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Modeling characterization and evaluation of efficiency and drying indices for microwave drying of Zingiber officianale and Curcuma mangga.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2011; 6: 912–920
Published online 16 July 2010 in Wiley Online Library
(wileyonlinelibrary.com) DOI:10.1002/apj.484
Research article
Modeling, characterization, and evaluation of efficiency
and drying indices for microwave drying of Zingiber
officianale and Curcuma mangga
Mahesh Ganesapillai,1 Lima Rose Miranda,1 Tejesh Reddy,2 Micheal Bruno2 and Aruna Singh3 *
1
Chemical Engineering Department, A. C. College of Technology, Anna University, Sardar Patel Road, Chennai 600025, India
Department of Biotechnology, Sathyabama University, I.T. Express Highway, Chennai 600119, India
3
Department of Food Technology, Laximinarayan Institute of Technology, RTM Nagpur University, Nagpur 440033, India
2
Received 24 January 2010; Revised 7 June 2010; Accepted 7 June 2010
ABSTRACT: Methods for efficiently drying agricultural products are an ever-increasing demand. Due to its rapid and
thorough dehydrating ability, microwave techniques were used to evaluate the thin-layer drying kinetics of organic
ginger and mango ginger. Microwave drying characteristics, efficiency and indices determined with respect to sample
thickness, microwave output power and sample load revealed higher power (300 W), lesser thickness (0.001 m) and load
(25 g), increased drying rates and reduced drying time. Effective diffusivity values were found within the range reported
in literatures (9.17 × 10−11 and 11.6 × 10−11 m2 s−1 ). Scanning electron microscope (SEM) and energy-dispersive
X-ray (EDX) images revealed that the surface morphology and the elemental composition gradually degraded during
drying. The ability of eight different thin-layer mathematical models was evaluated for representing the experimental
drying profiles. Among the eight new models derived from the basic diffusion model, statistical analysis inferred that
the modified diffusion model no. 4 could predict most accurately changes in drying behavior of organic ginger and
mango ginger rhizomes for all drying conditions applied.  2010 Curtin University of Technology and John Wiley &
Sons, Ltd.
KEYWORDS: microwave drying; mango ginger; rhizomes; surface morphology; empirical models; diffusion
INTRODUCTION
Drying is perhaps the oldest, most common simultaneous heat and mass transfer operation in which
the water activity of the material is lowered by the
removal of water to a specific level at which microbial spoilage and deteriorative chemical reactions are
greatly minimized.[1] However, it enhances substantial
reduction in weight and volume, minimizing packing,
storage and transportation costs, and enables storability of the product under ambient temperatures. Traditional techniques of drying agricultural feedstock like
rhizomes are time-consuming and energy-intensive as
they depend on heat conduction. Moreover, the high
temperature used can destroy, denature and also induce
some aerobic reaction, which is often detrimental to
the quality of dried product.[2] Microwave heating is
an excellent prospect to increase the rate of evaporation, where regions of higher moisture content within
*Correspondence to: Aruna Singh, Department of Food Technology,
Laxminarayan Institute of Technology, RTM Nagpur University,
Nagpur 440033, India. E-mail: arunapcs@gmail.com
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Curtin University is a trademark of Curtin University of Technology
the material will absorb more microwave energy and
heat generated throughout the material, leading to faster
heating rates and shorter processing times compared
to conventional heating, where heat is usually transferred from the surface to the interior. Other advantages
include space savings and energy efficiency, because
most of the electromagnetic energy was converted into
heat.[3]
In order to design and evaluate such new microwave
dehydration techniques, mathematical modeling of drying behavior of rhizomes in these systems is necessary. However, a number of complex theoretical models
have been developed in the recent past to describe
these phenomena, and both design and process engineers involved in industrial drying operations clearly
need simple, but accurate, analytical tools to conduct
design analysis and relevant calculations. Availability
of such models and correlations, verified by experimental data, will enable designers and operators to provide
the optimum solution to various aspects of drying operations (energy use, operating conditions and process
control), without undertaking actual experimental trials
on the system itself. There has been extensive research
Asia-Pacific Journal of Chemical Engineering
MICROWAVE DRYING CHARACTERIZATION OF GINGER AND MANGO GINGER
into microwave drying, examining a broad spectrum of
fruits and vegetables including apples, green peas, cabbage, banana, tomato, brocolli, potato, carrots, onion
and garlic.[4 – 10] Despite those investigations, to the best
of our knowledge, no data currently exist in terms of
drying kinetics, drying efficiency and drying indices for
rhizomes undergoing microwave drying.
The objective of the research were 1) to study the
microwave drying characteristics and compare the two
species of organic rhizomes, ginger and mango ginger; 2) to calculate the effective diffusivity coefficient,
activation energy, specific energy consumption, drying
efficiency and rehydration ratio (RR) for the microwave
dehydrated rhizome samples and 3) to study the applicability of several thin-layer models selected from the
literature to the thin-layer drying of rhizomes and to fit
drying data into the most suitable models by appropriate
statistical analyses procedures.
MATERIALS AND METHODS
Materials
Organic ginger (Zingiber officianale) and mango ginger
(Curcuma mangga) rhizomes used were collected from
a local super market in Chennai, India, and were stored
at 4 ± 0.5 ◦ C, before experimentation. The samples
were thoroughly washed and peeled to remove skin and
were cut into dimensions of 0.035 × 0.02 m (length
× breadth) using a vegetable slicer. At least ten
measurements of the thickness were made at different
points with a dial micrometer; only slices that fell within
a 5% range of the average thickness were used. The
initial moisture content of the specimens determined by
vacuum oven method was 94.2 and 96.1% (db) for the
organic ginger and mango ginger, respectively.[11]
Drying equipment and procedure
The drying experiments were conducted using a programmable, domestic microwave oven, Model
C–103FL (Samsung Electronic Instrument Co. Ltd.),
with technical features of 230 V ≈ 50 Hz AC and a frequency of 2450 MHz (a wavelength of 12.24 cm). The
microwave oven has the capability of operating at six
different microwave output powers, 100, 180, 300, 450,
600 and 900 W. The area on which microwave drying
was carried out was 336 × 346 × 222 mm (W × D ×
H ) in size and consisted of a rotating glass plate of
300 mm diameter at the base of the oven. The adjustment of microwave output power and processing time
was performed with the aid of a digital control facility
located in the microwave oven. The power produced by
the oven in microwave function was continuous. The
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
fresh specimens were spread at middle of the turntable
in microwave cavity and the oven was switched on.
Microwave drying continued for a desired period with
constant power output. The mass change of specimen
during the drying process was measured online using
an electronic balance. The experiments were conducted
individually for sample thickness of 0.001, 0.002 and
0003 m, sample load of 25, 50, 75 and 100 g, with
microwave output power of 100, 180 and 300 W, with
ginger and mango ginger samples.
Effective moisture diffusivity (Deff )
In almost all the research, quantitative analysis of
dehydration characteristics is typically realized based
on the effective diffusion coefficient. The effective
moisture diffusivity as defined by Fick’s second law
describes the movement of moisture within the solid
solution, established on the basis of several simplifying
assumption that are widely adopted in drying research
as expressed in Eqn (1).[12] These assumptions include
uniform initial moisture content, constant directional
diffusivity, mass transfer that is symmetric with respect
to the center, negligible external resistance to heat and
mass transfer and more rapid heat transfer than mass
transfer.
δX
= Deff ∇ 2 X
(1)
δt
For moisture diffusion through a thin layer, the above
equation can be modified as suggested by Saravacos[13]
as
8
π 2 Deff
X
t
(2)
= 2 exp −
MR =
X0
π
L2
2
X
8
π Deff
ln(MR) = ln
= ln
−
t (3)
X0
π2
L2
where X is the moisture content at time t (kg kg−1 , dry
solid), MR the moisture ratio, X0 the initial moisture
content (kg kg−1 , dry solid) and L the half thickness of
specimen (m).
Activation energy coefficient
The Arrhenius type of equation was used in a tailored
form to illustrate the relationship between the diffusivity
coefficient and the ratio of the microwave output power
to sample thickness instead of the temperature, as the
temperature within the sample is not a measurable variable in the standard microwave oven. The dependency
of Deff on the ratio of microwave output power (P ) to
sample thickness (q) as suggested by Dadali et al .[14]
Asia-Pac. J. Chem. Eng. 2011; 6: 912–920
DOI: 10.1002/apj
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M. GANESAPILLAI et al.
Asia-Pacific Journal of Chemical Engineering
(Eqn 4) could be brought down to a straight-line form
as Eqn (5)
−Ea q
= D0 exp
P
q = ln D0 − Ea
P
Deff
ln Deff
(4)
(5)
where D0 represents the pre-exponential factor (m2 s−1 )
and Ea the activation energy (W m−1 ).
SEM and energy-dispersive X-ray microanalysis
The structure of the dehydrated samples was examined using a scanning electron microscope (SEM; JEOL
JSM-5800). Thin slices of about 0.001 m thick cut from
the dried samples were fixed on the SEM stub which
was subsequently coated with gold in order to provide
a reflective surface for the electron beam. Gold coating
was carried out in a sputter coater (BIO-RAD E-5200)
under low vacuum in the presence of inert gas (Argon).
The coated samples were photographed at an accelerating voltage of 15 kV. The inspected location of the
rhizomes was between the epidermal layer and the vascular bundle. The elemental composition of the samples
was examined using an energy-dispersive X-ray (EDX)
micro-analyzer (Thermo Scientific NORAN System 7
model). To obtain information about the sample elemental composition, the characteristic spectrum of X-rays
emitted by the specimen was used after excitation by
high-energy electrons. The samples were examined for
a live time of 100 s, at a take-off angle of 35.0◦ .
Efficiency indices
Effect of material thickness on the energy efficiency
of microwave drying at 300 W microwave output
power was evaluated by two different efficiency indices:
microwave drying efficiency (%) and specific energy
consumption (MJ kg−1 ) [H2 O]. The efficiency indices
of ginger and mango ginger samples of 0.001–0.003 m
thickness were determined from the experimental data.
Specific energy consumption (Qs )
The drying of food material, a process of simultaneous
heat and mass transfer, represents an energy-intensive
operation of some industrial significance. The Qs for
each drying condition was estimated considering the
drying time involved and energy utilization by the
various components of the microwave dryer, expressed
in terms of MJ kg−1 of water removed, and it is used
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
as one of the factors in the optimization of process
parameters:
ton P × 10−6
(6)
Qs =
mw
where, ton represents the total drying time (s), P is the
microwave output power (W) and mw is the mass of
evaporated water (kg).
Microwave drying efficiency (η)
The microwave drying efficiency (Eqn 7) was calculated as the ratio of heat energy utilized for evaporating
water from the specimen to the heat supplied by the
microwave oven. Here λw represents the latent heat
of vaporization of water at the evaporating temperature (100 ◦ C), taken as 2257 kJ kg−1 as suggested by
Hayes.[15]
(mw )(λw )
(100)
(7)
ηd =
(P ton )
Rehydration ratio
After dehydration, samples were subjected to rehydration trials to check their capability to rehydrate in distilled water. The rehydration ability, as determined by
the RR, depends on material property and drying conditions. The rehydration parameters were determined
according to USDA (1944) as in the following equation.
RR =
WR
Wd
(8)
where WR is the drained weight of rehydrated sample
and Wd is the weight of dehydrated sample.[16]
Empirical modeling
Effectively modeling the drying behavior is important
for the investigation of drying characteristics. In this
study, the microwave experimental drying data at different process parameters were fitted to Page, Henderson,
Logarithmic, Wang and Singh, Diffusion, Verma, Two
term exponential and Midilli[17 – 21] and semi-empirical
models. These models were derived by simplifying the
general series solution of Fick’s second law and considering a direct relationship between the average moisture
content and the drying time. The constants and coefficients of these equations are further described with
various types of expressions like Arrhenius, logarithmic, linear, exponential and power type in terms of
temperature.[22] As the temperature inside the chamber
directly depends on the power input to the system, all
Asia-Pac. J. Chem. Eng. 2011; 6: 912–920
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
MICROWAVE DRYING CHARACTERIZATION OF GINGER AND MANGO GINGER
the expressions were derived in terms of power in the
current research.
A suitable mathematical model to represent the effect
of power on the constants and coefficients was investigated using multiple combinations of different equations
using Arrhenius and logarithmic type expressions.[23]
All nine models shown in Table 2 can be derived into
m n number of new models, where n is the total number of constants and coefficients in the model and m is
the number of combination equations. Fifty-eight new
equations were derived as detailed in Table 3 (shown
only for diffusion equation).[24] Regression analysis was
used to determine the model constants of all basic and
derived equations. Subsequently, the best model was
selected based on the most commonly used statistical
parameters namely coefficient of determination (R 2 ),
root mean square error (RMSE), reduced chi-square
(χ 2 ) and t-value.
efficiency, which may be due to rapid movement of
water at higher microwave output power, lower sample
thickness and sample load. The Deff values obtained
from this study were within the general range of 10−11
to 10−9 m2 s−1 for food materials.[26]
RESULTS AND DISCUSSION
SEM and EDX microanalysis
Effective moisture diffusivity
The SEM images reveal that the microwave-dried samples have honey comb morphology after dehydration.
The surface morphology of organic ginger has gradually degraded from semi-continuous intermittent globular pattern to a continuous undifferentiated morphology
(Fig. 3). This structural deformation may be due to
higher diffusion rate enhanced by greater microwave
power. Compared to 100 and 180 W, the presence
of open structures was higher when the sample was
exposed to 300 W, which may be due to some tissue
expansion from internal water vapor during dehydration. Whereas in organic mango ginger, the presence
of starch granules as indicated by elliptical shapes was
The Deff was calculated using the methods of slopes,
where the logarithm of MR values was plotted against
drying time (t) for various sample thickness, sample
load and microwave output power.[25] The Deff values
ranged from 9.17 × 10−11 to 7.86 × 10−11 m2 s−1 for
ginger samples, whereas for mango ginger it varied
from 11.6 × 10−11 to 9.46 × 10−11 m2 s−1 for samples
of 0.001–0.003 m thickness (Fig. 1). During the initial
stage of drying, the values of Deff increased greatly with
decrease in sample thickness and load and increase in
microwave output power, indicating better mass transfer
Activation coefficient
The activation energies involved in microwave drying
of rhizome specimens under different drying conditions
were estimated from the slopes of the curve plotted
according to Eqn (5), which was 23.19 and 30.59
(W m−1 ), while the pre-exponential factor D0 was
estimated to be 9.96 × 10−11 and 12.7 × 10−11 m2 s−1 .
The data more accurately fitted to Eqn (5), with a
highest R 2 of 0.999 and 0.991 for ginger and mango
ginger samples, respectively (Fig. 2).
1.50E-10
ln (Deff)
-22.5
0
y = -1E-08x + 1E-10
R2 = 0.9861
0.006
0.009
0.012
-22.75
L/P (m2 W-1)
1.00E-10
Deff (m2 s-1)
0.003
y = -7E-09x + 1E-10
R2 = 0.9972
5.00E-11
y = -30.59x - 22.781
R2 = 0.9919
-23
-23.25
y = -23.191x - 23.037
R2 = 0.9991
0.00E+00
0
0.001
0.002
Thickness (m)
0.003
0.004
Figure 1. Comparison of Deff for organic rhizomes: ,
organic mango ginger and ◊, organic ginger (microwave
output power: 300 W, thickness: 0.001 m, sample
load: 25 g).
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
-23.5
Figure 2. Comparison of activation energy for organic
rhizomes: , organic mango ginger and ◊, organic ginger
(microwave output power: 300 W, thickness: 0.001 m,
sample load: 25 g).
Asia-Pac. J. Chem. Eng. 2011; 6: 912–920
DOI: 10.1002/apj
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M. GANESAPILLAI et al.
Asia-Pacific Journal of Chemical Engineering
(a)
(b)
Figure 4. Energy-dispersive X-ray spectrum of microwave
dehydrated organic (a) mango ginger and (b) ginger.
traces of chlorine, sodium, bromine and magnesium
around 3.15, 1.25, 0.59 and 0.20% in mango ginger
rhizomes (Fig. 4).
Figure 3. SEM micrographs of microwave dehydrated
(a) organic ginger (inset shows fresh ginger) and (b) organic
mango ginger (inset shows fresh mango ginger) sample.
highly disrupted as the samples underwent drying. Due
to the presence of volatile matter and excess initial
moisture content, the specimens became rigid during
the early stages of dehydration. The tissues split and
ruptured internally forming cracks in the inner structure when the interior dries finally, pulling the tissues apart forming highly porous due to the internal
stresses at higher power (Fig. 3), thus resulting in more
homogeneous texture. The SEM analyzer fitted with an
EDX micro-analyzer allows a quantitative detection and
localization of elements in the rhizome specimens. The
EDX images illustrated the presence of larger amount
of carbon and oxygen; in addition, elements like silicon, calcium and potassium were identified in a range of
2.54, 2.12 and 1.31%, respectively, (compound percentage) in ginger rhizomes (Fig. 4). Whereas for mango
ginger, the presence of oxygen, carbon and sodium were
50.60, 36.01 and 7.46%, respectively. Also, there were
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Specific energy consumption and microwave
drying efficiency
As sample thickness rose from 0.001 to 0.003 m, the
specific energy consumption of ginger rose to 3.2060
from 2.8926 MJ kg−1 for a stipulated microwave output power of 300 W. A similar trend was observed
for organic mango ginger samples at the same process
conditions. However, mango ginger samples showed a
lesser energy consumption while compared with ginger rhizomes, suggesting that high initial moisture content resulted in higher absorption of microwave energy.
The best result with regard to energy consumption was
obtained for 0.001 m sample thickness. The drying
efficiency was about 70.39% for 0.003-m thick ginger samples and showed a rapid increasing tendency
as the sample thickness decreased to 0.001 m with an
efficiency factor of 78.02%. However, for mango ginger samples, the efficiency ranged between 74.59 and
82.94% (Table 1). Conversely, a significant increase
in drying efficiency with increasing initial moisture
content indicated that microwave efficiently absorbed
water, as water is dielectric in nature. As water depleted,
microwave absorption reduced leading to lower efficiency values.[27]
Asia-Pac. J. Chem. Eng. 2011; 6: 912–920
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
MICROWAVE DRYING CHARACTERIZATION OF GINGER AND MANGO GINGER
Table 1. Comparison of efficiency indices and drying indices for organic rhizome specimens at 300 W microwave
output power and 25 g sample load.
Characterization
Sl no
Material
1
Ginger
2
Mango ginger
Sample
thickness (mm)
Specific energy
consumption (MJ kg−1 )
Microwave drying
efficiency (%)
Rehydration
ratio
1
2
3
1
2
3
2.8926
2.9225
3.2060
2.6220
2.7741
3.0256
78.02
77.22
70.39
82.94
81.35
74.59
5.4805
4.9178
4.3734
4.9848
4.8394
4.5352
Rehydration ratio
Table 1, compares the experimental rehydration ratio
obtained for different sample thickness of organic
ginger and mango ginger rhizomes, dried at 300 W
microwave output power. The RR decreased with
increasing sample thickness, suggesting a hardened
structure of the solid material, thereby reducing the
ingress of water molecules. Ginger rhizomes exhibited
a higher RR compared to mango ginger. The higher
rehydration at lower sample thickness (0.001 m) and
higher microwave output power (300 W) attributed to
the development of greater internal stresses during
drying at higher power levels. The quick microwave
energy absorption causes rapid evaporation of water,
creating a flux of rapidly escaping water vapor, which
helps in preventing shrinkage and case hardening, thus
improving the rehydration characteristics.[28]
Empirical modeling
Comparison of all eight drying models yielded diffusion
equation as the best fit to the experimental data for
both ginger and mango ginger rhizomes, with higher
R 2 (0.99958 and 0.99620), lower RMSE (0.00117 and
0.00625), χ 2 values (0.00019 and 0.00962) and t-values
(0.0042 and 0.03129) (Table 2). The constants a, k and
b of the diffusion model for ginger and mango ginger
were found to be 0.3481 and 0.9986, 0.0371 and 0.1302,
and 0.9999 and 1.0001, respectively, in that order.
These constants were independent of the microwave
output power, sample thickness, sample load and drying
time. The other models except that of diffusion do not
account much for the effect of drying variables, which
lead to further modification of basic diffusion model
to the present system by expressing the constants and
coefficients in terms of microwave output power and
drying time through eight different derived diffusion
expressions using multiple combinations of Arrhenius
and logarithmic type equations (Table 3). Among the
eight newly derived diffusion models, Model 4 gave
the highest R 2 value of 0.9995 and 0.9926, and lowest
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
t-values of 0.2615 and 0.5063, for ginger and mango
ginger samples, respectively. Based on the multiple
regression analysis, the acceptable and suggested model
was diffusion model no. 4 for both rhizome specimens,
followed by model no. 6 for ginger and model no. 1 for
mango ginger. Thus, the regression equations of these
parameters against microwave power level of 300 W,
sample thickness of 0.001 m and sample load of 25 g,
for the accepted model are as follows.
For microwave dried organic ginger
MR = 1.3150 + 1.0166 ln
−0.0458
t
P × exp −0.0005 exp
8.314P
+ 1 − (1.3150 + 1.0166 ln P )
−0.0458
exp −0.0005 exp
8.314P
−0.9967
×(−2.1316) × exp
t
8.314
R 2 = 0.9995,
(9)
χ 2 = 0.0135,
t-value = 0.2615,
RMSE = 0.1162
(10)
for microwave-dried organic mango ginger
MR = 1.0130 + 1.2735 ln
−0.9997
P × exp −1.0498 exp
t
8.314P
+ 1 − (1.5815 + 1.2735 ln P )
−0.9997
exp −1.0498 exp
8.314P
−1.0003
×(−0.0535) × exp
t
8.314
R 2 = 0.9926,
(11)
χ 2 = 0.0594,
t-value = 0.5063,
RMSE = 0.0594
(12)
Asia-Pac. J. Chem. Eng. 2011; 6: 912–920
DOI: 10.1002/apj
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M. GANESAPILLAI et al.
Asia-Pacific Journal of Chemical Engineering
Table 2. Results of statistical parameters estimated by regression analyses for organic rhizome specimens of
0.001 m thickness and 25 g sample load.
Microwave output power
100 W
180 W
300 W
Statistical
parameters Ginger Mango ginger Ginger Mango ginger Ginger Mango ginger
Model
Page
MR = exp(−kt n )
Henderson
MR = a exp(−kt)
Logarithmic
MR = a exp(−kt) + c
Wang and Singh
MR = 1 + at + bt 2
Diffusion
MR = a exp(−kt) + (1 − a) exp(−kbt)
Verma
MR = a exp(−kt) + (1 − a) exp(−gt)
Two term exponential
MR = a exp(−kt) + (1 − a) exp(−kat)
Midilli
MR = a exp(−kt n + bt)
R2
RMSE
χ2
t-value
R2
RMSE
χ2
t-value
R2
RMSE
χ2
t-value
R2
RMSE
χ2
t-value
R2
RMSE
χ2
t-value
R2
RMSE
χ2
t-value
R2
RMSE
χ2
t-value
R2
RMSE
χ2
t-value
0.9690
0.1417
0.2321
0.3317
0.9678
0.2644
0.4521
0.5667
0.9663
0.3410
0.6156
0.7579
0.9721
0.1067
0.1093
0.1669
0.9854
0.0065
0.0389
0.0944
0.9704
0.1727
0.1734
0.2461
0.9651
0.3905
0.9431
0.9940
0.9823
0.0908
0.0956
0.1334
0.9672
0.2014
0.2100
1.1094
0.9664
0.2525
0.3229
1.3055
0.9651
0.3435
0.4121
1.6616
0.9697
0.0155
0.0793
0.9155
0.9820
0.0083
0.0251
0.7328
0.9681
0.1609
0.1105
1.0293
0.9648
0.4683
0.6250
1.9685
0.9809
0.0127
0.0223
0.8440
0.9792
0.0966
0.1908
0.1266
0.9781
0.1483
0.3273
0.3294
0.9773
0.2926
0.5114
0.6316
0.9834
0.0298
0.0510
0.0292
0.9921
0.0043
0.0105
0.0098
0.9802
0.0771
0.0679
0.1094
0.9765
0.3688
0.8273
0.9505
0.9903
0.0091
0.0330
0.1104
0.9768
0.1629
0.1409
1.0299
0.9757
0.2349
0.2134
1.0851
0.9745
0.3016
0.4008
1.0889
0.9801
0.0142
0.0311
0.8158
0.9915
0.0081
0.0151
0.5753
0.9784
0.1216
0.0798
0.9306
0.9733
0.4637
1.0155
1.0968
0.9889
0.0166
0.0185
0.4874
0.9889
0.0751
0.1503
0.0251
0.9886
0.1016
0.2139
0.1124
0.9869
0.2662
0.4826
0.3905
0.9916
0.0244
0.0497
0.0241
0.9995
0.0017
0.0001
0.0042
0.9893
0.0613
0.0531
0.0868
0.9867
0.3168
0.8980
0.9481
0.9986
0.0082
0.0237
0.0957
0.9901
0.0976
0.0865
0.9707
0.9884
0.1298
0.1034
1.0468
0.9869
0.2019
0.3039
1.0795
0.9933
0.0126
0.0376
0.5474
0.9962
0.0062
0.0096
0.3129
0.9918
0.0406
0.0699
0.7999
0.9855
0.3962
0.7364
1.0486
0.9951
0.0102
0.0165
0.4474
Table 3. Derived diffusion models for moisture ratio determination of organic rhizome specimens.
Diffusion equation
Arrhenius type
Logarithmic type
Model no.
1
2
3
4
5
6
7
8
MR = a exp(−kt) + (1 − a) exp(−kbt)
a exp(−b/8.314P )
a + b ln(P )
Derived diffusion equations
a exp(−a1 /8.314P ) exp −(k exp(−k1 /8.314P )t) + 1 −
(a exp(−a1 /8.314P )) exp −(k exp(−k1 /8.314P ))(b exp(−b1 /8.314P )t)
a exp(−a1 /8.314P ) exp −(k exp(−k1 /8.314P )t) + 1 −
(a exp(−a1 /8.314P )) exp −(k exp(−k1 /8.314P )(b + b1 (ln P )t)
a exp(−a1 /8.314P ) exp −(k + k1 (ln P )t) + 1 − (a exp(−a1 /8.314P )) exp −(k +
k1 (ln P )b exp(−b1 /8.314P )t
a + a1 (ln P ) exp −(k exp −(k1 /8.314P )t) + 1 − (a +
a1 (ln P ) exp −(k exp(k1 /8.314P )(b exp(−b1 /8.314P ))t
a exp(−a1 /8.314P ) exp −(k + k1 (ln P )t) + 1 − (a exp(−a1 /8.314P )) exp −(k + k1 (ln P ))(b + b1 (ln P )t
a + a1 (ln P ) exp −(k + k1 (ln P )t) + 1 − (a + a1 (ln P )) exp −(k + k1 (ln P ))(b + b1 (ln P )t
a + a1 (ln P ) exp −(k + k1 (ln P ))t + 1 − (a + a1 (ln P )) exp −(k + k1 (ln P ))(b exp(−b1 /8.314P ))t
a + a1 (ln P ) exp −(k exp(−k1 /8.314P ))t + 1 − (a + a1 (ln P )) exp −(k exp(−k1 /8.314P ))(b +
b1 (ln P ))t
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2011; 6: 912–920
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
MICROWAVE DRYING CHARACTERIZATION OF GINGER AND MANGO GINGER
1
MR (Predicted)
0.75
0.5
0.25
0
0
0.25
0.5
MR (Experimental)
0.75
1
Figure 5. Comparison of experimental MR with predicted
MR from the derived diffusion model no. 4 for rhizomes (♦:
organic mango ginger; : organic ginger).
with respect to microwave power were revealed by
SEM images. The sample thickness strongly affected
the moisture diffusivity where the lower sample thickness provided higher values of effective diffusivity of
9.17 × 10−11 and 11.6 × 10−11 m2 s−1 for organic ginger and mango ginger, respectively. In spite of higher
initial moisture content of mango ginger, the efficient
moisture transport within the sample led to lower values of specific energy consumption (2.622 MJ kg−1 )
and higher microwave drying efficiency (82.94%). The
derived diffusion model no. 4 gave a best fit for experimental data of moisture ratio of rhizomes during this
investigation. The models and parameters established
in this study can be applied to food, ayurveda (traditional medicine), cosmetic and pharmaceutical industrial design and serve as an operational guide for the
microwave drying of ginger and mango ginger to produce spices, essential oils and drugs.
NOMENCLATURE
These expressions were used to estimate the moisture
ratio of ginger and mango ginger at any time during the
drying process with an acceptable accuracy.
Model validation
Validation of the established model was made by
comparing the experimental moisture ratio with the
calculated ones in any particular drying run under
certain conditions. The plots of experimental moisture
ratio and predicted moisture ratio by modified diffusion
model no. 4 for organic ginger and organic mango
ginger are shown in Fig. 5. It can be seen that the model
presented a little over- or underestimation in comparison
with the experimental data at different stages of drying
process, but they are all very close to the experimental
data for both organic ginger and mango ginger. The
performance of the derived diffusion model (Eqn (4)),
at 300 W microwave output power, 0.001 m sample
thickness, and 25 g sample load (Fig. 5), gave a higher
R 2 of 0.996 and 0.991 for ginger and mango ginger
specimens, thus indicating the suitability of the derived
model in describing drying behavior of the organic
rhizomes.
CONCLUSIONS
Drying of organic ginger and mango ginger rhizomes
mostly occurred in the falling rate period with higher
drying rates at higher microwave power (300 W), lower
sample thickness of 0.001 m and load of 25 g, respectively. The changes in the surface morphology like
severe tissue shrinkage and collapse during drying
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
a, b, k , n Empirical constants
D0
Pre-exponential factor (m2 s−1 )
Effective moisture diffusivity (m2 s−1 )
Deff
Ea
Activation energy (W m−1 )
L
Half of thickness of specimen (m)
MR
Moisture ratio
Mass of evaporated water (kg)
mw
P
Microwave power output (W)
Qs
Specific energy consumption (MJ kg−1 )
q
Specimen thickness (m)
RMSE
Root mean square error
Coefficient of determination
R2
RR
Rehydration ratio
t
Drying time (s)
Total drying time (s)
ton
Wd
Weight of dehydrated sample (kg)
WR
Drained weight of rehydrated sample (kg)
X
Moisture content at time t (kg kg−1 ), dry
solid
Initial moisture content (kg kg−1 ), dry solid
X0
Greek symbols
ήd
λw
Microwave drying efficiency (%)
Latent heat of vaporization (J kg−1 )
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