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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

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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: azharul.karim@qut.edu.au

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.

REFERENCES

1. Chua, K.J.; Mujumdar, A.S.; Hawlader, M.N.A.; Chou, S.K.; Ho,

J.C. Convective drying of agricultural products. Effect of continuous

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