
evaluate
goodnessmodels
of fit of
modelsis(Sacilik&Elicin
MR pre,
tt used
i -how
only a falling2006;
rate drying period for all
(2)exp,to
MR toMevaluate
in order
thei )the
developed
fitthe there
t (2)
Özdemir&Devres 1999).
test functions used to determine the best fit are given below:
2 iThese
M
1 o (2)
MR
changes in the moisture
 obtained
χ data
to the
from the experiments. Among experimental cases. The(4)
o
Mo N - n
1 error (RMSE) and reduced
ratio
versus
drying
time
and
the drying rate versus
these, root mean
square
N
MS
software
the
of
the
drying
constants
and
coefficients
of
semi2 used
1MRfor
MS Excel
Excel chi-square
software was
was
used
for
the calculation
calculation
ofdrying
the
drying
constants
and
coefficients
of
semi2
drying
time
for
temperatures
and airflow velocity
(χ
)
have
a
common
use
in
related
- MR
22) was
RMSE
(MR
 iMRof
(3)
100
exp,
ithe
MS Excel
software
was
used 1.
for
calculation
ofmultiple
constants and
coefficients
of as
semiconsidered
as
the
empirical
drying
models
inTable
Table
1.
The
coefficient
of
multiple
determination(R
pre,
i pre,
exp,
i )the drying
) was
considered
the
empirical
drying
models
in
The
coefficient
determination(R
2
P

studied
is
presented
in
Figure
2, and Figure 3
(5)
studies
(Krokida
et
al
2002;
Yaldiz
&
Ertekin
2001;
N
i 1model
) was
as the
empirical
drying
in the
Table
1.
The coefficient
multiple
determination(R
main
criteria
for
selecting
best
to
convection
drying
of
artichoke
main
criteria
for models
selecting
the
best
model
to obtain
obtainofthe
the
convection
drying curves
curves
of considered
artichoke leaves.
leaves.
MR
2Midilli &N
exp,
i
respectively.
Kucuk
2003;
Akgun
&
Doymaz
2005).
In
2
main
criteria
selecting
best model
to obtain
the in
convection
drying curves
artichoke models
leaves.
N the
some
other
statistical
testswere
achieved
in
order
to evaluate
evaluate
how the
theofdeveloped
developed
models
Besides
the R
R for
,, some
other
statistical
testswere
achieved
order
to
how
Besides
the
2
2achieved
Thebetter
of
the
fit experiments.
means
the
value
ofinRorder
should
be
higher
whilethe
value of reduced
RMSE,
, some other
statistical
evaluate
thethese
developed
models
Besides
R2goodness
addition
to
these
methods,
mean
relative
deviation
fit
data
obtained
from
the
these,
root
mean
square
error(RMSE)and
(MR
- testswere
MRthat
)Among
fit2 to
to the
thethe
data
obtained
from
theexp,
experiments.
Among
these,
root to
mean
squarehow
error(RMSE)and
reduced
From
figures
it is clear that the moisture
i
pre,
i
2obtained
chi-square
P should
be 2lower.
Selection
ofinthe
bestAmong
suitable
drying
done
using this
criteria.The
fitand
to the
data
from
the experiments.
rootmodel
mean
square
error(RMSE)and
reduced
)have
aa common
use
drying
related
studies
(Krokida
et
al
2002;
Yaldiz&Ertekin
((
(P)
was
also
used
tothese,
evaluate
the was
i 1 value
22modulus
)have
common
use
in
drying
related
studies
(Krokida
et
al
2002;
Yaldiz&Ertekin
chi-square
ratio
of
artichoke
leaves
χ a
(4)decreases continuously
)have
common
use models
in drying
related
studiesto
(Krokida
et al mean
2002;relative
Yaldiz&Ertekin
chi-square
( goodness
2001;Midilli&Kucuk
2003;
Akgun&Doymaz
2005).In
addition
to2006;
these methods,
methods,
mean
relative
deviation
of fit
of N
the
(Sacilik
&
Elicin
2001;Midilli&Kucuk
2003;
Akgun&Doymaz
2005).In
addition
these
deviation
n
with
drying
time.
As
seen
from Figure 2, it is
1
2001;Midilli&Kucuk
2003;
Akgun&Doymaz
2005).In
addition
these
methods,
relative deviation
modulus
was
also
used
evaluate
the
goodness
of
of
models
(Sacilik&Elicin
2006;
modulus (P)
(P) value
value
was
also
used to
to
evaluate
the test
goodness
oftofit
fitused
of the
the
modelsmean
(Sacilik&Elicin
2006;
Özdemir
&
Devres
1999).
These
functions
obvious
that
the
main
factors
effecting the drying
modulus
(P) value1999).
was100
also
used
to
evaluate
the to
of the
fit best
of the
models
2006;
Özdemir&Devres
These
test
functions
used
determine
fit
given
below:
- MR
MR
Özdemir&Devres
1999).
These
test
functions
used
togoodness
determine
the
best
fit are
are
given(Sacilik&Elicin
below:
exp,
i are
pre,i below:
to determine
the
best
fit
given
kinetics
of
artichoke
leaves
are the drying air
Özdemir&Devres
1999).
These
test
functions
used
to
determine
the
best
fit
are
given
below:
P
∑
∑
∑ ∑
∑
(5)
∑ MR
4
N
temperature and drying airflow velocity. Drying
exp,i
N
N
1 means
2
N (MR
timewhilethe
went down
drying
air temperature and
Thebetter goodness
of 
the fit
that
the
value
of)22R(3)
should be higher
valueasofthe
RMSE,
RMSE
 MR
(3)
(3)
1∑
pre,
exp,
pre,ii
exp,ii 2
2
N
(MR

MR
)
(3)
∑
 and P should beRMSE
lower. Selection
of
the
best
suitable
drying
model
was
done
using
this
criteria.The
airflow
velocity
increases.
Drying
air temperature
1
ii 
pre,
i
exp,
i
N i 11
N
N
N
∑(MR
∑(MR

was reported to be the most important factor
22
influencing drying rate by many researchers.
exp,ii - MR pre,
pre,ii )2
exp,
MR
)
11
exp,i
pre,i
22
increases drying
ii 
(4)
(4) Using higher drying temperatures
χ 2 i 1
(4)
4 & van Boxtel 1999;
χ 
rate significantly (Temple
(4)
N - n11
N - n1
Panchariya et al 2002). Drying of artichoke leaves
- MR pre,
MRexp,
100
exp,ii
pre,ii
down to 10% wet based(5)
(5)moisture content at air
P  100 ∑MRexp,i - MR pre,i
(5)
P N ∑
(5) and 70 °C lasted about
temperatures
of
40,
50,
60
MRexp,
exp,ii
N the fit means
MRexp,
i the value of R22should be higher whilethe value of RMSE,
Thebetter
goodness
of
that
Thebetter goodness of the fit means that the value of R2should be higher whilethe value of RMSE,
2 Thebetter goodness of the fit means that the value of R should be higher whilethe value of RMSE,

22and
and P
P should
should be
be lower.
lower. Selection
Selection of
of the
the best
best suitable
suitable drying
drying model
model was
was done
done using
using this
this criteria.The
criteria.The
 and P should be lower. Selection of the best suitable drying model was done using this criteria.The
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
4
4
419
Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
1.0
1.0
40⁰C 0.6 m
m/ss-1
0.9
40⁰C 1.2 m
m/ss-1
0.7
0.6
0.5
0.4
0.3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Drying Time (h)
3.5
4.0
4.5
0.5
0.4
0.3
0.0
5.0
1.0
0.0
0.5
1.0
1.5
Drying Time (h)
2.0
2.5
3.0
1.0
60⁰C 0.6 m
m/ss-1
0.9
0.6
0.5
0.4
0.3
70⁰C 0.9 m
m/ss-1
0.8
Moisture Ratio (MR)
60⁰C 1.2 m
m/ss-1
0.7
70⁰C 0.6 m
m/ss-1
0.9
60⁰C 0.9 m
m/ss-1
0.8
Moisture Ratio (MR)
0.6
0.1
0.1
0.2
70⁰C 1.2 m
m/ss-1
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
50⁰C 1.2 m
m/ss-1
0.7
0.2
0.2
0.0
50⁰C 0.9 m
m/ss-1
0.8
Moisture Ratio (MR)
Moisture Ratio (MR)
0.8
50⁰C 0.6 m
m/ss-1
0.9
40⁰C 0.9 m
m/ss
-1
0.1
0.0
0.5
1.0
Drying Time (h)
1.5
0.0
2.0
0.0
0.5
1.0
Drying Time (h)
1.5
2.0
Figure 2- Variations of moisture ratio as a function of time for different air-drying temperatures and velocities
Şekil 2- Kurutma havasının farklı sıcaklık ve hızlarında nem oranının zamana göre değişimleri
25.0
25.0
40⁰C 0.9 m
m/ss-1
20.0
40⁰C 1.2 m
m/ss-1
15.0
10.0
5.0
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Drying Time (h)
3.5
4.0
4.5
50⁰C 0.6 m
m/ss-1
ΔM/Δt (kg water⋅kg-1 dm⋅h-1)
ΔM/Δt (kg water⋅kg-1 dm⋅h-1)
40⁰C 0.6 m
m/ss-1
25.0
50⁰C 1.2 m
m/ss-1
15.0
10.0
5.0
0.0
5.0
50⁰C 0.9 m
m/ss-1
20.0
0.0
0.5
1.0
1.5
Drying Time (h)
2.0
2.5
25.0
60⁰C 0.9 m
m/ss-1
20.0
60⁰C 1.2 m
m/ss-1
15.0
10.0
5.0
0.0
0.5
1.0
Drying Time (h)
1.5
2.0
70⁰C 0.6 m
m/ss-1
ΔM/Δt (kg water⋅kg-1 dm⋅h-1)
ΔM/Δt (kg water⋅kg-1 dm⋅h-1)
60⁰C 0.6 m
m/ss-1
0.0
3.0
70⁰C 0.9 m
m/ss-1
20.0
70⁰C 1.2 m
m/ss-1
15.0
10.0
5.0
0.0
0.0
0.5
1.0
Drying Time (h)
1.5
2.0
Figure 3 - Variations of drying rate as a function of time for different air-drying temperatures and velocities
Şekil 3 - Kurutma havasının farklı sıcaklık ve hızlarında kuruma hızının zamana göre değişimleri
420
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
Predicted "k"
4.08, 2.29, 1.32 and 0.98 h respectively at a constant can be achieved the higher values than 0.99941
drying air velocity of 0.6 m s-1 while drying at an for R2, lower values than 0.00485 for RMSE,
air velocity of 0.9 m s-1 took about 3.83, 1.60, 0.96 lower values than 0.00025 for χ2 and lower values
and 0.75 h. Increasing the drying air velocity up than 7.202 for P. Therefore, the Midilli et al model
to 1.2 m s-1 at air temperatures of 40, 50, 60 and was preferred because of its better fit to drying
70 °C reduced the drying time down to than
3.5, 0.00485
1.54, data.
The Midilli
et al model
has theforfollowing
for RMSE,
lower values
than 0.00025
2.and lower values tha
1.04 and 0.71 h respectively. From these
findings
and
can
reveal satisfactory
order
the Midilliet alform
model
was
preferred
because of itsresults
better in
fit to
drying data. The M
it could be stated that drying time for following
artichoke form
to predict
experimental
values
of the
moisture
and canthe
reveal
satisfactory
results
in order
to predict the exp
leaves at 70 °C was 4.9 times shorter than
that ofratio ratio
moisture
values
for artichoke
leaves.leaves.
values
for artichoke
40 °C. The experimental data showed that there
is no constant drying rate period (Figure 3). The
 =  (  ) +  (6)
drying process of artichoke leaves during all of the
results
as obtained
bywere tabulated i
tests took place in the falling rate period. As
seen
The
statisticalThe
basedstatistical
results asbased
obtained
byMidilliet
al model
Midilli
et
al
model
were
tabulated
in
Table
3.
As
table,
from Figure 3, the drying rate increasesthe
while
thethe drying constant kincreases once the temperature of the drying ai
from
the table,a,n
theand
drying
constant k increases
while the
model
constants,
b fluctuate.
time is shortened as the drying air temperature
andotherseen
once
the
temperature
of
the
drying
air and velocity
the velocity increases. The main factor that causes
this is the temperature of the drying air as followed increases while the other model constants, a, n and
Table
Statistical
analysis of drying models at various drying air temperatures
b fluctuate.
by velocity. The effect of either 1.2 or 0.9
m s−12-air
Çizelge
2Kurutmahavasınınfarklısıcaklıkvehızlarıiçinkurumamodellerininistatistikse
velocity in all of the drying tests was similar and
Some other regression
analysis were also made
(Table 2:Ensondanalınıpburayayerleştrilecek)
increasing the air velocity above 1.0 m s−1 did not
in order to consider the effect of the drying air
increase the drying rate too much.
temperature and velocity variables on the drying
The moisture content data obtained from the constant k (h-1) of the Midilli et al model. The
experiments were converted to the moisture ratio drying constants (k) were correlated to the drying
values and then curve fitting calculations were air temperature and velocity by considering the
performed on the drying models as tabulated different combinations of the equations as in the
in Table 1. These models and the results of the form of simple linear, polynomial, logarithmic,
Some other regression analysis were also made in order to
statistical analyses are shown in Table 2.
power,
exponential
and Arrhenius
typetheusing
theconstant k (h-1)
temperature
and velocity
variables on
drying
The coefficient of multiple determination (R2) software
Datafit
6.0
(Oakdale
Engineering).
The
constants (k) were correlated to the drying air temperature and
indicating the goodness of the fit is over the values power
model was
assumed
to beasthein appropriate
combinations
of the
equations
the form of simple line
of 0.99395 in all drying conditions. Root mean model
due toand
theArrhenius
easiness intype
use using
even though
some Datafit 6.0 (Oa
exponential
the software
square error (RMSE) which gives the deviation higher
was assumed
to
be
the
appropriate
model
due
to the easiness in
order polynomial functions produced better
between the predicted and experimental values predictions.
polynomial functions produced better predictions.
is in the range of 0.001413 and 0.021848 in the
(7)
 =     all drying conditions. The reduced chi-square (χ2)
is in the range of 0.000002 and 0.001032 in all
In
In model,
model, TT isistemperature
temperature(°C),
(C),VVisisthe
thedrying
drying air velocity (
drying conditions. The mean relative deviation
-1
),
A,
B
and
C
are
constants.
The A, B and C was
air
velocity
(m
s
modulus (P) values were found in the range of fitting to the above written model, the coefficients,
fitting
to
the
above
written
model,
the
coefficients,
1.495 and 39.388 in the all drying conditions. 0.563268, respectively with a coefficient of determination of 97.82
drying
constant
of the
al model
by use of the develope
B and
C was(k)
found
to Midilliet
be 0.0002048,
2.408351
The statistical analysis results of experiments A,
from0.563268,
the comparison
are depicted
respectively
with ina Figure4.
coefficient of
generally indicate high correlation coefficients and
for the all drying models. The highest values of determination of 97.829%. The experimental and
R2 and the lowest values of RMSE, χ2 and P can predicted drying constant (k)7.0of the Midilli et al
be obtained by using the Demir et al and Midilli model by use of the developed model is compared
6.0
et al models in all drying air temperatures and and the findings from the comparison are depicted
velocities. When the Midilli et al model used, it in Figure 4.
5.0
20 (2014) 415-426
4.0
3.0
2.0
1.0
421
422
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
m s-1
R2
RMSE
χ2
5.638 0.99988 0.002864 0.000008
0.6
7.237 0.99983 0.003197 0.000011
1.2
4.496 0.99990 0.002561 0.000007
0.6
4.899 0.99991 0.002426 0.000006
7.202 0.99982 0.003266 0.000011
1.2
0.9
4.351 0.99992 0.002272 0.000006
0.9
4.141 0.99991 0.002459 0.000006
0.6
0.6
18.099 0.99537 0.016748 0.000296
7.220 0.99890 0.008657 0.000079
1.2
1.2
27.499 0.99395 0.021064 0.000460
0.9
10.664 0.99811 0.011074 0.000129
25.533 0.99681 0.016758 0.000291
0.6
0.9
6.548 0.99982 0.003367 0.000012
18.473 0.99811 0.012933 0.000173
1.2
7.628 0.99984 0.003422 0.000012
6.548 0.99982 0.003367 0.000012
1.2
0.9
7.629 0.99984 0.003422 0.000012
0.9
5.638 0.99988 0.002864 0.000008
39.388 0.99530 0.031848 0.001032
1.2
0.6
33.291 0.99808 0.023750 0.000574
25.177 0.99888 0.019353 0.000381
P
40°C
0.9
0.6
Velocity
R2
RMSE
χ2
RMSE
χ2
RMSE
χ2
6.369 0.99980 0.002907 0.000009
6.678 0.99953 0.004047 0.000017 11.469 0.99923 0.005183 0.000028
6.037 0.99972 0.003518 0.000013
9.883 0.99944 0.004212 0.000018
6.369 0.99980 0.002907 0.000009
6.678 0.99953 0.004047 0.000017 11.469 0.99923 0.005183 0.000028
6.037 0.99972 0.003518 0.000013
6.059 0.99964 0.003669 0.000014
3.999 0.99969 0.003480 0.000013
3.555 0.99946 0.004995 0.000027
4.902 0.99969 0.003443 0.000013
3.322 0.99973 0.003291 0.000012
2.916 0.99949 0.004850 0.000025
5.289 0.99962 0.003762 0.000015
4.206 0.99969 0.003493 0.000013
4.065 0.99945 0.005052 0.000027
5.401 0.99806 0.008565 0.000076
1.693 0.99954 0.003839 0.000016
3.578 0.99958 0.003669 0.000014
2.140 0.99981 0.002668 0.000008
2.955 0.99956 0.003747 0.000015
2.524 0.99961 0.003563 0.000014
1.495 0.99983 0.002501 0.000007
5.207 0.99910 0.005356 0.000030
9.015 0.99902 0.005598 0.000033
1.939 0.99992 0.001413 0.000002
1.573 0.99939 0.004108 0.000018
1.884 0.99988 0.002046 0.000004
3.170 0.99987 0.001847 0.000004
1.705 0.99941 0.004038 0.000017
1.991 0.99987 0.002142 0.000005
2.242 0.99961 0.003157 0.000010
5.838 0.99899 0.005293 0.000029
7.436 0.99897 0.006238 0.000041 12.324 0.99820 0.007929 0.000066
9.725 0.99537 0.014316 0.000212
6.410 0.99900 0.005758 0.000034 10.542 0.99895 0.005570 0.000032
5.285 0.99893 0.006462 0.000043
9.589 0.99954 0.004607 0.000022 14.476 0.99894 0.006677 0.000046
6.608 0.99964 0.004024 0.000017
6.048 0.99941 0.005371 0.000030
9.035 0.99958 0.004143 0.000018 14.989 0.99912 0.006563 0.000045 10.924 0.99967 0.003860 0.000015
6.294 0.99963 0.003992 0.000016
5.725 0.99938 0.005479 0.000031
9.035 0.99958 0.004143 0.000018 14.989 0.99912 0.006563 0.000045 10.924 0.99967 0.003860 0.000015
6.294 0.99963 0.003992 0.000016
5.725 0.99938 0.005479 0.000031
R2
8.209 0.99815 0.011472 0.000134
P
70°C
6.596 0.99902 0.006048 0.000037 10.523 0.99892 0.005612 0.000032
5.599 0.99897 0.007478 0.000057
R2
60°C
9.952 0.99962 0.005548 0.000031 14.431 0.99890 0.006692 0.000046
6.820 0.99969 0.004546 0.000021
P
Drying air temperature
6.257 0.99945 0.005927 0.000036
P
50°C
P, mean relative percent error; R2, coefficient of determination; RMSE, root mean square error; χ2, reduced mean square of the deviation
Demir
et al
Midilli
et al
Logarithmic
Henderson and
Pabis
Modified
Page
Page
Levis
Model
name
Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
Table 2- Statistical analysis of drying models at various drying air temperatures and velocities
Çizelge 2- Kurutma havasının farklı sıcaklık ve hızları için kuruma modellerinin istatistiksel analizi
20 (2014) 415-426
Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al
0.6
40
0.9
1.2
0.6
50
0.9
1.2
0.6
60
0.9
1.2
0.6
70
0.9
1.2
Replication
Velocity
m s-1
Temperature
°C
Table 3- Statistical results of the Midilli et al model and its constants and coefficients at different drying
conditions
Çizelge 3- Kurutma havasının farklı sıcaklık ve hızları için Midilli vd modelinin sabitleri, katsayıları ve istatistik analizi
k
a
n
b
P
R2
RMSE
χ2
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1.112265
1.148662
1.094725
1.249831
1.329317
1.273962
1.356235
1.413097
1.320560
1.834230
1.913430
1.854856
2.512386
2.529225
2.465516
2.851674
2.859636
2.747172
2.881234
3.324264
2.854406
3.808960
4.264571
3.994963
4.171691
4.833548
4.123418
4.042290
4.367799
3.685662
5.579094
5.659406
5.200341
6.017516
6.342867
6.137372
0.994631
0.996646
0.996981
0.998437
1.002016
1.001094
0.998106
1.001369
0.998131
0.985748
0.987839
0.989230
0.992101
0.988270
0.992277
0.992316
0.989110
0.992062
0.990799
0.990232
0.992319
0.989667
0.990612
0.988930
0.994334
0.991000
0.991314
1.007230
1.004047
1.008259
0.993387
0.992359
0.994378
1.000903
1.001279
1.001025
0.883051
0.875175
0.899273
0.862140
0.851355
0.849801
0.788721
0.786712
0.796229
1.010571
1.019477
1.007723
1.005202
1.002063
1.004665
0.984463
0.981150
0.989060
1.108364
1.125468
1.083662
1.086432
1.080361
1.082727
1.065097
1.070963
1.037263
1.137207
1.163435
1.125381
1.061496
1.081631
1.032644
1.046930
1.052964
1.035744
0.000700
0.001010
0.000900
0.001325
0.001509
0.001481
-0.000587
-0.000040
-0.000756
0.002182
0.003203
0.003885
0.003502
0.002949
0.003752
0.002619
0.003525
0.003475
0.003324
0.005456
0.004832
0.003214
0.005065
0.002063
0.009271
0.008885
0.008903
0.000496
0.002166
0.007454
0.006544
0.007641
0.007303
0.007840
0.010255
0.008883
4.628
4.671
3.304
4.916
4.321
3.909
7.491
6.728
7.436
3.613
3.159
2.213
3.044
4.240
2.828
5.036
5.682
4.119
2.150
1.556
1.268
2.710
1.895
3.747
3.001
3.099
2.693
2.847
4.797
1.552
1.717
1.920
1.472
3.222
2.994
3.571
0.999894
0.999890
0.999919
0.999901
0.999920
0.999923
0.999824
0.999854
0.999665
0.999396
0.999450
0.999577
0.999823
0.999275
0.999833
0.999742
0.999515
0.999760
0.999805
0.999780
0.999844
0.999644
0.999582
0.999506
0.999719
0.999403
0.999487
0.999823
0.999929
0.999812
0.999348
0.999284
0.999568
0.999891
0.999821
0.999861
0.002674
0.002711
0.002364
0.002557
0.002272
0.002226
0.003269
0.002949
0.004546
0.005310
0.005069
0.004427
0.002656
0.005345
0.002581
0.003127
0.004261
0.003035
0.002744
0.002872
0.002423
0.003418
0.003628
0.003998
0.003044
0.004313
0.004050
0.002496
0.001577
0.002564
0.004244
0.004473
0.003447
0.001678
0.002136
0.001877
7.653E-06
7.865E-06
5.980E-06
7.020E-06
5.545E-06
5.324E-06
1.150E-05
9.353E-06
2.223E-05
3.018E-05
2.749E-05
2.097E-05
7.547E-06
3.057E-05
7.127E-06
1.046E-05
1.943E-05
9.858E-06
8.058E-06
8.829E-06
6.283E-06
1.250E-05
1.408E-05
1.710E-05
9.915E-06
1.991E-05
1.755E-05
6.667E-06
2.660E-06
7.033E-06
1.928E-05
2.141E-05
1.272E-05
3.013E-06
4.881E-06
3.769E-06
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
423
polynomial functions produced better predictions.
 =    
(7)
In model, T is temperature (C), V is the drying air velocity (ms-1), A, B and C are constants. The
Some
otherabove
regression
analysis
made in order
to consider
the effect
of 0.0002048,
the drying air
fitting
to the
written
model,were
the also
coefficients,
A, B and
C was found
to be
2.408351 and
MidillietThe
al model.
The drying
temperature
and
velocity
variables
onofthethedrying
constant
k (h-1) of the
0.563268,
respectively
with
a
coefficient
of
determination
97.829%.
experimental
and
predicted
lysis were also made
in
order
to
consider
the
effect
drying
air
Mathematical Modelling
of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
-1
constants
(k)
to al
themodel.
drying
air drying
temperature
anddeveloped
velocity bymodel
considering
the different
) of
the
The
bles on the dryingdrying
constant
k (hwere
constant
(k)correlated
of Midilliet
the Midilliet
al model
by use of the
is compared
and the findings
combinations
of velocity
the equations
as in
thetheform
of simple linear, polynomial, logarithmic, power,
to the drying air from
temperature
and
considering
different
the comparison
areby
depicted
in Figure4.
Arrhenius
type using
the software
Datafit 6.0 (Oakdale Engineering). The power model
s as in the formexponential
of simpleand
linear,
polynomial,
logarithmic,
power,
depicted in Figure 5. As seen from this figure, the
7.0
was
assumed
to be theEngineering).
appropriate model
due to
the easiness in use even though some higher order
e using the software
Datafit
6.0 (Oakdale
The power
model
7.0
predicted values generally accumulate around the
polynomial
functions
bettersome
predictions.
priate model due to
the easiness
in useproduced
even though
higher order
6.0
straight line. This indicates how the developed
better predictions.
6.0
 =    
model fits to the data obtained (7)
in the laboratory for
5.0
(7)
the drying
of artichoke leaves.
-1
0
0
0.0
1.0
2.0
1.0
3.05.0 4.0
5.0
Experimental "k"
Predicted "k"
0
6.0
0.7
2.0
4.0
0.0
0.0
6.0
1.0
7.0
2.0
Tahminlenen ANO değerleri
0.0
0
0
7.0
1.0
0
0
Predicted "k"
Predicted "k"
In model, T is temperature (C),
5.0 V is the drying air velocity (ms ), A, B and C are constants. The
1.0
4.0to the above written
fitting
theare
coefficients,
B and C was
found to be 0.0002048, 2.408351 and
B and C
constants. A,
The
(C), V is the drying
air
velocity (ms-1), A, model,
0.563268,
respectively
with
a
coefficient
of
determination
of
97.829%.
The experimental and predicted
del, the coefficients, A, B and C was found to be 0.0002048,
2.408351 and
4.0
0.9
3.0constant (k) of the Midilliet al model by use of the developed model is compared and the findings
drying
coefficient of determination of 97.829%. The experimental and predicted
from
the comparison
are depicted
in Figure4.
0.8
liet al model by use
of the
developed model
is compared
and the findings
3.0
2.0
ed in Figure4.
0.6
0.5
0.4
3.0
4.0
5.0
0.3"k"
Experimental
and
6.0
7.0
Figure 4- Comparison of the experimental
3.0
predicted drying constant (k) of the Midilli et al
0.2
model
2.0
Figure 4- Comparison of the experimental and predicted drying
constant (k) of the Midilli et al model.
0.1
Şekil 4Midilli vd modelindeki kuruma katsayısının
Şekil
4-Midillivdmodelindekikurumakatsayısının
(k) (k)
deneyselvetahminlenendeğerlerilekarşılaştırılması.
1.0
deneysel ve tahminlenen değerler
ile karşılaştırılması
0.0
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Deneysel ANO değerleri
(R2=0.97829) (8)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Figure 5- Comparison of the experimental and
The drying
drying
constant, kk was
was employed
employed in
in model
model developed
Experimental
"k"
The
constant,
bymoisture
Midillietratio
alandfor
predictions
weremodel
made.
predicted
the developed
developed
by Midilli
et al and
predictions
weredrying
For
this
purpose,
regression
analysis
were
made
and the
predicted
results
were
correlated with the
Figure
4- Comparison
of the experimental
and
predicted
constant
(k)
of
the
Midilli
et
al
model.
Şekil 5- Deneysel ve geliştirilen model yardımıyla
made.
For
this
purpose,
regression
analysis
while reducing the RMSE and 2and the values of a, n and
experimental
in order
R2were
Şekil 4-Midillivdmodelindekikurumakatsayısının
(k) deneyselvetahminlenendeğerlerilekarşılaştırılması.
perimental and predicted
drying data
constant
(k) of to
theobtain
Midilliaethigher
al model.
tahminlenen nem oranı değerlerinin karşılaştırılması
wereand
found
be 0.983970,
and 0.0074083
made
the to
predicted
results1.039708
were correlated
with respectively.
makatsayısının (k) b
deneyselvetahminlenendeğerlerilekarşılaştırılması.
Midilli et2.408351
al model
as atofunction
the temperature
of drying air2 and velocity in order to use for
the The
experimental
data
in order
obtain aofhigher
R2
0.563268
 = 0.0002048

(R =0.97829) (8)
2
4.
Conclusions
artichoke
drying
has
the
following
form:
while reducing the RMSE and2 χ and the values of a,
63268
(R =0.97829) (8)
n and
were constant,
found tok be
1.039708
and Inby this
study,
drying were
behavior
Thebdrying
was0.983970,
employed in
model developed
Midilliet
alandthe
predictions
2 made. of artichoke
2.408351
0.563268

) 1.039708
] investigated.
+ were
0.0074083(R
=0.992995)(9)

= 0.983970exp[(0.0002048
Fordeveloped
this
purpose,
regression
werewere
made
and the predicted
results
correlated
with
the
0.0074083
respectively.
leaves
was
Drying
artichoke
leaves
employed in model
by Midilliet
alandanalysis
predictions
made.
2
2
while
reducing
the
RMSE
and

and
the
values
of
a,
nvelocity
and
experimental
data
in
order
to
obtain
a
higher
R
-1
nalysis were made and the predicted results were correlated with the
at
constant
1.2
m
s
drying
air
down
to
Thefound
Midilli
et
aldrying
model
as a isand
function
of the
2 model
The
generalised
valid
under
the following conditions of air temperature (T) and air
b were
to be
0.983970,
0.0074083
reducing
the
RMSE
and 1.039708
and the values
of a,
n andrespectively.
btain a higher R2 while
approximately
10%
(wet
basis)
moisture
content
at
temperature
velocity
in temperature
order to of drying air and velocity in order to use for
The
Midilli
al modelair
as and
a function
of the
velocity
(V). ofet drying
039708 and 0.0074083
respectively.
air
temperature
of
40,
50,
60
and
70
°C
in
the
dryer
artichoke
drying
hasdrying
the
following
use
for artichoke
has
theform:
following
function of the temperature
of drying
air and
velocity
in order toform:
use for
about
1.04 and 0.71 h respectively.
ng form:
1.23.50,
ms-11.54,
40°C
T 70°C
0.6lasted
ms-1 V
2
2.408351
 0.563268 ) 1.039708
]
+
0.0074083(R
=0.992995)(9) data there is no
 = 0.983970exp[(0.0002048
It is evident from the experimental
2
(9) from
) 1.039708
] + 0.0074083(R
2048 2.408351  0.563268
constant
rate dryingdata
period.
The
dimensionless
moisture=0.992995)(9)
ratio values found
experimental
and predicted models are
The generalised drying model is valid under the following conditions of air temperature (T) and air
depicted
in
Figure
5.
As
seen
from
this
figure,
the
predicted
values
generally
accumulate
the
(V).
For describing the drying
behavior around
of artichoke
del is valid under velocity
the The
following
conditions
of airmodel
temperature
(T)under
and air
generalised
drying
is valid
the
seven
models were applied to the drying
following conditions of air temperature
(T) and
air leaves,
-1
1.2 msThe
40°C T 70°C
0.6 ms-1 V
process.
different
mathematical drying models
(V).
V 1.2 ms-1
40°C T 70°C velocity
0.6 ms-1
considered
in
this
study
were evaluated according
The
ratio
-1 values found -1from experimental data and predicted models are
40 °Cdimensionless
≤ T ≤ 70°C moisture
0.6 ms
≤ V ≤ 1.2 ms
2
2
to
the
R
,
RMSE,
χ
and
P
to estimate
drying curves.
depicted
Figure 5. Asdata
seenand
from
this figure,
theare
predicted values generally accumulate
around the
ure ratio values found
frominexperimental
predicted
models
The
dimensionless
moisture
ratio
values
found
The
correlation
coefficients
of
all
of
the models
from this figure, the predicted values generally accumulate around the
9
from experimental data and predicted models are considered in this study was found to be close to
0
0.0
1.0(R2=0.97829)
2.0
3.0 (8)4.0
 = 0.0002048 2.408351  0.563268
5.0
6.0
7.0
Experimental "k"
424
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
9
20 (2014) 415-426
9
Enginar Yapraklarının (Cynara scolymus L.) Konveksiyonel Kuruma Karakteristiklerinin Matematiksel Modellenmesi, Günhan et al
each other while the RMSE, χ2 and P values were
the smallest once the Midilli et al model was used.
Based on these findings the Midilli et al model
was selected and a drying constant model of k as
a function of the temperature of drying air and
airflow velocity was developed and a final model
was proposed. The drying model explains the drying
of artichoke leaves the air temperature T range of
40 °C ≤ T ≤ 70 °C and 0.6 m s-1 ≤ V ≤ 1.2 m s-1 drying
airflow velocity. The predictions by the Midilli et al
model were found to be in good agreement with the
data obtained in the laboratory.
Wang et al (2003) found that the phenolic content
of artichokes did not significantly change during the
drying at a temperature of 70 °C and freeze-drying.
Using this argument, it can be stated that artichoke
leaves can be dried at either 60 or 70 °C if a faster
drying is needed.
Acknowledgements
The authors would like to acknowledge the financial
support provided by the Ege University Research
Fund.
References
Akgun N A & Doymaz I (2005). Modelling of olive cake
thin-layer drying process. Journal of Food Science
and Technology 68: 455-461
Alibas İ (2012). Asma yaprağının (Vitis vinifera L.)
mikrodalga enerjisiyle kurutulması ve bazı kalite
parametrelerinin belirlenmesi. Tarım Bilimleri
Dergisi-Journal of Agricultural Sciences 18: 43-53
Alonso M R, García M C, Bonelli C G, Ferraro G &
Rubio M (2006). Validated HPLC method for cynarin
determination in biological samples. Acta Farm.
Bonaerense 25(2): 267-70
Artnaseaw A, Theerakulpisut S & Benjapiyaporn C
(2010). Drying characteristics of Shiitake mushroom
and Jinda chili during vacuum heat pump drying.
Food and Bioproducts Processing 88: 105–114
Baysal T, Içier F, Ersus S & Yildiz H (2003). Effects of
microwave and infrared drying on the quality of carrot
and garlic. Eur. Food Res. Technology 218: 68–73
Bundy R, Walker A F, Middleton R W, Wallis C &
Simpson H C R (2008). Artichoke leaf extract (Cynara
scolymus) reduces plasma cholesterol in otherwise
healthy hypercholesterolemic adults: A randomized,
double blind placebo controlled trial. Phytomedicine
15: 668–675
Abbreviations and Symbols
A, B, C
a, b, c, g, h, n
k
M0
Me
MR
MRexp
MRpre
Mt
N
n1
P
R2
RMSE
T
t
V
χ2
constants
dimensionless coefficients in the drying models
drying coefficients in the drying models, h−1
initial moisture content, dry basis (kg water kg-1 dm-1)
equilibrium moisture content, dry basis (kg water kg-1 dm-1)
moisture ratio, dimensionless
experimental moisture ratio, dimensionless
predicted moisture ratio, dimensionless
moisture content at any time, dry basis (kg water kg-1 dm-1)
total number of observations
number of constants
mean relative percent error
coefficient of determination
root mean square error
air temperature, °C
time, h
air velocity, m s-1
chi-square
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
425
Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves, Günhan et al
Demir V, Gunhan T & Yagcioglu A K (2007). Mathematical
modelling of convection drying of green table olives.
Biosystems Engineering 98(1): 47-53
Doymaz İ (2013). Determination of infrared drying
characteristics and modelling of drying behaviour of
carrot pomace. Tarım Bilimleri Dergisi-Journal of
Agricultural Sciences 19: 44-53
FAO (2013). FAOSTAT Agricultural Database Web Page
Retrieved in December, 18, 2013 from. http://faostat3.
fao.org/faostat-gateway/go/to/download/Q/QC/E
Figiel A (2010). Drying kinetics and quality of beetroots
dehydrated by combination of convective and
vacuum-microwave methods. Journal of Food
Engineering 98: 461–470
Hawlader M N A, Chou S K & Chua K J (1997).
Development of design charts for tunnel dryers.
International Journal of Energy Research 21(11):
1023-1037
Krokida M K, Maroulis Z B & Kremalis C (2002).
Process design of rotary dryers for olive cake. Drying
Technology 20(4-5): 771–788
Menges H O & Ertekin C (2006). Thin layer drying
model for treated and untreated stanley plums. Energy
Conversion and Management 47(15-16): 2337–2348
Sanchez-Rabaneda F, Jauregui O, Lamuela-Raventos
R M, Bastida J, Viladomat F & Codina C
(2003). Identification of phenolic compounds
in artichoke waste by high-performance liquid
chromatography–tandem mass spectrometry. Journal
of Chromatography A 1008: 57–72
Shimoda H, Ninomiya K, Nishida N, Yoshino T,
Morikawa T, Matsuda H & Yoshikawa M (2003).
Anti-hyperlipidemic sesquiterpenes and new
sesquiterpene glycosides from the leaves of artichoke
(Cynara scolymus L.): structural requirement and
mode of action. Bioorganic & Medicinal Chemistry
Letters 13(2): 223-228
Silva E M, Da Silva J S, Pena R S & Rogez H (2011). A
combined approach to optimize the drying process of
flavonoid-rich leaves (Inga edulis) using experimental
design and mathematical modelling. Food and
Bioproducts Processing 89: 39–46
Strumillo C & Kudra T (1986). Drying: Principles,
Applications and Design. Gordon and Breach Science
Publishers, New York
Temple S J & van Boxtel A J B (1999). Thin layer drying
of black tea. Journal of Agricultural Engineering
Research 74: 167–176
Midilli A & Kucuk H (2003). Mathematical modelling of
thin layer drying of pistachio by using solar energy.
Energy Conversion and Management 44(7): 11–22
Togrul I T & Pehlivan D (2003). Modelling of drying
kinetics of single apricot. Journal of Food Engineering
58: 23–32
Nicoleti J F, Telis-Romero J & Telis V R N (2001). Airdrying of fresh and osmotically pre-treated pineapple
slices: Fixed air temperature versus fixed temperature
drying kinetics. Drying Technology 19: 2175–2191
Wang M, Simon J E, Aviles I F, He K, Zheng Q &
Tadmor Y (2003). Analysis of antioxidative phenolic
compounds in artichoke (Cynara scolymus L.).
Journal of Agricultural and Food Chemistry 51: 601608
Özdemir M & Devres Y O (1999). The thin layer drying
characteristics of hazelnuts during roasting. Journal
of Food Engineering 42: 225-233
Yaldiz O & Ertekin C (2001). Thin layer solar drying of
some vegetables. Drying Technology 19(3): 583–596
Panchariya P C, Popovic D & Sharma A L (2002). Thin
layer modelling of black tea drying process. Journal
of Food Engineering 52: 349–57
Yaldiz O, Ertekin C & Uzun H I (2001). Mathematical
modelling of thin layer solar drying of Sultana grapes.
Energy 26(5): 457–465
Sacilik K & Elicin A K (2006). The thin layer drying
characteristics of organic apple slices. Journal of
Food Engineering 73(3): 281-289
Zhu X F, Zhang H X & Lo R (2005). Antifungal activity
of Cynara Scolymus L. extracts. Fitoterapia 76: 108–
111
426
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
20 (2014) 415-426
Download

Mathematical Modelling of Convection Drying Characteristics of