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Effective Diffusivity and Evaporative Cooling inConvective
Drying of Food MaterialChandan Kumar a , Graeme J. Millar a &
M. A. Karim aa Science and Engineering Faculty , Queensland
University of Technology , Brisbane ,Queensland , AustraliaAccepted
author version posted online: 31 Aug 2014.Published online: 06 Dec
2014.
To cite this article: Chandan Kumar , Graeme J. Millar & M.
A. Karim (2015) Effective Diffusivity and EvaporativeCooling in
Convective Drying of Food Material, Drying Technology: An
International Journal, 33:2, 227-237,
DOI:10.1080/07373937.2014.947512
To link to this article:
http://dx.doi.org/10.1080/07373937.2014.947512
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Effective Diffusivity and Evaporative Cooling in
ConvectiveDrying of Food Material
Chandan Kumar, Graeme J. Millar, and M. A. KarimScience and
Engineering Faculty, Queensland University of Technology, Brisbane,
Queensland,Australia
This article presents mathematical models to simulate
coupledheat and mass transfer during convective drying of food
materialsusing three different effective diffusivities: shrinkage
dependent, tem-perature dependent, and the average of those two.
Engineering simu-lation software COMSOL Multiphysics was utilized
to simulate themodel in 2D and 3D. The simulation results were
compared withexperimental data. It is found that the
temperature-dependent effec-tive diffusivity model predicts the
moisture content more accurately atthe initial stage of the drying,
whereas the shrinkage-dependent effec-tive diffusivity model is
better for the nal stage of the drying. Themodel with
shrinkage-dependent effective diffusivity shows evaporat-ive
cooling phenomena at the initial stage of drying. This
phenomenonwas investigated and explained. Three-dimensional
temperature andmoisture proles show that even when the surface is
dry, the insideof the sample may still contain a large amount of
moisture. Therefore,the drying process should be dealt with
carefully; otherwise, microbialspoilage may start from the center
of the dried food. A parametricinvestigation was conducted after
validation of the model.
Keywords Effective diffusivity; Evaporative cooling;
Experi-mental investigation; Food drying; Mathematicalmodeling
INTRODUCTION
Food drying is a process that involves removingmoisture in order
to preserve fruits by preventing microbialspoilage. It also reduces
packaging and transport cost byreducing weight and volume. Compared
to other food pres-ervation methods, dried food has the advantage
that it canbe stored at ambient conditions. However, drying is
anenergy-intensive process and accounts for up to 15% ofall
industrial energy usage and the quality of food maydegrade during
the drying process.[13] The objective offood drying is not only to
remove moisture by supplyingheat energy but also to produce quality
food.[4] To reducethis energy consumption and improve product
quality, aphysical understanding of the drying process is
essential.
Mathematical models have been proved useful tounderstand the
physical mechanism, optimize energyefciency, and improve product
quality.[5] Mathematicalmodels can be either empirical or
fundamental models.Empirical expressions are common and relatively
easy touse.[2] Many empirical models for drying have been
developedand applied for different products; for instance,
banana,[6]
apple,[7] rice,[8] carrot,[9] cocoa,[10] etc. Erbay and
Icier[11]
reviewed empirical models for drying and found that the
bestttedmodel is different for different products. However,
theseempirical models are only applicable in the range used to
col-lect the experimental parameters.[12] In addition, they
typi-cally are not able to describe the physics of drying.
Incontrast to empirical relationships, fundamental models
cansatisfactorily capture the physics during drying.[1315]
Funda-mental mathematical modeling is applicable for a wide rangeof
applications and optimization scenarios.[12]
Several fundamental mathematical models have beendeveloped for
food drying. For example, Barati and Esfa-hani[16] developed a food
drying model wherein they con-sidered the material properties to be
constant. However,in reality, during the drying process physical
propertiessuch as diffusion coefcients and dimensional changesoccur
as the extent of drying progresses.[17] Consequently,if these
latter issues are not considered, the model predic-tions may be
erroneous in terms of estimating temperatureand moisture
content.[18] In particular, the diffusioncoefcient can have a
signicant effect on the dryingkinetics.
Calculation of the effective diffusivity is crucial for dry-ing
models because it is the main parameter that controlsthe process
with a higher diffusion coefcient, implyingan increased drying
rate. The diffusion coefcient changesduring drying due to the
effects of sample temperature andmoisture content.[19]
Alternatively, some authors con-sidered effective diffusivity as a
function of shrinkage ormoisture content,[20] whereas others
postulated it astemperature dependent.[21] In the case of a
temperature-dependent effective diffusivity value, the
diffusivityincreases as drying progresses. On the other hand,
effective
Correspondence: M. A. Karim, Science and EngineeringFaculty,
Queensland University of Technology, 2 George Street,Brisbane, QLD
4001, Australia; E-mail: [email protected]
Color versions of one or more of the gures in the article can
befound online at www.tandfonline.com/ldrt.
Drying Technology, 33: 227237, 2015
Copyright # 2015 Taylor & Francis Group, LLCISSN: 0737-3937
print=1532-2300 online
DOI: 10.1080/07373937.2014.947512
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diffusivity decreases with time in the case of shrinkage
ormoisture dependency. This latter behavior is ascribed tothe
diffusion rate decreasing as the moisture gradient drops.However,
Baini and Langrish[22] mentioned that shrinkagealso tends to reduce
the path length for diffusion, whichresults in increased
diffusivity. Consequently, there aretwo opposite effects of
shrinkage on effective diffusivity,which theoretically may cancel
each other out. Silvaet al.[23] analyzed the effect of considering
constant andvariable effective diffusivities in banana drying. They
foundthat the variable effective diffusivity (moisture dependent)
ismore accurate than the constant effective diffusivity in
pre-dicting the drying curve. Some authors[20] considered
effec-tive diffusivity as a function of moisture content,
whereasothers[24] considered it as a function of temperature.
How-ever, there are limited studies comparing the inuence
oftemperature-dependent and moisture-dependent
effectivediffusivity. Recently, Silva et al.[25] considered
effectivediffusivity as a function of both temperature and
moisturetogether (i.e., D f(T, M)), not temperature- or
moisture-dependent diffusivities separately. Therefore, it was
notpossible to compare the impact of considering temperature-and
moisture-dependent effective diffusivities. Moreover,they did not
report the impact of variable diffusivities onmaterial temperature.
A comparison of drying kineticsfor both temperature- and
moisture-dependent effectivediffusivities can play a vital role in
choosing the correcteffective diffusivity for modeling purposes.
Though thereare several modeling studies of food drying, there
arelimited studies that compare the impacts of
temperature-dependent and moisture-dependent effective
diffusivities.
Understanding the exact temperature and moisturedistribution in
food samples is important in food drying.Joardder et al.[26] showed
that the temperature distributionplays a critical role in
determining the quality of driedfood. Similarly, moisture
distribution plays a critical rolein food safety and quality.
Vadivambal and Jayas[27]
showed that despite the fact that the average moisturecontent
was lower than what was considered a safe value,spoilage started
from the higher moisture content area.Therefore, it is crucial to
know the moisture distributionin the sample. Unfortunately, it is
difcult to measuretemperature and moisture distribution inside the
sampleexperimentally, which means that appropriate
modelingapproaches are required to determine the moisture
distri-bution. Mujumdar and Zhonghua[28] argued that
technicalinnovation can be intensied by mathematical modeling,which
can provide better understanding of the dryingprocess. Karim and
Hawlader[20] developed a mathematicalmodel to determine temperature
and moisture changes withtime, but it did not provide the
temperature and moisturedistribution within the sample. Moisture
distribution is akey parameter for evaporation because
evaporationdepends on surface moisture content.
Evaporation plays an important role during drying interms of
heat and mass transfer, with higher evaporationresulting in
enhanced drying rates. During the initial stageof drying, the
surface is almost saturated, which inducesboth higher evaporation
and moisture removal rates. Dueto this higher evaporation rate, the
temperature dropsat this stage for a short period of time.[29,30]
RecentlyGolestani et al.[31] also observed reduced temperature
inthe initial drying phase and they attributed this phenomenonto
the high enthalpy of water evaporation. The temperatureevolution
depends on the heat ux. During drying, tworeverse heat uxes take
place: inward convective heat uxand outward evaporative heat ux.
Again, there are limitedstudies that have investigated the
temperature variation dur-ing the initial stage of convection
drying based on heat ux.
In this context, the aims of this article are threefold: to(1)
develop three drying models based on three effective
dif-fusivities: namely, moisture-dependent, temperature-dependent,
and average effective diffusivities; (2) investigatethe evaporative
cooling phenomena in terms of heat ux;and (3) conduct a parametric
study with validated models.
MODEL DEVELOPMENT
The model developed in this research considered the cyl-indrical
geometry of the food product as shown in Fig. 1.
Governing Equations
Mass transfer equation:
@c
@tr Deffrc uc R; 1
where c is the moisture concentration, t is time, Deff is
theeffective diffusivity, R is the production or consumption
ofmoisture, and u is convective ow, which is neglected inthis
study.
Heat transfer equation:
qcp@T
@t qcpu rT r krT Qe; 2
where T is the temperature at time t, q is the density, Cpis the
specic heat of the material, k is the thermal
FIG. 1. (a) Actual geometry of the sample slice and (b) simplied
2D
axisymmetric model domain.
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conductivity, and Qe is the internal heat source or sink.
Theheat source term is zero for convection drying but
whenelectromagnetic heating such as microwave is involved thenit
should be added to the heat transfer equation.
Initial and Boundary Conditions
Initial Conditions
Initial moisture content;M0 4 kg=kg db
Initial temperature T0 38C
Boundary Conditions
Heat transfer boundary conditions. Both convectionand
evaporation were considered at the open boundaries.Thus, the heat
transfer boundary condition was denedby Eq. (3).
n krT hT Tair T hmq M Me hfg; 3
where hT is the heat transfer coefcient (W=m2=K), hm is
the mass transfer coefcient (m=s), Tair is the drying
airtemperature (C), Me is the equilibrium moisture content(kg=kg,
db), and hfg is the latent heat of evaporation (J=kg).
At symmetry and other boundaries:
n krT 0 4
Mass transfer boundary conditions. At open bound-aries:
n Drc hm cb c ; 5
where cb is the bulk moisture concentration.At symmetry and
other boundaries:
n Drc 0: 6
Variable Thermophysical Properties
In food processing, thermophysical properties play animportant
role in heat and mass transfer simulation.[32] Inthis simulation,
the specic heat and thermal conductivitywere considered as function
of moisture content (Mw) bythe following equations[33]:
Specific heat; Cp 0:811Mw2 24:75Mw 1742 7
Thermal conductivity; K 0:006Mw 0:120: 8
Effective Diffusivity Calculation
In this study, three simulations were performed withthree
different effective diffusivities. The effective diffusiv-ity
formulations are discussed below.
Moisture- or Shrinkage-Dependent Effective Diffusivity
Karim and Hawlader[20] presented the effective
diffusioncoefcient as a function of moisture content for
productsundergoing shrinkage during drying. In this study,
thefollowing equation was used to incorporate the
shrinkage-dependent diffusivity:
DrefDeff
b0b
2; 9
where Dref is the reference effective diffusivity, which
isconstant and calculated by the slope method from theexperimental
value, and b0 and b are the half thickness ofthe material at times
0 and t, respectively.
The thickness ratio was obtained by the
followingequation[34]:
b b0 qw Mwqsqw M0qs
; 10
where qw is the density of water, and qs is the density of
asolid.
Temperature-Dependent Effective Diffusivity
Temperature-dependent diffusivity was obtained froman
Arrhenius-type relationship to the temperature withthe following
equation[18,35]:
Deff D0eEaRgT ; 11
where Ea is the activation energy (kJ=mol), Rg is the univer-sal
gas constant (kJ=mol=K), and D0 is an integrationconstant
(m2=s).
Average Effective Diffusivity
The third model considered the average effective diffu-sivity,
Deff_avg, which is the average of the temperature-and
moisture-dependent effective diffusivities.
Deff avg D0e
EaRgT Dref bb0 2
2: 12
Heat and Mass Transfer Coefficient Calculation
The heat and mass transfer coefcients are calculatedfrom
well-established corelations of Nussel and Sherwoodnumbers for
laminar and turbulent ows over at plates
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as shown in Eqs. (13)(16). These relationships have beenused in
drying by many other researchers[20,31,36,37] andhence justify the
use of these relationships.
The average heat transfer coefcient was calculatedfrom the
Nusselt number (Nu) using Eqs. (13) and (14)for laminar and
turbulent ows, respectively.[38]
Nu hTLk
0:664Re0:5 Pr0:33 13
Nu hTLk
0:0296Re0:5 Pr0:33; 14
where L is the characteristic length, Re is the Reynoldsnumber,
and Pr is the Prandtl number.
Because Fouriers law and Ficks law are similar inmathematical
form, an analogy was used to nd the masstransfer coefcient. The
Nusselt number and Prandtl num-ber were replaced by Sherwood number
(Sh) and Schmidtnumber (Sc), respectively, as in the following
relationships:
Sh hmLD
0:332Re0:5Sc0:33 15
Sh hmLD
0:0296Re0:8Sc0:33: 16
The values of Re, Sc, and Pr were calculated by Eqs. (17),(18),
and (19), respectively.
Re qavLla
17
Sc laqaD
18
Pr Cpalaka
; 19
where qa is the density of air, la is the dynamic viscosity
ofair, v is the drying air velocity, ka is the thermal
conduc-tivity of air, and Cpa is the specic heat of air. The
valuesof these parameters along with their units are presentedin
Table 1.
Simulation Methodology
Simulation was performed by using COMSOL Multy-physics, a nite
elementbased engineering simulation soft-ware. The software
facilitated all steps in the modelingprocess, including dening
geometry, meshing, specifyingphysics, solving, and then visualizing
the results. COMSOLMultiphysics can handle the variable properties,
which area function of the independent variables. Therefore,
thissoftware was very useful in drying simulation where
TABLE 1Input conditions for modeling studies
Properties Value (unit) Reference
Density of banana, q 980 kgm3
[20]
Initial moisture content (db), M 4 kgkg
Measured
Latent heat of evaporation, hfg 2; 358; 600Jkg
[40]
Thermal conductivity of air, kair 0:0287WmK
[40]
Density of water, qw 994:59kgm3
[40]
Dynamic viscosity of air, lair 1.78 104(Pa s) [40]
Specic heat of air, Cpa 1; 005:04J
kgK
[40]
Density of air, qa 1:073kgm3
[40]
Equilibrium moisture content, Me 0:29kgkg
[41]
Specic heat of water, Cpw 4; 184Jkg
[40]
Diffusion coefcient, D 2:41 1010 m2s
[20]
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material properties changed with temperature and
moisturecontent. The simulation methodology and
implementationstrategy followed in this projectis shown in Fig. 2.
Bananawas taken as a sample for this study.
Input Properties
The physical properties of banana and other input para-temers
used in the simulation program are listed in Table 1.
DRYING EXPERIMENTS
Drying tests were performed based on the AmericanSociety of
Agricultural and Biological Engineers (ASABES448.1) standard. The
procedures for ASABE standardare as follows:
Tests should be conducted after drying equipmenthas reached
steady-state conditions. A steady stateis achieved when the
approaching air stream tem-perature variation about the set point
is less thanor equal to 1C.
The sample should be clean and representative inparticle size.
It should be free from broken,cracked, weathered, and immature
particles andother materials that are not inherently part ofthe
product. The sample should be a fresh onehaving its natural
moisture content.
The particles in the thin layer should be exposedfully to the
air stream.
Air velocity approaching the product should be0.3m=s or
more.
Nearly continuous recording of the sample massloss during drying
is required. The correspondingrecording of material temperature
(surface orinternal) is optional but preferred.
The experiment should continue until the moistureratio, MR,
equals 0.05. Me should be determinedexperimentally or numerically
from establishedequations.
A tunnel-type drying chamber was used in this experi-ment. The
dryer is equipped with a heater, a blower fan,and two dampers. Two
dampers were used to facilitateair recirculation and fresh air
intake. Both closed-loopand open-loop tests were possible by
adjusting the dam-pers. A temperature controller and blower speed
controllerwere used to maintain constant drying air temperature
andair velocity.
The weight of the sample was measured using a loadcell, which
was calibrated using standard weights. Air velo-city has a
considerable effect on the load cell reading anddifferent
calibration curves were prepared for different owvelocities through
the dryer. The load cell was calibratedafter installation in the
dryer. Air ow rate was calculatedby measuring the air velocity at
the entrance of the dryingsection. A calibrated hot wire anemometer
measured theair velocity. A T-type thermocouple and humidity
trans-mitter were used to measure the temperature and
relativehumidity. All of the sensors were connected to a data
log-ger to store the information.
For experimental investigation, ripe bananas (Musaacuminate) of
nearly the same size were used for drying.First, the bananas were
peeled and sliced 4mm thick withdiameter of about 36mm. Initial
moisture content wasabout 4 kg=kg (db) and the nal moisture content
wasbetween 0.22 to 0.25 kg=kg (db); that is, the moisture ratiowas
0.055 to 0.062. Then the slices were put on trays madeof plastic
net. Plastic net was used to reduce conductionheat transfer because
this effect was neglected in the model.The plastic tray was put
into the dryer after reachingsteady-state condition. Each run
included approximately600 g of material. Following each drying
test, the samplewas heated at 100C for at least 24 h to obtain the
bone-drymass.
UNCERTAINTY ANALYSIS
Uncertainty analysis of the experiments was doneaccording to
Moffat.[39] If the result R of an experiment
FIG. 2. Simulation strategy in COMSOL Multiphysics.
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is calculated from a set of independent variables so thatRR(X1,
X2, X3, . . ., XN), then the overall uncertaintycan be calculated
using the following expression:
dR XNi1
@R
@Xi dXi
2( )1=220
and the relative uncertainty can be expressed as follows:
e dRR
XNi1
1
R @R@Xi
dXi 2( )1=2
: 21
Uncertainty Analysis of Temperature
The temperature was directly obtained from the cali-brated
thermocouple and the accuracy was within theAmerican Society of
Heating, Refrigerating and Air Con-ditioning Engineers recommended
range, which is0.5C. Therefore, the uncertainty of the
temperaturewould be
T Tmeasured 0:5: 22
Uncertainty Analysis of Moisture Content
The dry basis moisture content ratio of the weight ofmoisture,
Wm, to that of bone-dry weight, Wd, of the sam-ple was calculated
from the following equation:
M WmWd
W WdWd
: 23
Therefore, dM @M@W dW @M@Wd dWd dWWd W dWdWd
2 and
dMM dWWWd
W dWdWWd Wd.
Now the relative uncertainty associated with themeasurement of
the moisture content of the sample canbe expressed:
em dWW Wd
2 W dWd
W Wd Wd
2( )1=2: 24
The present work considers the following value of thebanana
sample to be dried in the drying chamber:W 600 g and Wd 120 g.
Because these two values areobtained using the same load cell, and
as per the manufac-turers specication, the percentage error of the
load cell is0.1%; therefore, dW dWd 0.0001. Substituting all ofthe
values in Eq. (24), the relative uncertainty for moisturecontent,
em, is obtained, and the value is found to be1.06%.
RESULTS AND DISCUSSION
Validation of the model was done by comparing themoisture and
temperature proles obtained from experi-ment and simulation. Figure
3 represents a comparisonof the moisture prole obtained by
experiments andmodels considering three different effective
diffusivities.Results show that simulated moisture content with
FIG. 3. Moisture prole obtained for experimental and simulation
with shrinkage and temperature-dependent diffusivities (T 60C and V
0.7m=s).
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temperature-dependent diffusivity closely agreed with
theexperimental moisture data in the initial stage of the
dryingprocess. On the other hand, the shrinkage-dependent
diffu-sivity model exhibited a faster drying rate in the
initialstage but followed experimental data closely in the nalstage
of drying. This higher drying rate during the initialstage can be
attributed to the higher diffusion coefcientin that stage.
Moisture-dependent effective diffusivity ishigher in the initial
stage, as can be seen from Eqs. (9)and (10). These two equations
show that initially the diffu-sivity value was greater at higher
moisture content and thendecreased with moisture content. Golestani
et al.[31] alsofound a higher drying rate compared to the
experimentalresults for both models obtained from two effective
diffu-sivities with and without shrinkage. Therefore, a morecomplex
and physics-based formulation is necessary to cal-culate effective
diffusivity and predict the moisture contentmore accurately.
However, consideration of effective diffu-sivity as an average of
those two effective diffusivities pro-vided a better match with
experimental data. A similarresult was found by Golestani et
al.[31]
The temperature prole of the material is shown in Fig. 4for a
drying air temperature of 60C and velocity of 0.5m=s.The predicted
temperatures agreed reasonably well with theexperimental data.
However, interestingly, for theshrinkage-dependent effective
diffusivity model there wasan drop in temperature at the beginning
of the drying pro-cess. This was probably due to the evaporative
cooling of
the product. In the initial stage of drying, the surface ofthe
sample was saturated with moisture and the evapor-ation rate was
higher. Thus, evaporative heat was takenaway from the material,
resulting in a temperature drop.The increased evaporation (higher
drying rate) can alsobe seen in Fig. 3 for the shrinkage-dependent
effective dif-fusivity curve. For better visualization, the
temperature
FIG. 4. Temperature prole obtained for experimental and
simulation with shrinkage and temperature-dependent diffusivities
(for T 60C andV 0.5m=s).
FIG. 5. Temperature curve from simulation for
shrinkage-dependent
diffusivity (T 60C and V 0. 5m=s).
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prole was plotted for small time steps in Fig. 5, wherein
atemperature reduction was noted for the rst few minutesof drying.
A decreasing temperature prole in the initialstage of drying was
also obtained by Turner and Jolly[30]
and Zhang and Mujumdar[29] for microwave convectivedrying and
Golestani et al.[31] for convective drying simula-tions. However,
they reported these results without anyinterpretation of this
event. To investigate this observationfurther, the inward heat ux,
outward heat ux, and totalheat ux were plotted in a single graph as
shown inFig. 6. The inward heat ux was due to convection (fromair
to material) and outward heat ux was due to evapor-ation (from
material to air). Figure 6 shows that for therst 15min of drying
the total heat ux was negative due
to evaporation, which caused a temperature drop in theproduct.
This phenomenon is important in food dryingwhere an increase in
temperature can cause quality degra-dation. If this mechanism of
cooling could be sustainedlonger, then the quality of the dried
food may be improved.Sometimes intermittent drying can be executed
to achievemore evaporation when drying resumes after each
temper-ing period.
More experimentation with continuous temperaturemeasurement
should be undertaken to further validate thisphenomenon.
As outlined above, temperature and moisture distri-bution in the
food at any instance is important becausespoilage can start from
higher moisture content region.
FIG. 6. Evolution of inward (convective), outward (evaporative),
and total (convective evaporative) heat ux.
FIG. 7. (a) Moisture and (b) temperature distribution in the
food after 40min of drying at T 60C and V 0.7m=s.
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Sometimes the center may have a higher moisture contentthough
the surface is already dried. Consequently, investi-gating the
temperature and moisture distribution is criti-cal in the case of
food drying. The modeling andsimulation study was helpful in this
regard, because it
was difcult to measure the moisture distribution
exper-imentally. Figure 7 shows three-dimensional temperatureand
moisture distribution after 40min of drying. It isinteresting that,
although the surface moisture contentultimately became 0.2 kg=kg
(db), the center contained
FIG. 8. Moisture content for different air temperatures for
velocity of 0.7m=s.
FIG. 9. Moisture content for different air velocities at
60C.
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0.6 kg=kg (db) moisture (Fig. 7a). Similar moistureproles were
obtained by Perussello et al.[37] Though thedrying process may
appear to be visually complete, spoil-age or microbial growth could
still initiate from the moistcentral region. Therefore, the
difculty in removingmoisture from the product center is a major
disadvantageof convective drying.
In regard to temperature distribution, Fig. 7b indicatesthat the
temperature gradient was not signicant insidethe material because
the thickness of the material was verysmall in the simulation.
PARAMETRIC STUDY
A parametric study was important to examine the effectof various
process parameters on drying kinetics. Aftervalidation of the
model, a parametric analysis was conduc-ted in COMSOL Multiphysics.
Figure 8 illustrates theeffect of drying air temperature on the
drying curve at aconstant air velocity of 0.7m=s. It is clear from
Fig. 8 thatthe increase in drying air temperature greatly increased
thedrying rate. For example, it took 500, 300, and 200min toreach a
moisture content value of 0.75 kg=kg (db) at dryingair temperatures
of 40, 50, and 60C, respectively. How-ever, the elevated drying air
temperature can decrease theproduct quality (e.g., nutrients).
Therefore, the drying pro-cess has to be optimized and product
quality should beinvestigated along with drying kinetics.
Figure 9 shows the drying curve for different air veloci-ties.
It is evident that increasing drying air velocityincreased the
drying rate, but the effect was not as signi-cant as the effect of
temperature. This is because, in con-vective drying, drying is
dominated by internal diffusion.Because the drying rate is very
high in the beginning, noconstant drying rate period is evident.
The surface becomesdry quickly and the increasing velocity does not
affect theevaporation because sufcient moisture has not
accumu-lated on the surface. Therefore, the velocity increasehas no
effect on the drying rate. These ndings conformwith the drying rate
curves presented by Karim andHawlader[20] showing that the drying
rate is signicantlydifferent for temperature differences, whereas
it is almostthe same for velocity changes.
CONCLUSIONS
In this study, three simulation models were developedbased on
three different effective diffusivities. The modelswere validated
with experimental results. Variable materialproperties were
considered in the simulation. Thetemperature-dependent effective
diffusivity model pre-dicted the initial stage of drying
accurately, whereasmoisture-dependent effective diffusivity
simulations pre-dicted the nal stage well. The evaporative
coolingphenomena that occurred during the initial stage of
dryingwas investigated and explained. This observation may have
signicant implications with regard to product
qualityimprovement. Further research to verify this latter
phenom-enon experimentally may lead to better fundamental
under-standing and ultimately be applied to limit
producttemperature to ensure higher product quality.
Three-dimensional temperature and moisture distribution
werepresented. The three-dimensional graphs suggested thatalthough
the surface of the product was dry, the centermoisture content was
signicant. Parametric analysisshowed that by increasing the drying
air temperature, thedrying rate can be signicantly improved.
However, dryingair velocity (ow rate) has a negligible impact on
drying rate.
ACKNOWLEDGMENTS
The authors acknowledge the contributions of Dr.Zakaria Amin and
M.U.H. Joardder for their support inchecking the manuscript.
FUNDING
The rst author acknowledges the nancial supportfrom the
International Postgraduate Research Award(IPRS) and Australian
Postgraduate Award (APA) tocarry out this research.
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