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MODELING THE KINETICS OF DRYING BEET ROOTS
Safarov J.E.
1
Sultanova Sh.A.
1,2
Najafli M.R.
3
Usenov A.B.
1
1
Tashkent state technical university, Uzbekistan
2
Deputy Mayor Tashkent city, Uzbekistan
3
Alov Inshaat LLC, Azerbaijan
https://doi.org/10.5281/zenodo.15125094
Introduction.
Drying involves complex thermal processes in which mass
and heat are transferred simultaneously, interrelatedly and unstably both inside
and on the surface of the sample. Accordingly, it is necessary to have a complete
understanding of the control parameters in this process. In the literature, the
drying process is described using three mathematical models: theoretical, semi-
theoretical and empirical [1, 2]. Understanding the basic phenomena and
mechanisms of the drying process helps to develop various theoretical models.
Both theoretical models and computer simulations are used as a means to
predict the drying curves of various products.
Theoretical calculations and process modeling are able to explain the
phenomena occurring during the drying process. Empirical models can be built
on the basis of a direct correlation of humidity with drying time without taking
into account the principles of this process. Accordingly, empirically developed
models can predict drying curves for real conditions. However, their parameters
have no physical meaning and are not able to accurately explain the important
phenomena of the process. As a compromise between theory and convenient
application, semi-theoretical models are derived from a simplified second law of
Fick’s diffusion or are obtained by modifying any simplified widely used model
[3].
The aim of this work was to study the drying process of crushed beetroot
using hot air and infrared drying methods and find the best drying model to
explain the drying of crushed plant materials with hot air and infrared
radiation.
Materials and methods.
Fresh beets were collected and crushed before
each series of experiments. Beets were selected based on visual assessment of
their uniformity, color and size.
The initial moisture content was 82.2 ± 0.2%. Before each experiment,
large, uncrushed beets were removed from the mass.
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A laboratory setup consisting of a drying chamber, an air flow control unit,
temperature control unit, and radiation source (infrared lamp and electric
heater) was developed for the research. The drying chamber was made of sheet
metal, the outer surface of which was completely insulated to prevent heat loss
to the environment by an additional casing. A heater power control unit was
used to regulate the air temperature. The temperature inside the drying
chamber was constantly monitored by a thermocouple, which was built into the
control element. A digital anemometer was used to measure the air velocity. A
250 W infrared lamp was installed on the upper side of the drying chamber. The
height of the lamp was adjusted by a tripod. The intensity of infrared radiation
was adjusted by an autotransformer.
For the hot air drying experiments, different air flow rates at three levels of
0.5, 1 and 1.5 m/s and three temperatures at three levels of 30, 45 and 60°C
were selected. In addition, different irradiance levels (1500, 3000 and 4500
W/m2), lamp-to-sample distances (10, 30 and 50 cm) and air flow rates (0.5, 1.0
and 1.5 m/s) were used for infrared drying. The temperature and air flow rates
were selected based on a literature review of industrial air drying applications,
in particular, thin-layer drying of medicinal plants. As practice shows, low
temperatures (i.e. 30–50°C) should be used for drying plants in order to obtain
an optimal product quality without losing protein and protein. Before each
experiment, the dryer was left idle for approximately 30 minutes to ensure a
steady state based on the predetermined experimental drying conditions. For
each treatment, 200 ± 1 g of plant material was uniformly spread in a thin layer
on an aluminum weighing bottle.
Drying was stopped once the sample moisture content reached the target
10-13%. All drying procedures were performed in triplicate. Drying curves
were then plotted using the average moisture content at each time point.
The mass fraction of moisture in percent in the test sample was calculated
using the formula:
𝑋 =
𝑚
2
−𝑚
3
𝑚
2
−𝑚
1
∙ 100
,
(1)
where
𝑋
is the mass fraction of moisture, %;
𝑚
1
is the mass of the weighing
bottle without the test sample, g;
𝑚
2
is the mass of the weighing bottle with the
test sample before drying, g;
𝑚
3
is the mass of the weighing bottle with the test
sample after drying, g.
The energy expended in evaporation of moisture was calculated. The
energy expended in evaporation was calculated using the Arrhenius equation [1,
2]:
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𝐷
𝐴𝑟
= 𝐷
𝑜
𝑒𝑥𝑝 (−
𝐸
3
𝑅𝑇
)
(2)
where
𝐷
𝑜
is the pre-exponential coefficient of the Arrhenius equation,
𝐸
3
is
the energy of evaporation (kJ/mol),
𝑅
is the ideal gas constant (8.314 J/kmol),
𝑇
is the drying temperature.
Results and discussion.
The time required for drying the crushed plant
material is described in detail in our previous works [4, 5]. The graphs of the
experimental data on hot air drying of crushed plant material at different
temperatures (30, 40 and 50°C) and air flow rates (0.5, 1.0 and 1.5 m/s) were
analyzed in terms of the decrease in the moisture content as a function of the
drying time. This is due to the fact that the moisture content curves explain the
drying behavior of the products better than the final moisture content curves,
since the initial moisture content for all experiments was compared to 82.2%.
The results of the study showed that temperature had the most significant
effect on the drying kinetics of the samples. Air flow rate had the second most
significant effect.
The effect of infrared radiation level on the moisture content of the samples
was significant, as expected. Both at constant air flow rate and at varying
distance between the emitter and the sample, the moisture content decreased
faster with increasing infrared radiation level. The results of infrared drying
showed that, in contrast to hot air drying, the moisture content decreased faster
with decreasing air flow rate at the same infrared radiation intensity and
emitter-sample distance. Increasing the air flow rate increased the cooling
effect, which decreased the temperature of the product.
At the same infrared radiation intensity and air flow rate, the decrease in
moisture release accelerates when the infrared emitter is placed closer to the
sample. As the distance between the sample and the emitter increases, the
thermal radiation hits the surface of the sample but does not effectively
penetrate inside. Therefore, the absorbed moisture energy inside the leaves of
the sample decreases sharply. Accordingly, the degree of moisture removal
decreased due to the increase in the distance between the infrared emitter and
the sample.
Fig. 1 shows the moisture diffusion values at different temperatures and air
flow rates. It is expected that the moisture diffusion values increase with
increasing drying temperature. This was due to the increase in the vapor
pressure of the samples, which accelerated the moisture exchange at higher
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temperatures. When drying plants at a higher temperature, the heating energy
increases, which leads to an increase in the activity of water molecules. As a
result, higher moisture diffusion values can be obtained.
Using higher air flow rates at all drying temperatures results in higher
moisture diffusion values. This may be due to the lower vapor pressure
resulting from the higher air flow rate, which in turn reduces the evaporative
resistance.
Fig.
1. Effect of air velocity and temperature on the effective diffusion
coefficient during hot air drying of crushed beets
The lowest moisture diffusion value was observed at 0.5 m/s air flow
velocity at 30°C, while its highest value was recorded using 50°C drying air at
1.5 m/s. These results indicated that higher air temperature and air velocity
were preferable for drying the ground plant material when using hot air drying
under the given experimental conditions. The effect of air temperature on the
moisture diffusion of the ground plant material was greater than that of air flow
velocity.
𝐷
𝐴𝑟
= 10
−12
∙ (0,11𝑇 + 5,9𝑉 + 0,01𝑇
2
− 1,39𝑉
2
+ 0,59),
𝑅
2
= 0,98
(3)
The calculated moisture evaporation values for the ground plant material
during infrared drying are shown in Fig. 2. It can be seen from the figure that
the moisture diffusion increases when the infrared intensity increases at a
constant air flow rate and a constant distance between the emitter and the
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sample. This can be caused by the increased levels of infrared intensity, which
quickly increases the temperature of the sample. As a result, the vapor pressure
also increased, leading to faster drying.
Fig. 2.
Change in the effective diffusion coefficient depending on the
intensity of infrared radiation, air velocity and distance to the sample
Studies on shredded cabbage also showed similar effects of infrared
radiation on moisture diffusion. Increasing the air flow velocity at a constant
infrared intensity and distance between the emitter and the sample reduces
moisture diffusion. This is because the faster air flow cools the surface of the
sample, while the internal temperature of the sample remains relatively higher
than the surface and ambient air temperatures. This results in a negative
temperature gradient. For drying with an IR heat source, the lowest moisture
diffusion value was at an air flow velocity of 1.5 m/s, a radiant intensity of 1500
W/m
2
and a distance between the emitter and the sample of 20 cm, while the
highest moisture diffusion value was recorded at an air velocity of 0.5 m/s.
The moisture diffusion values from this study were in the range of 10.1 to
10.8 m
2
/s for drying plant materials. Accordingly, the highest moisture diffusion
values were related to the infrared drying experiments. This is mainly due to
the fact that the drying time in the infrared dryer is much shorter than that of
the hot air drying system. Therefore, the infrared drying method was found to
be more effective in drying the shredded plant material than the hot air drying.
Conclusions.
The drying kinetics of ground plant materials under two
drying methods, hot air and infrared drying, were analyzed and modeled. In
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both drying methods, moisture removal was observed during the decreasing
velocity period rather than during the constant velocity period. The drying
efficiency of infrared drying was higher than that of hot air drying due to its
higher drying velocity. In order to gain a deeper understanding of the mass
transfer mechanism of ground plant materials during the drying process, the
effective moisture diffusion was also determined. It was found that the moisture
diffusion values ranged from 1.096 ·10
-11
to 2.486 10·10
-11
m
2
/s and from
3.312·10
-11
to 5.928·10
-11
m2/s for hot air drying and infrared drying,
respectively. In hot air drying, the moisture diffusion value was greater at higher
temperatures and higher air flow rates.
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