Available via license: CC BY-NC-ND 4.0
Content may be subject to copyright.
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446 4437
MODELING OF THIN-LAYER KINETICS AND COLOR CHANGES OF
APPLE SLICES DURING FAR-INFRARED VACUUM DRYING
by
Vangel~e MITREVSKIa
*
, Cvetanka MITREVSKAb, and Ljupco TRAJCEVSKIa
aFaculty of Technical Sciences, University St.Kliment Ohridski, Bitola, Republic of North Macedonia
bFaculty of Safety Engineering, International Slavic University Gavrilo Romanovic Derzhavin,
Bitola, Republic of North Macedonia
Original scientific paper
https://doi.org/10.2298/TSCI220201077M
In this study far infrared vacuum drying kinetics and change of color quality pa-
rameters of apple slices were analyzed. The experimental data set of drying kinet-
ics was obtained on the experimental set-up designed to imitate an industrial far
infrared vacuum dryer. For approximation of the experimental data with regard
to the moisture ratio four well known thin-layers drying models from scientific
and engineering literature and new developed model of Mitrevski et al., were
used. The performed statistical analyzes show that the model of Mitrevski et al.,
has the best statistical performance than well-known thin-layer drying models.
The estimated values of moisture diffusivity of apple obtained from this study are
within the range from 2.80·10–11 to 1.70·10–10 m2/s. A negative effect on the total
color change of far infrared vacuum dried apple slices was observed with in-
creasing of temperature of infrared heaters and vacuum pressure.
Key words: far infrared vacuum drying, apple, color change
Introduction
In recent few decades the consumers’ demand evolving in the direction of dry food
materials that keep their original characteristics to a higher degree i.e. to dry materials with
high sensorial and microbiological quality. Convective drying is the most used method for the
production of dried fruits and vegetables. The main disadvantages of this classical method of
drying are [1]: the material is exposed at high temperature for a long time during the contact
with hot air which is the reason for decreases on nutritive values and color change, shrinkage,
and low dehydration capacity of the dried material, structure and flavor changes during dry-
ing. In recent years, far infrared drying is popular method for thin-layer drying of various food
materials [2-4]. In comparison with convective drying the method of far infrared drying has
more advantage as: high energy efficiency, uniform heating of material, acceleration of drying
time and improved dried product quality [5], minimization of color change and shrinkage of
dried materials [6]. According to Nimmol fact is that infrared radiation accelerates the drying
process, but heat sensitive materials as agricultural and foods materials could be damaged or
degraded along with the quality decreasing, if radiation intensity is not properly applied [7].
____________
*
Corresponding author, e-mail: vangelce.mitrevski@uklo.edu.mk
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
4438 THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446
The effects of far infrared drying method can improve the quality and nutritional value of
dried materials if was used in conjunction with vacuum drying. With combination on the ad-
vantages of both drying methods, energy efficiency of the drying processes is enhanced and
degradation of dried product quality is reduced [8]. In scientific and engineering literature,
several researchers investigated far infrared vacuum drying of various fruits and vegetables
[9-15]. But, limited study of drying kinetics and change of color parameters of far infrared
vacuum dried materials at high value of temperature of infrared heaters from 120-200 °C and
vacuum pressure from 20-80 kPa were conducted. So, the objectives of this study were:
research drying kinetics of far infrared vacuum drying apple slices and development of
new thin-layer drying model,
estimate to moisture diffusivity of apple slices and compared estimated values with the
values published in scientific and engineering literature by other authors, and
research of the influence of boundary conditions on total color changes of dried apple
slices.
Material and methods
Sample preparation
Fresh apples variety Golden Delicious was used as raw material in the experimental
part of the research. Prior to processing, the apples were stored in a cold chamber at a temper-
ature of 4 °C and a relative air humidity of 75%. The apples were washed, peeled and sliced
with a slicer machine in order to obtain uniform samples. The spherical samples with diameter
43 ±10–1 mm and thickness of 3 ±10–1 mm, obtained from the central medulla region where
the cell structure is more uniform, were used in the drying experiments. Several measure-
ments were made using a caliper, and only the samples with a tolerance of ±2% were used in
the experimental part of research.
The apple slices were dried in a far-infra red vacuum set-up [15]. The experimental
conditions were chosen such as that of temperature of infrared heaters and vacuum pressure
were in the range to be used on the industrial dryer. The effect of temperature of infrared heaters
120 °C, 140 °C, 160 °C, 180 °C, and 200 °C, and vacuum pressure 20 kPa, 40 kPa, 60 kPa, and
80 kPa on the drying kinetics of apple slices were investigated from [15]. After each experi-
ment the dried samples were stored in an air tight paper packet for further analysis. The tran-
sient temperatures of drying samples were measured with thee micro-thermocouples placed in
each of the mid-plane of the drying samples. The measurement of samples mass changes with
time was enabled with load cell type OMEGA LCL-040 (Omega, Inc., USA), which was
connected to data acquisition system. The temperature and mass changes of dried samples
were registered on the personal computer. The initial moisture content of the samples was
obtained according to the AOAC method no. 934.06 (AOAC 1995). The experiments were
carried out in triplicate and an arithmetic average value was used for data processing. The
drying experiments were performed until obtaining the moisture content of dry apple samples
of 0.04 kg/kg.
Drying kinetics
The experimental moisture content data obtained at different temperature of infrared
heaters and vacuum pressure were converted to the moisture ratio (MR) using:
0
= eq
eq
u – u
MR uu
(1)
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446 4439
were MR is the dimensionless moisture ratio and u
, u0, and ueq are moisture content at any
time, initial moisture content and equilibrium moisture content. Because of the values of equi-
librium moisture content, ueq are relatively small compared to those of moisture content of
material, u
or initial moisture content, u0 the error involved in the simplification is negligible.
Thus MR was then calculated:
0
u
MR u
(2)
Calculation of moisture diffusivity
The moisture diffusivity of foods is very often considered as an Arrhenius-type tem-
perature function [16, 17]:
0
0
exp R
mm
E
aa T
(3)
where am0 is the Arrhenius factor, E0 – the activation energy for moisture diffusion, R – the
ideal gas constant, and T – the absolute temperature. In this study the values of moisture dif-
fusivity were estimated on the basis of an accurate and easy to perform single thermocouple
temperature measurement by using an inverse approach [16, 17]. An arithmetical mean of the
readings from the three thermocouples inserted in the mid-palate position separately of each
of the three drying slices of apple was used as a transient temperature reading [16, 17].
The estimation methodology is based on the minimization of the ordinary least
square norm:
T
E
P Y T P Y T P
(4)
where, YT = [Y1,Y2, … ,Yimax] is the vector of measured temperatures, TT = [T1(P), T2(P), …
Timax(P)] is the vector of estimated temperatures at time
i (i = 1, 2, …, imax), PT = [P1, P2, …
PN] is the vector ofunknown parameters, imax is the total number of measurements, and N is
the total number of unknown parameters (imax ≥ N). For the minimization of E(P) represent-
ing the solution of the present parameter estimation problem the Levenberg-Marquardt meth-
od were utilized [16, 17].
Color measurement and kinetics on color changes
The colour changes in food materials during drying are due to degradation of pig-
ments (chlorophylls, carotenoids, anthocyans, and betalaines), Maillard reactions or enzymat-
ic browning [18]. In order to research the effect of temperature of infrared heaters and vacu-
um pressure on the color changes of dried apple, a three-filter colorimeter Konica Minolta
CR-400 (Konica Minolta Sensing Americas, Inc., USA) was used. This instrument shows the
quantitative parameters of color change in different systems. The measured values of the color
parameters are represented in the CIE, L*, a*, b*, color space. In this color space, L* values are
used as an indicator of lightness/darkness (ranges from 0 to 100), co-ordinate a* to indicate
chromaticity on a green (–) to red (+) axis (ranges from –120 to 120), and co-ordinate b* to
indicate chromaticity on a blue (–) to yellow (+) axis (ranges from –120 to 120). The color
measurements were conducted before and after far infrared vacuum drying. Five measure-
ments were performed for each sample which is selected randomly. The values used for total
color change calculations encompassed the average values of L*, a*, and b* of each sample.
The total color change, E is calculated on the basis of the equation [19]:
0 0 0
( ) ( ) ( )
* * * * * *
E L L a a b b
(5)
where
0 0 0
* * *
L , a , b
are initial values for lightness, redness, and yellowness.
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
4440 THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446
In order to determine the rate of color changes during drying of far infrared vacuum
drying, the kinetics of the parameters of lightness, L*, redness, a*, and yellowness, b*, were
investigated. For approximation of the total color changes, E data during far infrared vacu-
um drying process new developed model were used:
2
+
h
B
E A Cp
t
(6)
where A, B, C, are parameters, th, – the temperature of infrared heaters, and p – the vacu-
um pressure. In this study multiple regression relationship between dependent variable,
E and independent variables, temperature of infrared heaters and vacuum pressure were
used.
Results and discussion
Fitting of drying curves
In the most number existing thin-layer drying models which is used to for approxi-
mation experimental data of drying kinetics the effect of boundary conditions on the empirical
parameters it is not take into account. It that reasons in this study the new generalized thin-
layer drying model was developed. For approximation of experimental data on the drying
kinetics of apple slices five thin-layer mathematical models from scientific literature and new
developed model of Mitrevski et al. were used, tab. 1.
MR = M
/M0 is the moisture ratio, A, B, C, D, E, F – the parameters, k1 [min–1] – drying rate constant,
[min] – drying time, th [°C] – the temperature of infrared heatres, and p [kPa] – the vacuum pressure
The method of multiple indirect non-linear regression and estimation methods of:
Quasi-Newton, Simplex, Simplex and quasi-Newton, Hooke-Jeeves pattern moves, Hooke-
Jeeves pattern moves and quasi-Newton, Rosenbrock pattern search, Rosenbrock pattern
search and quasi-Newton, Gauss-Newton and Levenberg-Marquardt from computer program
StatSoft Statistica (Statsoft Inc., Tulsa, OK, http://www.statsoft.com), were used to for calcu-
lation of the statistical parameters and estimate the parameters in the given models. Because
the regression method, estimation method, the initial step size, the start values of parameters,
convergence criterion and form of the function have significant influence on accuracy of es-
timated parameters [24], a large number of numerical experiments were performed. On the
basis of thin-layer data and each model from, tab. 1, the values of: coefficient of determina-
Table 1. Thin-layer drying models
Model
Equation
Name of model
References
M01
1
exp m
MR A k B
Midilli
[20]
M02
11
exp 1 expMR A k A k B
Diffusion approach
[21]
M03
1
= exp 1 expMR A k A B
Verma
[22]
M04
05
1
exp .
MR A k B C
Jena and Das
[23]
M05
11
1 1 1 1
exp 1 exp **
C D E F
hh
MR A k B / A k B
p t p t
Mitrevski et al.
This study
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446 4441
tion, R2, root mean squared error, RMSE, and mean relative deviation, MRD, were calculated.
When the value for coefficient of determination obtained from different estimation methods
was different, the greatest value was accepted as relevant. In order to estimate and select the
best thin-layer drying model the value of performance index,
, and chi-squared,
2 were
calculated:
2
R
RMSE MRD
(7)
2 2 2
12
zz
(8)
where z1 and z2 are individual statistics for testing of the population of skewness and kur-
tosis [25].
The best model that is describing the thin-layer drying characteristics apple slices
has to be chosen on the basis of higher,
and
2 the value lower than tabled critical 0.05 chi-
square value
2
0 05 5 99
..
for degrees of freedom, Dof = 2, tab. 2.
From tab. 2 it is evident that model M05 i.e. new developed model, has the highest
value of performance index,
= 31.869, (Rank 1) in comparison with the other models. Also
it can be seen that all models have smaller average value of,
2 than tabled critical chi-square
value. In accordance with statistical criteria, the new developed model of Mitrevski et al., is
able to correlate the experimental values of drying kinetics of apple slices with 3.63% root
mean squared error. The estimated values of parameters in new generated model of Mitrevski
et al., are presented in tab. 3.
The analysis of variance (ANOVA) results indicated that the temperature of heatres
(p ≤ 0.001), vacuum pressure (p ≤ 0.05), and the interaction of the temperature of heatres and
vacuum pressure (p ≤ 0.05) significantly affected the drying time of apple slices.
In fig. 1, the experimental and predicted values of MR with drying time at tempera-
ture of infrared heaters 120 °C, 140 °C, 160 °C, 180 °C, and 200 °C for apple slices at vacu-
um pressure of 20 kPa are shown.
From fig. 1 is evident that has a good agreement between the experimental and pre-
dicted values of moisture data of apple slices.
Table 2. Statistic summary of the regression analysis
Model
R2
RMSE
MRD
2
Rank
M01
0.9393
0.1170
1.8162
4.4197
4.6435
5
M02
0.9394
0.1166
1.7277
4.6620
4.5585
3
M03
0.9394
0.1166
1.7197
4.6836
4.5413
2
M04
0.9394
0.1166
1.8089
4.4512
4.6225
4
M05
0.9942
0.0363
0.8602
31.869
1.1539
1
Table 3. The values of estimated parameters
A
K1
B
C
D
E
F
–0.0004
0.0054
0.0052
–0.0872
1.3645
0.0253
–1.2991
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
4442 THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446
Moisture diffusivity
The values of the parameters of effective moisture diffusivity, am0, and activation
energy E0 are determined by application of inverse approach. In tab. 4 the initial guesses of
parameters and computationally obtained values of parameters using the Levenberg-
Marquardt method and RMS-error for the one of real realized experiment E17 (th = 180 °C,
p = 40 kPa, 2L0 = 3 mm, u0 = 5.24 kg/kg, and t0 = 24.82 °C), [26] are shown.
am0 – the Arrhenius factor, E0 – the activation energy, and RMSE – the root mean squared error
The estimated values of moisture diffusivity of apple obtained from this study are
within the range from 2.80·10–11 to 1.70·10–10 m2/s. These values are comparable with values
for other dried food materials which values generally were reported in scientific literature,
from 10–13 to 10–6 m2/s [27, 28]. The determined values of moisture diffusivity in this study
showed that the higher values of temperature of infrared heaters and lower value of vacuum
pressure is better to dry the apple slices in the selected experimental domain, because the
obtained values of moisture diffusivity are relatively higher.
Color change
In tab. 5 the average value changes in lightness, L*, redness, a*, yellowness, b*, and
total color changes, E, of apple slices for different value of temperature of infrared heaters
and vacuum pressure were presented.
From tab. 5 it is evident that, the L* value of dried apple slices decreased during dry-
ing. The, L* decreased from initial value Lo* = 83.32 to L* = 63.32, when apple slices are
dried at 200 °C and 80 kPa. The changes in L* parameter value was less at lower temperature
of infrared heaters and lower vacuum pressure. As temperature of infrared heaters increased
from 120-200 °C and vacuum pressure changes from 20-80 kPa the lightness of apple slices
Table 4. Estimated values of unknown parameters and RMS-error
am0·103 [m2s–1]
E0 [kJmol–1]
RMSE
Initial guess
0.274
38.50
7.660
Estimated values
0.085
36.40
0.710
Figure 1. Experimental and predicted MR values by the
Mitrevski
et al. model for different temperatures of
infrared heaters at vacuum pressure 20 kPa
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446 4443
decreased from 81.07 to 63.32. The decrease in L* value was in correlation with non-
enzymatic browning reactions which accelerates at high temperatures. The reduction in L*
value may be attributed to intense browning reaction and increase crust formation due to ex-
posure to high temperature [29]. Because the lightness is a very important color quality pa-
rameter, lower temperature of infrared heaters and lower vacuum pressure are preferable to
preserve of dried apple slices. The temperature of infrared heaters and vacuum pressure also
have an effect on the redness parameter, a*. From instance, a* value increased from initial
value
0
*
a
= –6.16 to a* = 6.67 at the end point when apple slices were dried at 200 °C and 80
kPa. As shown in tab. 5 the yellowness of dried slices increased during drying from 2.41 to
6.67. The values of yelowness, b* increased from initial value
0
*
b
= 21.86 to b* = 25.67 when
apple slices were dried at 200 °C and 80 kPa. As the temperature of infrared heaters increased
from 120-200 °C and value of vacuum pressure varied between 20 to 80 kPa the yellowness
of apple slices increased from 22.23 to 25.67. Similar effects on the drying kinetics on chang-
es of color parameters were reported for banana [10].
th – heaters temperature, p – vacuum pressure, a* – redness, b* – yellowness, L* – lightness, E – total color change,
mean ± standard deviation
From tab. 5 obviously that E values, increased during drying apple slices and color
changes intensity is more intense at higher temperature of infrared heaters and higher vacuum
pressure. The total color change, E values increased from 8.67 to 23.32, when apple slice are
dried at temperature of heaters from 120200 °C and vacuum pressure from 20-80 kPa. Similar
results were reported from far infrared vacuum drying of peach [6] and kiwi [12].
Table 5. The effect on drying conditions on changes of color parameters
th
p
a*
b*
L*
E
120
20
2.41 ±3.81
22.23 ±9.36
81.07 ±2.09
8.67
140
20
2.98 ±3.84
22.29 ±9.78
73.01 ±3.26
13.10
160
20
4.14 ±3.60
23.40 ±10.66
71.73 ±3.09
14.85
180
20
4.98 ±3.84
23.50 ±19.40
70.03 ±3.26
16.67
200
20
5.56 ±4.16
23.95 ±11.36
68.99 ±3.19
17.87
120
40
2.87 ±3.76
22.66 ±9.40
80.15 ±3.26
9.32
140
40
3.41 ±3.60
23.11 ±10.36
71.12 ±3.39
14.78
160
40
4.61 ±3.84
23.67 ±10.78
70.66 ±3.56
15.98
180
40
5.33 ±3.94
24.41 ±11.32
69.16 ±3.36
17.66
200
40
5.99 ±4.60
24.89 ±11.56
67.22 ±3.89
19.62
120
60
3.13 ±3.92
22.91 ±10.36
77.42 ±3.09
10.56
140
60
3.89 ±3.84
23.35 ±11.40
69.68 ±3.26
16.22
160
60
4.98 ±3.60
23.97 ±11.36
68.09 ±3.49
18.19
180
60
5.88 ±4.84
24.59 ±11.40
67.30 ±3.56
19.44
200
60
6.34 ±3.73
25.32 ±11.66
66.34 ±4.09
20.58
120
80
3.41 ±3.64
23.22 ±10.40
73.44 ±3.26
13.13
140
80
4.24 ±3.60
23.66 ±11.36
66.32 ±3.39
19.17
160
80
5.21 ±3.84
24.44 ±12.40
65.21 ±3.46
20.70
180
80
6.11 ±4.14
25.24 ±13.40
64.89 ±3.66
21.58
200
80
6.67 ±4.60
25.67 ±13.56
63.32 ±4.49
23.32
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
4444 THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446
For estimation of the statistical parameters in the model of total color change, eq.
(5), the method of multiple indirect non-linear regression and estimation method of Quasi-
Newton, from computer program StatSoft Statistica (Statsoft Inc., Tulsa, OK,
http://www.statsoft.com), were used. In tab. 6 the estimated values of parameters from the
mathematical model with eq. (5) are presented.
In fig. 2 the total colour change as functions of temperature of infrared heaters at
different vacuum pressure was presented. The high value of coefficient of determination,
R2 = 0.9821 and small value of root mean squared error, RMSE = 0.062 showed that the total
color change, E during far infrared vacuum drying apple slices could be modeled by new
generated model of Mitrevski et al.
Conclusions
In the present study the effects of temperature of infrared heaters and vacuum pres-
sure on the drying kinetics and color quality of apple slices were examined. The experimental
drying data in terms of MR were approximated with four thin-layer drying models from scien-
tific literature and new generated model of Mitrevski et al. According to the statistical evalua-
tion, the new developed model of Mitrevski et al., has the best statistical performances than
other literature thin-layer drying models. The estimated values of moisture diffusivity for
apple obtained by inverse approach are in the range from 2.80·10–11 to 1.70·10–10 m2/s and are
comparable with values for other dried food materials. This study verified that the boundary
conditions on the surface of dried apple slices (the temperature of infrared heaters and vacu-
um pressure) have a strong effect on the change of color parameters (L*, a*, b*, and E). The
high temperature of infrared heaters and high value of vacuum pressure has a negative effect
on the total color change of dried apple slices. For the preserved nutritional values of dried
apple slices the optimum drying conditions for combined far infrared vacuum drying is 120 °C
and 20 kPa. The new developed thin-layer drying model and the results of kinetics on color
Table 6. The values of estimated parameters (eq.5)
A
B
C
32.264
–2.838.4
0.0009
Figure 2. Effect of temperature of infrared heaters on total
color change at different vacuum pressure
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446 4445
changes presented in this study will find the technological application on far infrared vacuum
drying for preservation of other food materials.
Nomenclature
A,B,C,D,E,F– parameters
a* – redness
am – moisture diffusivity, [m2s–1]
am0 – Arrhenius factor, [m2s–1]
b* – yellowness
E0 – activation energy, [Jkg–1]
k1 – drying rate constant, [min–1]
L* – lightness
MR – moisture ratio [–]
MRD – mean relative deviation
P – vector of unknown parameter
R – absolute gas constant, [JK–1mol–1]
R2 – coefficient of determination
RMSE – root mean squared error
p – pressure, [Pa]
t – temperature, [°C]
Tk – temperature, [K]
T – vector of estimated temperature, [°C]
Y – vector of measured temperature, [°C]
u – moisture content, [kg–1kg–1db]
z1, z2 – individual statistics for testing of
the population of skewness and
kurtosis
Greek symbols
E – total color change
– performance index
– time, [minute]
2 – chi-squared value
Subscripts
eq – equlibrium
h – heater
0 – initial
References
[1] Kanevce, G., et al., Vacuum Drying of Mushrooms, Proceedings, 14th International Drying Symposium
of Tehnologist for Drying and Storing, Stubicke Toplice, Croatia, 1998, Vol. 1, pp. 220-229
[2] Doymaz, I., Infrared Drying Characteristics of Bean Seeds, J. of Food Process. Preserv., 39 (2015), 6,
pp. 933-939
[3] Pawar, S. P., Pratape, V. M., Fundamentals of Infrared Heating and its Application in Drying of Food
Materials: A review, J. Food Process. Eng., 40 (2017), 1, e12308
[4] Riadh, M. H., et al., Infrared Heating in Food Drying: An overview, Dry. Technol., 33 (2015), 3, pp.
322-335
[5] Mongpraneet, S., et al., Accelerated Drying of Welsh Onion by Far Infrared Radiation under Vacuum
Conditions, J. Food Eng., 55 (2002), 2, pp. 147-156
[6] Alaei, B., Chyjan, R. Z., Modelling of Nectarine Drying near Infrared-Vacuum Conditions, Acta
Sci.Pol.Techol.Aliment., 14 (2015), 1, pp. 15-27
[7] Nimmol, C., Vacuum Far-Infra Red Drying of Foods and Agricultural Materials, King Mong
Univ.tehnol.north Bang., 20 (2010), 1, pp. 37-44
[8] Hafezi, N., et al., Evaluation of Energy Consumption of Potato Slices Drying Using Vacuum-Infrared
Method, Int. J. Adv. Biol. Biomed. Res., 2 (2014), 10, pp. 2651-2658
[9] Pliestic, S., Mitrevski, V., The Observation of Red Pepper in Vacuum by Measurement Temperature,
Strojartsvo, 45 (2003), 1, pp. 47-54
[10] Swasdisevi, T., et al., Optimization of a Drying Processes Using Infrared-Vacuum Drying of Cavendish
Banana Slices, Songklanakarin J. Sci. Technol., 29 (2007), 3, pp. 809-816
[11] Liu, Y., et al., Drying Characteristics and Modeling of Vacuum Far-Infrared Radiation Drying of Flos
Lonicerae, J. of Food Process. Preserv., 39 (2015), 4, pp. 338-348
[12] Aidani, E., et al., Experimental and Modeling Investigation of Mass Transfer During Combined
Infrared-Vacuum Drying of Hayward Kiwifuits, Food Sci. Nutr., 5 (2016), 3, pp. 596-601
[13] Salehi, F., Kashaninejad, M., Modeling of Moisture Loss Kinetics and Color Changes in the Surface of
Lemon Slice During the Combined Infrared-Vacuum Drying, Inf. Process. Agric. 5 (2018), 4, pp. 616-
523
[14] Mitrevski, V., et al., Vacuum Far-Infrared Drying of Apple, J. Process. Energy in Agr., 20 (2016), 1, pp.
1-3
[15] Mitrevski, V., et al., Mathematical Modelling of Far Infrared Vacuum Drying of Apple Slices, Thermal
Sciences, 23 (2019), 1, pp. 393-400
Mitrevski, V., et al.: Modelling of Thin-Layer Kinetics and Color Changes …
4446 THERMAL SCIENCE: Year 2022, Vol. 26, No. 5B, pp. 4437-4446
[16] Kanevce, G., et al., Inverse Approaches to Drying of Thin Bodies with Significant Shrinkage Effects,
Int. J. Heat Mass Transf., 129 (2007), 3, pp. 379-386
[17] Mitrevski, V., et al., Estimation Thermophysical Properties of Far-Infrared Vacuum Drying Potato by
Application of Inverse Approach, Thermal Sciences, 25 (2021), 1B, pp. 603-6111
[18] Bonazzi, C., et al., Food Drying and Dewatering, Dry.Technol., 14 (1996), 9, pp. 2135-2170
[19] Ghaboos, S. H. H., et al., Combined Infrared-Vacuum Drying of Pumpkin Slices, J.Food Sci.Technol, 53
(2016), 5, pp. 2380-2388
[20] Midilli, A., et al., A New Model for Single-Layer Drying, Dry. Technol., 20 (2002), 7, pp. 1503-1513
[21] Erbay, Z., Icier, F., A Review of Thin-Layer Drying of Foods: Theory, Modeling and Experimental
Results, Crit. Rev. Food Sci Nutr., 50 (2009), 5, pp. 441-464
[22] Verma, L. R., et al., Effects of Drying Air Parameters on Rice Drying Models, Trans. ASAE, 28 (1985),
1, pp. 296-301
[23] Jena, S., Das, H., Modelling for Vacuum Drying Characteristic of Coconut Presscake, J. Food Eng., 79
(2007), 1, pp.92-99
[24] Mitrevski, V., et al., Adsorption Isotherms of Pear at Several Temperatures, Thermal Sciences, 19
(2015), 3, pp. 1119-1129
[25] Sheskin, D. J., Handbook of Parametric and Nonparametric Satistical Procedures, Champan and Hall
CRC, London, UK, 2011
[26] Bundalevski, S., Modelling of Far-Infrared Vacuum Drying Processes by Applying Inverse Approach,
Ph. D. thesis, University St. Climent Ohridski, Bitola, Macedonia, 2015
[27] Saravacos, G. D., Maroulis, Z. B., Moisture Diffusivity Compilation of Literature Data of Food
Materials, in: Transport Properties of Foods (ed T.W. Fennema et al.), Marcel Dekker Inc., New York&
Basel, USA, 2001, pp. 163-236
[28] Panagiotou, N., et al., Moisture Diffusivity: Literature Data Dompilation for Foodstuffs, Int. J.Food
Prop., 2 (2004), 2, pp. 273-299
[29] Mariscal, M., Bouchon, P., Comparison Between at Atmospheric and Vacuum Drying of Apple Slices,
Food Chem., 107 (2008), 4, pp. 1561-1569
Paper submitted: February 1, 2022 © 2022 Society of Thermal Engineers of Serbia.
Paper revised: April 4, 2022 Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia.
Paper accepted: April 14, 2022 This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.
