Drying Technology, 24: 1683–1689, 2006
Copyright # 2006 Taylor & Francis Group, LLC
ISSN: 0737-3937 print/1532-2300 online
DOI: 10.1080/07373930601031588
An Experimental and Modeling Investigation on Drying
of Ragi (Eleusine corocana) in Fluidized Bed
C. Srinivasakannan1 and N. Balasubramaniam2
1
Curtin University of Technology, Sarawak Campus Malaysia, Miri, Sarawak, Malaysia
AC College of Technology, Anna University, Chennai, India
2
Experimental investigation on drying of ragi (Eleusine corocana)
in a fluidized bed has been attempted covering the operating parameters such as temperature, flow rate of the drying medium, and
solids holdup. The drying rate was found to increase significantly
with increase in temperature and marginally with flow rate of the
heating medium and to decrease with increase in solids holdup.
The duration of constant rate period was found to be insignificant,
considering the total duration of drying and the entire drying period
was considered to follow falling rate period. The drying rate was
compared with various simple exponential time decay models and
the model parameters were evaluated. The Page model was found
to match the experimental data very closely with the maximum root
mean square of error (RMSE) less than 2.5%. The experimental
data were also modeled using Fick’s diffusion equation and the
effective diffusivity coefficients were estimated. The effective
diffusion coefficient was found to be within 5.7 to 14 3 1011 m2/s
for the range of experimental data covered in the present study with
RMSE less than 5%.
Keywords Drying kinetics; Fluidized bed; Food grain drying
INTRODUCTION
Ragi is one of the principal cereal crops for many peoples in India, Sri Lanka, and East Africa, in India, over
2.5 million hectares are cultivated annually. Although it
does not enter international markets, it is a very important
cereal grain in areas of adaptation. Grain is higher in protein, fat, and minerals than rice, corn, or sorghum.[1] It is
usually converted into flour and made into cakes, puddings, or porridge. When consumed as food it provides a
sustainable diet, especially for people doing hard work.
Grain may also be malted and flour of the malted grain
is used as a nourishing food for infants. Ragi is considered
an especially wholesome food for diabetics.
Earheads are gathered when they ripen; three or four
pickings are usually required to collect all earheads from
a field. The practice among farmers is to stack the just
Correspondence: C. Srinivasakannan, Curtin University of
Technology, Sarawak Campus Malaysia, CDT 250, 98009 Miri,
Sarawak, Malaysia. E-mail: [email protected]
cut ragi until the cold weather gives way to sunshine. By
the time ragi is threshed, it starts developing mold. Grains
that are not sun-dried thoroughly have high moisture content and are prone to accumulate mold and fungus. The
grain so produced suffers from microbial contamination,
which affects the health of the poor, who consume such
grains. A properly dried ragi grain can be stored up to 50
years, which points to the importance of drying.
Fluidized beds are widely used for the drying of granular
solids such as grains, fertilizers, chemicals, pharmaceuticals, and minerals. This technique offers advantages such
as the high heat capacity of the bed, improved rates of heat
and mass transfer between the phases, and ease in handling
and transport of fluidized solids.
The drying rates in fluidized beds are strongly influenced
by the characteristics of the material and the conditions of
fluidization. Drying of solids is generally understood to
follow two distinct drying zones known as constant rate
period and falling rate period demarcated with critical
moisture content. The critical moisture content is reported
to vary with operating parameters and with the type of drying equipment. The constant rate period is understood to
have maximum drying rate, which remains constant until
the critical moisture content with the resistance for moisture transfer in the gas phase. The rate of diffusion of
moisture to surface of solids becomes the limiting factor
for moisture transfer as far as the falling rate period is concerned. The extent of drying zones are decided based on the
type of material, with materials like sand, ion exchange
resin, glass beads, etc., reported to have larger duration
of constant rate period and short linear falling rate period
while the fibrous grains such as mustard, pepper, ragi,
poppy seeds, etc., are reported to have a very short duration constant rate period and a longer curvilinear falling
rate period.[2]
Knowledge of drying kinetics is essential for sizing the
dryer as well as for choosing the optimal drying conditions.
The complex hydrodynamics and process calculations are
material and dryer specific and hence numerous mathematical
1683
1684
SRINIVASAKANNAN AND BALASUBRAMANIAM
TABLE 1
List of various simple models tested with the drying data of the present study
Name of model
Newton model (NM)
Page model (PM)
Henderson and Pabis (HPB)
Two-term exponential model (TEM)
Approximate diffusion model (ADM)
models have been developed to estimate the drying kinetics.
These range from analytical models solved with a variety
of simplified assumptions to purely empirical models, often
built by regression of experimental data.
In general, the drying rate in constant rate period in fluidized bed drying is modeled using (a) simple empirical correlation relating drying rate to the influencing parameters
or utilizing heat=mass transfer coefficient between solids
and gas in fluidized bed[3–7] or (b) using mass transfer models, assuming the bed to made of bubble phase, emulsion
phase, and a dense phase with the exchange of mass and
energy between these phases.[8–14] Similarly, drying kinetics
in falling rate period is modeled with complex models,
which serve the purpose of improving the fundamental
understanding. However, these models may not serve for
practical applications in a straightforward manner, due
to their complexity.[15]
Simple models that can be used to design drying system
are much sought after to provide an optimum solution to
different aspects of drying operation, with a minimum number of parameters. A series of simple models based on exponential time decay were developed in the past and are being
continuously revised=improved; these are popularly known
as the Newton model, the Page model, the Henderson and
Pabis model, the two-term exponential model and the
approximate diffusion model. These simple models are
recently utilized for drying applications by Mujumdar,[16]
Diamante and Munro,[17] Zhang and Litchfield,[18]
Henderson,[19] Yaldeiz and Ertekin,[20] and Sharaf-Eldeen
et al.[21] to represent the drying kinetics. Different
approaches were reported for complex models, most common among them is based on second-order partial differential equation, commonly known as Fick’s diffusion equation.
The solution of partial differential equation differs based
on the boundary conditions, often requiring numerical
computations to estimate the drying rate.[7,14,22–25]
The objective of the present study is to experimentally
investigate the drying kinetics of ragi grain in a fluidized
bed with respect to the operating parameters such as the
temperature, flow rate of the drying medium, and the solids
holdup. Although the effect of operating parameters on the
drying rates are well known and one expects the influencing
parameters to respond in similar fashion qualitatively, the
Model equation
MR ¼ exp (kt)
MR ¼ exp (ktn)
MR ¼ a exp (kt)
MR ¼ a exp (kt) þ (1 a) exp (kat)
MR ¼ a exp (kt) þ (1 a) exp (kbt)
drying kinetics can vary quantitatively depending on the
nature of the material and the drying conditions. It is
further attempted to verify the compatibility of experimental drying kinetics with various simple models reported
in the literature (Table 1), and with complex models such as
Fick’s diffusion equation. The model parameters are estimated by minimizing the root mean square of error
(RMSE) between the experimental drying rate and the
model prediction (Tables 2 and 3).
EXPERIMENTAL SECTION
Drying experiments were conducted using fluidized columns of 0.148 m in internal diameter with a height of 1.2 m.
The gas distributor was 2 mm thick with 2 mm perforations
having 13% free area. A fine wire mesh was spot welded
over the distributor plate to arrest the flow of solids from
the fluidized bed in to the air chamber. Air from the blower
was heated and fed to the fluidization column through the
air chamber. The electrical heater consisted of a multiple
heating element each of 2 KW rating. A temperature controller, provided to the air chamber, facilitated control of
air temperature within 5C of the set temperature for
the entire operating range of 30 to 110C. Air flow was
measured using a calibrated orifice meter.
Table 4 shows the physical characters of ragi grain as
well as the experimental conditions covered in the present
study. A good fluidization behavior in terms of perfect
mixing of the bed material was observed visibly. This was
substantiated with low fluctuation in the bed pressure
drop, which is an indication for smooth fluidization without formation of slugs. The minimum fluidization velocity
was not found to vary with the temperature within the
range of temperatures covered in the present study.
A known quantity of ragi with known initial moisture
content was taken in the batch fluidized bed, and air at
the desired rate was introduced into the column. As fluidization continued, ragi samples were scooped out of the bed
at regular intervals of time for moisture content estimation.
The sample collector that had an approximate capacity of
five grams was utilized to scoop out the samples from the
fluidized bed. However, after transferring about 1 g to the
sample holder for moisture analysis, the rest of it was transferred back to the fluidized bed immediately. The ragi
1.73
1.43
2.03
2.46
1.15
4.14
1.68
2.25
3.09
3.60
3.92
3.0
4.3
4.7
4.3
4.6
9.1
4.8
6.2
6.2
9.1
8.4
4.52
4.59
4.66
4.14
4.60
2.90
4.53
3.51
3.51
2.90
2.95
1.96
0.43
2.27
1.23
1.53
2.76
2.87
2.08
2.08
2.76
3.81
2.8
0.7
2.5
1.5
1.1
3.6
3.2
2.13
2.8
3.7
4.7
7.6
3.4
9.5
6.1
9.4
9.9
18.8
8.6
8.1
9.9
11.6
1.94
4.27
2.41
2.60
2.17
2.17
2.39
2.09
2.69
2.93
2.92
4.7
1.7
4.5
3.5
3.1
5.5
5.1
4.2
4.7
5.1
6.0
1.7
2.0
2.8
2
2.5
2.5
3.2
2.0
2.7
3.8
4.5
9.23
9.85
9.49
9.59
9.59
9.23
9.44
9.37
9.54
9.67
9.68
0.06
1.05
1.23
1.47
0.71
0.64
0.51
0.27
1.86
2.39
2.47
7.02
9.18
7.25
8.05
8.05
6.61
6.74
7.3
7.21
6.74
5.89
12.2
3.4
15.2
7.1
8.5
21.2
22.5
11.7
14.5
24.8
44.9
5.7
1.8
4.8
3.9
3.5
6.3
5.5
4.9
5.2
5.2
6.2
1.8
2.1
3.1
2.1
2.6
2.8
3.3
2.3
3.1
4.0
5.0
1.6
1.6
1.6
1.6
1.6
1.2
1.6
1.2
1.6
1.6
1.6
0.15
0.30
0.60
0.15
0.30
0.30
0.60
0.60
0.15
0.30
0.60
60
60
60
80
80
80
80
80
100
100
100
T (C) W (kg) U (m=s) k 103 RMSE k 103 n 10 RMSE a 10 k 103 RMSE a 10 k 103 RMSE a 10 k 10 b 103 RMSE
TEM
HPB
PM
NM
TABLE 2
Evaluated model parameters at various operating conditions
ADM
DRYING OF RAGI IN A FLUIDIZED BED
1685
moisture content was determined by drying the samples to
constant weight in an air oven at 105C. The moisture contents were expressed on dry basis as kilograms of moisture
per kilogram of dry solid. Ragi as received from the farm,
with 41.2% moisture content, was used for all drying
experiments. The experimental data was checked for reproducibility and were found to deviate within 3%. The
equilibrium moisture content was estimated by keeping
the samples in an air oven at the desired temperatures until
no further weight change. The difference in weight between
a bone-dry sample and the weight of the sample obtained
at the desired temperature was utilized to calculate the
equilibrium moisture content.
RESULTS AND DISCUSSION
Experimental data showing the effect of temperature,
flow rate of the heating medium and solids holdup are
shown as plots of C=Ci versus time, in Figs. 1 to 4. Figures
1 through 4 show the drying rate decreasing, from the starting (t ¼ 0) until the end of drying, indicating the absence of
constant drying rate period or presence of constant rate period for an insignificant period of time compared to the total
drying time. The rate of drying is higher at the early stage of
drying while the moisture content was high and reduces as
the moisture content decreases. Figures 1 and 2 show the
effect of temperature of the heating medium at two different
solids holdup. An increase in temperature of the heating
medium increases the drying rate and it can be attributed
to the higher bed temperature of particles in the bed, which
increases the intra particle moisture diffusion to the surface
of the solid resulting in a higher drying rate.
Figure 3 show a marginal increase in drying rate with air
flow rate and it may be attributed to a reduction in external
mass transfer resistance during early stages of drying while
the drying rate and the moisture content is high. Looking
at the drying curve, as the rate of drying reduces from start
until the end of drying period one would expect the entire
operation to be an internal mass transfer controlled and
would expect a negligible effect of air flow rate on the drying rate. However, a continuous recording of the bed temperature indicated that the effective bed temperature
increased with flow rate of the heating medium, which
increases the moisture diffusion rate and thereby results
in higher drying rate. Repeat experiments were conducted
to eliminate the effect of experimental error on assessing
the effect of air flow rate on the drying rate and the conclusion of a marginal effect on drying rate was based on
the consistent observation on two sets of a experiments
conducted with two different solids holdups.
An increase in the solids holdup is found to decrease the
drying rate (Fig. 4) and it can again be attributed to the lower
effective bed temperature at higher solids holdup. The lower
effective temperature may be due to higher water content in
the bed due to increased solids holdup. This indirectly
1686
SRINIVASAKANNAN AND BALASUBRAMANIAM
TABLE 3
Evaluated effective diffusivity coefficient at various operating conditions
T (C)
60
60
60
80
80
80
80
80
100
100
100
W (kg)
U (m=s)
Ce (kg=kg)
Deff 10 11 (m2=s)
RMSE
0.15
0.30
0.60
0.15
0.30
0.30
0.60
0.60
0.15
0.30
0.60
1.6
1.6
1.6
1.6
1.6
1.2
1.6
1.2
1.6
1.6
1.6
0.042
0.042
0.042
0.029
0.029
0.029
0.029
0.029
0.011
0.011
0.011
9.6
6.8
5.7
11
8.4
7.9
6.5
6.0
14
12.5
9.2
2.14
4.01
2.04
1.20
3.37
4.19
4.25
5.12
3.64
3.12
2.97
reduces the rate of moisture diffusion from inside solid to the
surface of the solid, resulting in a reduced drying rate. All
three observations are in qualitative agreement with most
of the earlier observations reported in the literature.[7,14,26,27]
However, Topuz et al.[14] reported a reduction in drying rate
with increase in flow rate of the heating medium, which was
attributed to poor contact between the solid and gas phase,
due to spouting of the bed at higher flow rate.
The experimental drying data were converted to dimensionless moisture ratio, MR ¼ C Ce =Ci Ce , for the
sake of comparison with the various models. The list of
simple exponential time decay models, popularly known
as the Newton model, the Page model, the Henderson
and Pabis model, the approximation of diffusion model,
the two term exponential model, as listed in Table 4, were
compared with the experimental data. The experimental
drying rates were fitted with various model equations, by
minimizing the root mean square error (RMSE) between
the experimental drying rate and the model equation. The
RMSE is defined as
"
#0:5
n
1X
2
RMSE ¼
ðMRpre;i MRexp;i Þ
100 ð1Þ
N i¼1
The evaluated model parameters along with the RMSE
values are listed in Table 2. It can be seen from Table 2 that
among all the models, the most simple among all, the Page
model is found to match experimental data very closely,
with the RMSE error less than 2.5%. The standard deviation between the experimental data and the model prediction using the page model parameters is less than 6%.
Although three parameters are used in approximate diffusion model, the RMSE values are much higher than the
Page model. The model parameters can be utilized to estimate the drying time as well as for designing and scale up
of the drying process.
It is also attempted to model the experimental data
with a fundamental diffusion equation for moisture distribution within the solid particle with appropriate boundary conditions. The model assumes that the moisture
diffuses from inside the particle to the surface of the particle and evaporates at the surface and that all the particles are uniform in size and spherical in shape. The
fluidized beds are perfectly mixed beds, and the solids
at any point in the bed are exposed to same drying conditions. The general form of the diffusion equation known
as Fick’s diffusion equation is
"
#
dC
d2 C 2 dC
¼ Deff
þ
dt
dr2
r dr
ð2Þ
the boundary conditions are
FIG. 1. Effect of temperature of the heating medium (U: 1.6 m/s,
W: 0.3 kg, ^ T: 60C, ~ T: 80C, & T: 100C).
1687
DRYING OF RAGI IN A FLUIDIZED BED
FIG. 2. Effect of temperature of the heating medium (U: 1.6 m/s,
W: 0.6 kg, ^ T: 60C, & T: 80C, ~ T: 100C).
at t ¼ 0;
at t > 0;
at t > 0;
r ¼ Rs ;
0 < r < Rs ;
FIG. 4. Effect of solids holdup (T: 80C, U: 1.6 m/s, ~ W: 0.60 kg,
^ W: 0.30 kg, & W: 0.15 kg).
where bn are the roots of the equation
C ¼ Ci
dC=dr ¼ 0
bn cot bn þ Bim 1 ¼ 0
Deff ðdC=drÞ ¼ KðCsj Cbe Þ
The mass Biot number (Bim) is defined as K Rs=Deff and
the mass transfer coefficient (K) is calculated based on the
equation due to Richardson and Szekely[29] as given
below:
r ¼ 0;
where Csj is the moisture concentration just within the
sphere and Cbe is the concentration required to maintain
equilibrium with the surrounding atmosphere. Analytical
solution to Eq. (2) for the above boundary conditions
was provided by Crank[28] as given below:
1
2
C Ce X
6Bim
expðb2n Deff t=R2s Þ
¼
Ci Ce n¼1 b2n ðb2n þ Bim ðBim 1ÞÞ
ð3Þ
FIG. 3. Effect of flow rate of the heating medium (T: 80C, W: 0.6 kg,
. U: 1.6 m/s, ~ U: 1.2 m/s).
Sh ¼
Kdp
0:374 Re1:16 for 0:1 < Re < 15
¼
2:01 Re0:5 for 15 < Re < 250
D
ð4Þ
ð5Þ
Sherwood number is the ratio of external mass transfer
resistance to the molecular diffusivity, while Biot number
is the ratio of external mass transfer resistance to the
overall mass transfer resistance.
The evaluated effective diffusivities are reported in Table 3
along with the RMSE values. The effective diffusivity is
found to significantly increase with increase in temperature
of the heating medium, while a marginal increase is registered
with increase in the flow rate of the heating medium. Since
the effect of flow rate on effective diffusivity being marginal,
with significant RMSE values, statistically the optimized
effective diffusivity will have an overlapping range, varying
with the degree of confidence. Although the variations are
statistically not significant, the authors would like to emphasize that the air flow rate contributes to a marginal increase in
the drying rate and similar observations have been reported
in the literature. The increase or decrease in effective diffusivity coefficient is according to the increase or decrease in drying rate. An increase in the solids holdup is found to decrease
the effective diffusivity coefficient. The increase in drying rate
with flow rate and decreased solids holdup has been attributed to the increase in effective bed temperature. The effective
diffusivity is found to vary within 5.7 to 14 1011 m2=s with
RMSE less than 5%. Although the errors are higher, these
kinetic parameters are very essential in the design and scale
1688
SRINIVASAKANNAN AND BALASUBRAMANIAM
TABLE 4
Characteristics of the material and the range of experimental parameters covered in the
present study
Name of material
Shape of material
Size, dp 103 (m)
Particle density (kg=m3)
Minimum fluidization velocity, Umf (m=s)
Terminal velocity, Ut (m=s)
Temperature of fluidizing air (C)
Fluidizing air velocity (m=s)
Solid holdup (kg)
up of drying process with certain order of magnitude. Uckan
and Ulku[24] have reported an effective diffusivity of 2.1 to
3.9 1011 m2=s for drying of corn in fluidized bed and
Kundu et al.[23], have summarized the effective diffusion
coefficient estimated for different types of grains using a
modified Fick’s diffusion equation applied mostly to stationary beds reported a diffusion coefficient of 11 to
31 1011 m2=s for corn; for wheat, 5.5 to 15 1011 m2=s,
and for parboiled rice, 4.1 to 13 1011 m2=s. The estimated
effective diffusion coefficient in the present study is on the
same order of magnitude reported in the literature.
Although the simple models could closely match the
experimental data much better than the complex model,
they are more empirical in nature and lack scientific background, restricting their applicability to within the experimental range covered in the present study. However, the
fundamental models, although they have a higher error
rate, can be extended even beyond the experimental range
in the present study with a certain degree of confidence.
CONCLUSION
The drying characteristics of ragi, one of the popular
cereal crops in India and Srilanka, have been assessed in
a fluidized bed dryer with respect to the various operating
variables. The drying rate was found to increase significantly with increase in temperature and marginally with
flow rate of the heating medium, and to decrease with
increase in solids holdup. The duration of the constant rate
period was found to be insignificant, considering the total
duration of drying and the entire drying period was considered to follow falling rate period. The kinetics of drying
was tested with various simple exponential decay models
and the Page model was found to match the experimental
drying rate closely with the RMSE value less than 2.5%.
The experimental data were also modeled using more fundamental Fick’s diffusion equation and the effective diffusivity
coefficient was estimated to be within 5.7 to 14 1011 m2=s
for the range of experimental data covered in the present
study with RMSE less than 5%. The estimated effective
Ragi (Eleusine corocana)
Spherical
1.48
1200
0.47
6.9
60, 80, 100
1.2, 1.6
0.15, 0.30, 0.60
diffusion coefficient is compared with the literature reported
effective diffusion coefficient for other grains and found to be
within the same order of magnitude.
NOMENCLATURE
Bim Biot number (K Rs=Deff)
C
Moisture content of ragi grain at any time (kg of
moisture=kg of dry solid)
Ce
Equilibrium moisture content of ragi grain (kg of
moisture=kg of solid)
Ci
Initial moisture content of ragi grain (kg of moisture=kg of dry solid)
D
Molecular diffusivity of moisture in air (m2=s)
Deff Effective diffusion coefficient (m2=s)
dp
Particle diameter (m)
K
Mass transfer coefficient across particle surface
(m=s)
e
MR Moisture ratio CCC
i Ce
Re
Rs
r
Sh
T
t
U
W
Reynolds number (dpUq=m)
Particle radius (m)
Radial coordinate (m)
Sherwood number (K dp=D)
Temperature of heating medium (C)
Time (s)
Superficial velocity of heating medium (m=s)
Solids holdup (kg)
Greek Symbols
l
Viscosity of air (kg=ms)
q
Density of air (kg=m3)
REFERENCES
1. Bogdan, A.V. Tropical Pasture and Fodder Plants; Longman: London,
1977.
2. Strumillo, C.; Kudra, T. Drying: Principles, Applications and Design;
Gordon and Breach: New York, 1986.
3. Syromyatnikov, N.I.; Vasanova, P.K.; Shimanskii, D.N. Heat and
Mass Transfer in Fluidised Bed; Khimiya: Moscow, 1967.
4. Kunni, D.; Levenspiel, O. Fluidization Engineering; Wiley: New York,
1969.
DRYING OF RAGI IN A FLUIDIZED BED
5. Anantharaman, N.; Ibrahim, S.H. Fluidised bed drying of pulses and
cereals. In Recent Advances in Particulate Science and Technology,
Ibraham, S. H., Ed.; Madras, 1982.
6. Chandran, A.N.; Subbarao, S.; Varma, Y.B.G. Fluidised bed drying
of solids. AIChE Journal 1990, 36 (1), 29–38.
7. Thomas, P.P. Drying of solids in beach and continuous fluidized beds,
Ph.D thesis, Indian Institute of Technology, Madras, 1994.
8. Hoebink, J.H.B.J.; Rietema, K. Drying of granular solids in a fluidised bed I. Chemical Engineering Science 1980, 35, 2135.
9. Hoebink, J.H.B.J.; Rietema, K. Drying of granular solids in a fluidised bed II. Chemical Engineering Science 1980, 35, 2257.
10. Alebregtse, J.B. Fluidised bed drying: A mathematical model for
hydrodynamics and mass transfer. In Heat and Mass Transfer in Fixed
and Fluidised Bed; Van Swaajj, W.P.M., Afgan, N.H., Eds.; Hemisphere Publishing Corp.: New York, 1986; 511.
11. Palancz, B.A. Mathematical model for continuous fluidised bed drying. Chemical Engineering Science 1983, 38 (7), 1045.
12. Parti, M. Evaluation of selected mathematical model for grain drying.
In Drying 91; Mujumdar, A.S., Filkova, I., Eds.; Elsevier: Amsterdam,
1991; 369.
13. Kafarov, V.V.; Dorokhov, I.N. Modeling and optimisation of drying
process. International Chemical Engineering 1992, 32 (3), 475.
14. Topuz, A.; Gur, M.; Gul, M.Z. An experimental and numerical study
of fluidized bed drying of hazelnut. Applied Thermal Engineering
2004, 24, 1534–1547.
15. Keey, R.B. Drying of Loose and Particulate Materials; Hemisphere
Publishing Corporation: New York, 1991.
16. Mujumdar, A.S. Handbook of Industrial drying; Marcel Dekker:
New York, 1987.
17. Diamante, L.M.; Munro, P.A. Mathematical modeling of the thin
layer solar drying of sweet potato slices. Solar Energy 1993, 51, 271–276.
1689
18. Zhang, Q.; Litchfield, J.B. An optimization of intermittent corn drying in a laboratory scale thin layer dryer. Drying Technology 1991,
9, 383–395.
19. Henderson, S.M. Progress in developing the thin layer drying
equation. Transactions of the ASAE 1974, 17, 1167–1172.
20. Yaldiz, O.; Ertekin, C.; Uzun, H.I. Mathematical modeling of thin
layer solar drying of sultana grapes. Energy 2001, 26, 457–465.
21. Sharaf-Eldeen, Y.I.; Blaisdell, J.L.; Hamdy, M.Y. A model for ear
corn drying. Transactions of the ASME 1980, 23, 1261–1271.
22. Hajidavalloo, E.; Hamdullahpur, F. Mathematical modeling of simultaneous heat and mass transfer in fluidized bed drying of large particles. Transaction of the CSME, 1999, 23, 129–145.
23. Kundu, K.M.; Das, R.; Datta, A.B.; Chatterjee, P.K. On analysis of
drying process. Drying Technology 2005, 23, 1093–1105.
24. Ukan, G.; Ulku, S. Drying of corn grains in batch fluidized bed. In
Drying of Solids; Mujumdar, A.S., Ed.; Wiley Eastern Limited: New
Delhi, 1986; 91–96.
25. Feng, H. Analysis of microwave assisted fluidized bed drying of particulate product with simplified heat and mass transfer model. International Communications in Heat and Mass Transfer 2002, 29 (8),
1021–1028.
26. Syahrul, S.; Hamdullahpur, F.; Dicer, I. Energy analysis of fluidized
bed drying of moist particles. Energy, an International Journal
2002, 2, 87–98.
27. Kudras, T.; Efremov, G.I. A quasi-stationary approach to drying
kinetics in fluidized particulate materials. Drying Technology 2003,
21 (6), 1077–1090.
28. Crank, J. The Mathematics of Diffusion; Oxford University Press:
Oxford, 1975.
29. Richardson, J.F.; Szekely, J. Mass transfer in a fluidized bed. Transactions of the Institution of Chemical Engineering 1961, 39, 212–217.