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ARTICLE IN PRESSFBP-344; No. of Pages 9

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food and bioproducts processing x x x ( 2 0 1 2 ) xxx–xxx

Contents lists available at SciVerse ScienceDirect

Food and Bioproducts Processing

j our nal ho mepage: www.elsev ier .com/ locate / fbp

eat and mass transfer in apple cubes in aicrowave-assisted fluidized bed drier

.R. Askari, Z. Emam-Djomeh ∗, S.M. Mousaviransfer Phenomena Laboratory, Department of Food Science and Technology, Faculty of Agricultural Engineering and Technology,niversity of Tehran, Karaj 31587-77871, Iran

a b s t r a c t

In the present study, a pilot scale microwave assisted fluidized-bed dryer was designed and used to dry apple cubes.

A model was developed to describe heat and mass transfer in apple cubes during drying in a combined microwave-

assisted fluidized-bed dryer. A numerical solution based on the finite difference method was used to develop the

model for moisture distribution and temperature variation of samples. The model was validated using experimental

data, including average moisture content, center and surface temperature at various air temperatures and microwave

power densities.

© 2012 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.

Keywords: Microwave; Fluidized bed drying; Apple cube; Heat transfer; Mass transfer; Modeling

governed by the moisture profile, so these must be stud-

. Introduction

eat and mass transfer in fruits and vegetables during convec-ional drying is a complex process. The essence of all dryingrocesses is the removal of moisture from a mixture to yield

solid product. In general, drying is accomplished by ther-al techniques, and thus involves the application of heat,ost commonly by convection from a current of air. During

he convective drying of solids, two processes occur simul-aneously, namely: transfer of energy from the surroundingnvironment; and transfer of moisture from within the solid.herefore, this unit operation may be regarded as a simul-

aneous heat and mass transfer process. Moreover, the ratet which drying is accomplished is governed by the relativeagnitude of the two processes (Mujumdar and Menon, 1995).

n comparison with conventional heating, microwaves offerifferent heating capacities without requiring a medium as

vehicle for heat transfer. The basic physical phenomenonesponsible for the heating of food materials at microwaverequencies is dipole rotation (Schiffmann, 1995). This phe-omenon causes a higher loss of water than most solidsecause regions with higher water contents within the mate-ial absorb more microwave energy.

It is generally observed that the pattern of power absorp-

Please cite this article in press as: Askari, G.R., et al., Heat and mass tranBioprod Process (2012), http://dx.doi.org/10.1016/j.fbp.2012.09.007

ion in a food, heated in a microwave oven depends on the

∗ Corresponding author. Tel.: +982632248804.E-mail address: [email protected] (Z. Emam-Djomeh).Received 6 April 2012; Received in revised form 2 August 2012; Accept

960-3085/$ – see front matter © 2012 Published by Elsevier B.V. on behttp://dx.doi.org/10.1016/j.fbp.2012.09.007

oven and load factors, thus it could be concluded that the heat-ing process is directed by heat and mass transfer mechanisms(Bilbao-Sainz et al., 2006). The application of microwavessolely, can result in uneven heating of certain products,depending on their dielectric and thermophysical propertiesand inhomogeneous field distribution. An undesired inhomo-geneous heating pattern can be prevented by changing thefield configuration either by varying cavity geometries (e.g.mode stirrer) or by moving the product (on a conveyor beltor turntable); this also influences the field distribution. (AbbasiSouraki and Mowla, 2008; Regier and Schubert, 2005). However,problems related to fast temperature rise and its distributioninside the products must be considered. These limitations canbe overcome by combining microwave radiation with a flu-idized bed. Regarding high heat and mass transfer coefficients,fluidized bed drying is widely used for chemical, pharmaceu-tical and food processing (Mhimid et al., 2000; Reyes et al.,2002). The first study of a fluidized bed dryer combined withmicrowaving was presented by Smith in 1970, however a num-ber of subsequent investigations have described this method(McMinn et al., 2003; Hatamipour and Mowla, 2002, 2003;Campanone and Zaritzky, 2005).

Temperature distribution during microwave heating is

sfer in apple cubes in a microwave-assisted fluidized bed drier. Food

ed 28 September 2012

ied together. The present study developed a generalized

alf of The Institution of Chemical Engineers.

dx.doi.org/10.1016/j.fbp.2012.09.007

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dx.doi.org/10.1016/j.fbp.2012.09.007


2 food and bioproducts processing x x x ( 2 0 1 2 ) xxx–xxx

mathematical model to describe moisture and temperaturedistribution. A numerical model by means of MATLAB programwritten for this purpose is solved to simulate heat transfer infoodstuff with cubic geometry in microwave assisted fluidizedbed.

2. Theory

The general approach to modeling mass transfer is using theconcept of effective diffusivity (Deff) which allows describingdiffusion of moisture by the Fick’s second law:

∂X

∂t= Deff ∇2(X) (1)

Eq. (1) can be integrated for different geometries (slab,cylinder and sphere) and boundaries as well as initial con-ditions (Crank, 1975). The solution for an infinite slab of 2lthickness and constant diffusivity in terms of average mois-ture content (Xl) is given by:

X∗i = xi − xe

x0 − xe= 8

�2

∑∞

n=1

1

(2n − 1)2exp

×[−(2n − 1)2

(�2Deff

4 × l2

)× t

](2)

For a finite slab (a cube) the geometry corresponds to theintersection of three infinite slabs, with widths of 2x, 2y, and2z, which yields the following expression (Crank, 1975; Reyeset al., 2002):

X∗i = X∗

x × X∗y × X∗

z =(

xx − xe

x0 − xe

)×

(xy − xe

x0 − xe

)×

(xz − xe

x0 − xe

)(3)

For a finite slab with the same geometries (x = y = z = l), Eq.(3) reduced to:

X∗i = (X∗

i )3 =(

xi − xe

x0 − xe

)3(4)

where X* is the dimensionless moisture content in dryingcube.

Moisture content (X̄) of apple cubes can be calculated usingfollowing equation:

X∗i = X̄ − Xe

X0 − Xe→ X̄ = Xe + (X0 − Xe) × X∗ (5)

where X̄ is the time dependence moisture content of applecubes during drying.

It is quite clear that moisture diffusivity is a functionof the moisture and temperature of samples, therefore todescribe moisture changes a numerical method with vari-ant moisture diffusivity is necessary (Simal et al., 1997;Hatamipour and Mowla, 2002). In this case average mois-ture content (xi) of Eq. (4) is replaced by calculated (X)from one-dimensional numerical solution of Eq. (6) todetermine moisture content of cubic sample (X̄) fromEq. (5).

Moisture diffusion is the main mass transfer mechanismin the solid phase from the center of a product to the sur-face followed by convective moisture transfer to the air. Heattransfer mechanisms include the internal heat generation and


convective heat transfer mechanisms from/to the surface ofdrying samples to/from the drying air as well as evaporative

cooling. To describe moisture and temperature profiles withinsamples, a mathematical model was proposed that consid-ers mass and energy conservation laws and has the followingassumptions:

1. Uniform initial moisture and temperature distributionswithin the drying materials.

2. Heat transfer by conduction and convection only.3. Temperature and moisture dependency of moisture diffu-

sivity.4. Moisture transport inside a material occurring in the liquid

phase and evaporation only at the evaporating surface.5. Diffusion being the governing mass transfer mechanism

inside the material and moisture at the surface being atequilibrium with the drying air.

6. Uniform temperature distribution within the drying mate-rials. Internal resistance is negligible compared to externalresistance (lumped-heat capacity analysis).

7. Similar hydrodynamic properties and moisture content ofall particles in well mixed fluidized bed.

2.1. Mass transfer modeling

Researchers have noted that drying of agro-food products iscommonly done by single phase diffusion and no constantrate periods are displayed (Crank, 1975; Abbasi Souraki andMowla, 2008).

The unsteady state equation of conservation of mass in aslab (a one direction of Fig. 1) can be described by the followingequation:

∂X

∂t= ∂

∂y

(Deff

∂X

∂y

)→ ∂(�sX)

∂t= ∂

∂y

(Deff

∂(�sX)∂y

)(6)

The following initial and boundary condition are consid-ered as:

t = 0 0 < y < l, X = X0 (7)

t > 0 y = l, X = Xe (8)

t > 0 y = 0,∂X

∂y= 0 (9)

The physical properties of the apples are summarized inTable 1.

2.2. Heat transfer modeling

Energy balance in a particle can be written as (Datta, 2001):

d(MCpT̄)dt

= Qmicrowave + Ah(Ta − T̄) + �dM

dt(10)

This means that: (rate of temperature rise) = (microwaveheat generation) + (convective heat gain or loss) + (evaporativeheat loss). The following initial conditions are assumed as:

t = 0 X̄ = X0 and T̄ = T0 (11)

The rate of heat generation in a specific point in a sam-ple depends on its distance from the surface (Lambert’smicrowave absorption relationship). The mean diameter of


the apple cubes is smaller than the penetration depth of themicrowaves. Hence, a uniform electric and microwave fields

dx.doi.org/10.1016/j.fbp.2012.09.007


food and bioproducts processing x x x ( 2 0 1 2 ) xxx–xxx 3

with

awwc

c

C

2

2Tdtn2

�

Fig. 1 – Drying sample

nd a uniform temperature distribution inside the samplesere assumed. An average temperature inside the samplesas also assumed. The convective heat transfer coefficient (hs)

an be evaluated by (Ranz and Marshal, 1952):

T − Tair

T0 − Tair= exp

[−

(hsA

� · Cp · V

)× t

](12)

The specific heat capacity as a function of moisture contentan be calculated as (Perry and Chilton, 1985):

P (kJ/kg ◦C) = 1.675 +(

X̄

X̄ + 1× 2.5

)(13)

.3. Solution of mathematical model

.3.1. Discretization of mass transfer equationhe Crank–Nicolson finite difference method was chosen toiscretize mass transfer equation (6) considering the varia-ion of Deff and �s with moisture content. This method doesot require a stability condition (Constantinides and Mostoufi,001). Differentiation of Eq. (6) leads to:

s∂X

∂t+ X

∂�s

∂t= ∂

∂yDeff �s

∂X

∂y+ Deff �s

∂2X

∂y2(14)

Eq. (14) can be discretized using the following equations:

∂X

∂t

∣∣∣ = Xi,n+1 − Xi,n

�t(15)


i,n+(1/2)

[− �t

8�y2(Di,n+1 · �i,n+1 + Di,n · �i,n+1 + Di,n+1 · �i,n + Di,n · �i,n)

]× (X

+Di+1,n+1 · �i+1,n+1 + Di,n · �i,n + Di+1,n · �i+1,n)

]× (Xi, n + 1) +

[−

−Di,n · �i,n+1 + 2 × Di+1,n · �i+1,n − Di,n · �i,n)

]× (Xi+1, n + 1) =

[−

8

× (Xi−1, n) +[

(�i,n) + �t

4�y2(Di,n · �i,n+1 + Di,n+1 · �i,n + Di+1,n+1 · �i+

+[

�t

8�y2(Di,n · �i,n+1 + Di,n+1 · �i,n + 2 × Di+1,n+1 · �i+1,n+1 − Di,n · �

boundary conditions.

∂�s

∂t

∣∣∣i,n+(1/2)

= �s i,n+1 − �s i,n

�t(16)

∂X

∂y

∣∣∣i,n+(1/2)

= Xi+1,n+1 − Xi,n+1 + Xi+1,n − Xi,n

2�y(17)

∂2X

∂y2

∣∣∣i,n+(1/2)

= Xi+1,n+1 − 2Xi,n+1 + Xi−1,n+1 + Xi+1,n − 2Xi,n + Xi−1,n

2�y2

(18)

∂

∂y�s · Deff

∣∣∣i,n+(1/2)

= Deff i+1,n+1 · �s·i+1,n+1−Deff ·i,n+1 · �s·i,n+1 + Deff ·i+1,n · �s·i+1,n − Deff ·i,n · �s·i,n2�y2

(19)

X|i,n+(1/2) = Xi,n+1 + Xi,n

2(20)

�s|i,n+(1/2) = �s i,n+1 + �s i,n

2(21)

Deff

∣∣i,n+(1/2)

= Deff ·i,n+1 + Deff ·i,n2

(22)

where i = node position; n = the time interval, �y = space incre-ment and �t = time step such that y = i �y and t = n �t; n = t,while (n + 1) corresponds to time (t + �t).

Substituting Eqs. (15)–(22) into Eq. (14) and rearranging onthe basis of proper terms leads to the general equation for thenumerical calculation of a moisture profile as followings:

i−1, n + 1) +[

(�i,n+1) + �t

4�y2(Di,n · �i,n+1 + Di,n+1 · �i,n

�t

8�y2(Di,n · �i,n+1 + Di,n+1 · �i,n + 2 × Di+1,n+1 · �i+1,n+1

�t

�y2(Di,n+1 · �i,n+1 + Di,n · �i,n+1 + Di,n+1 · �i,n + Di,n · �i,n)

]

1,n+1 + Di,n · �i,n + Di+1,n · �i+1,n)

]× (Xi, n)

i,n+1 + 2 × Di+1,n · �i+1,n − Di,n · �i,n)

]× (Xi+1, n) (23)


dx.doi.org/10.1016/j.fbp.2012.09.007



Table 1 – Physical properties of apples used in modeling.

Property Correlation Reference

Density (kg/m3) � = 770 + 16.18 × X − 295.1 × e−X Krokida and Maroulis (1999)

Effective diffusivity (m2/s) D = 2.74 × 10−6 exp(

24,034.2)

Simal et al. (1997)
eff
2.3.2. Discretization of heat transfer equationThe sample mass as a function of average moisture contentcan be defined as:

M = Ms(1 + X̄) (24)

where M and Ms are the mass of drying solid and dried solidrespectively. By substituting M from Eq. (24) and Cp from Eq.(13) into Eq. (10), the following equation is obtained:

dT̄

dt+ 2.5 × Ms · (dX̄/dt) + Ah

Ms(1.675 + 2.5 × X̄)· T̄

= Qmicrowave + AhTa + �Ms(dX̄/dt)

Ms(1.675 + 2.5 × X̄)(25)

Using the subsequent equations,

dX̄

dt

∣∣∣∣n+(1/2)

= X̄n+1 − X̄n

�t(26)

dT̄

dt

∣∣∣∣n+(1/2)

= T̄n+1 − T̄n

�t(27)

T̄∣∣n+(1/2)

= T̄n+1 + T̄n

2(28)

X̄∣∣n+(1/2)

= X̄n+1 − X̄n

2(29)

Eq. (25) can be discretized to Eq. (30) in the following form:

T̄n+1 = T̄n ·

⎛⎜⎜⎜⎜⎜⎜⎜⎝

⎛⎝1 − 1

2

2.5×Ms·(

X̄n+1−X̄n�t

)+Ah

Ms

(1.675+2.5×

(X̄n+1+X̄n

2

))⎞⎠

⎛⎝1 + 1

2

2.5×Ms·(

X̄n+1−X̄n�t

)+Ah

Ms·(

1.675+2.5×(

X̄n+1+X̄n2

))⎞⎠

+

⎛⎝Qmicrowave+AhtTa+�Ms

(X̄n+1−X̄n

�t

)Ms

(1.675+2.5×

(X̄n+1+X̄n

2

))⎞⎠

⎛⎝1 + 1

2

Ms·CWP

·(

X̄n+1−X̄n�t

)Ms·

(1.675+2.5×

(X̄n+1+X̄n

2

))⎞⎠

⎞⎟⎟⎟⎟⎟⎟⎟⎠

× �t (30)

Eq. (30) is the general correlation for the calculation of tem-perature variation during drying. The equation for the stabilitycondition of heat transfer determines the minimum value forthe time increment as:


�t ≤ 2Ms(1.675 + 2.5 × X̄)

2.5 × Ms × (dX̄/dt) + Ah(31)

R(T+273)

3. Materials and methods

3.1. Apples

Golden Delicious apples produced in Karaj, Iran were pur-chased from a local supermarket and stored at 4 ◦C. Apple waschosen because the cells of parenchyma tissue are homoge-nous and structurally less complex. One batch of apples wasused in the experiments, which is usually available for alimited period of time. Firm apples at the same stage ofmaturity with no bruises on the skin were selected for thedehydration experiments. For all experiments, apples werewashed and cut (10 mm × 10 mm × 10 mm) with special cut-ting tools and immediately immersed in tap water at 20 ◦C. Toavoid undesirable enzymatic reactions and improve structuralproperties, apple slices were blanched in hot water (80 ◦C) for1 min.

3.2. Drying equipment

Drying experiments were conducted using a modified domes-tic microwave oven (900 W) as illustrated in Fig. 2. This devicewas designed to dry samples while the temperature and veloc-ity of air and microwave power were controlled.

Microwave power can be adjusted in domestic ovens bycontrolling operation time, but this approach does not yieldsufficient power control accuracy. Accordingly, power wasadjusted as directed by the manufacturer (in increments of150 W) and moreover, a time controller was installed to achievesmaller stepwise power changes. Therefore, resulting outputpower could be adjusted by increments of 50 W.

The drying chamber (1.2 kg) consisted of a Pyrex duct of10 cm diameter and 35 cm height which was positioned insidethe microwave oven. This configuration was necessary toensure careful adjustment of air velocity around the samplesand prevent the exposure of moisture to the internal partsof the microwave oven which could lead to power loss andelectrical hazards.

An external duct made of stainless steel was connected toan 8 kW electric heater to heat the air to the desired dryingtemperature which was controlled by a PID temperature con-troller. Air velocity was controlled by a fan speed controller.For all experiments, air velocity was maintained at a constantvalue of 21 m/s inside the cavity. It could be noted that cubeswas fluidized at 21 m/s air velocity which was higher than val-ues that reported in similar cases (Reyes et al., 2002; Zielinskaand Markowski, 2007). The higher velocity was necessary dueto lower amount of cubes introduced in fluid bed and to elim-inate the external mass transfer resistance.

Before entering raw materials, the system was run for15 min until temperature stabilized. In each experiment about90 g (100 pieces) of apple cubes were placed in drying chamber.Drying chamber is positioned on a digital balance with accu-racy of 0.01 g (Fig. 2). Samples’ weight was measured whenthe blowing air was switched off, instead of the less reliable


method of removing the sample from the drying chamber.The surface and internal temperatures of the samples were

dx.doi.org/10.1016/j.fbp.2012.09.007



assi

mfiiimu

oaMmuu

Q

wshifu

03prt

ε

(

ε

(Holman, 2009). Aluminum cubes with the same geometry as

Table 2 – Operative conditions of microwave assistedfluidized bed drying of apple cubes.

Test# Air temperature(◦C)

Microwave powerlevel (W/g)

1 50 0.0002 60 0.1133 70 0.0004 60 0.1135 50 0.2636 60 0.1137 70 0.2638 60 0.1139 60 0.263

10 50 0.11311 60 0.11312 70 0.113

Fig. 2 – Microwave

easured using a thermocouple (Ebro. TFI 500, Germany). Aber optic thermometer attached to a universal multichannel

nstrument (Fiso Technologies, Quebec, Canada) was insertednto the apple cubes to monitor temperature of sample during

icrowave heating. The water content of apples determinedsing the vacuum oven method at 70 ◦C for 24 h (AOAC, 1990).

To determine the average absorbed power, the methodf power measurement developed in previous studies wasdopted (Yang and Gunasekaran, 2004; Abbasi Souraki andowla, 2008). Warming of time of distilled water duringicrowave heating at different power levels was measured

sing a thermometer and the absorbed power was obtainedsing the following relationship:

microwave = � · V · Cp · �Tave + ��m

�t(32)

here Qmicrowave is the microwave power, � the density, Cp thepecific heat and V the volume of distilled water, � the latenteat of evaporation, �m the changes in samples weight and �t

s the necessary time to heating of samples. �Tave is obtainedrom 3 replications. Since the samples heated far from its sat-ration temperature of water, �m = 0.

The measured power densities were 0.113, 0.263 and.413 W/g at 150, 300 and 450 W, respectively. Only 150 and00 W power levels were used in this study. On the other handower dissipated is a linear function of loss factor (ε′′) andecent factor is a linear function of moisture content accordingo following equation (Feng et al., 2002):

′′ = 2.95 × ln(X̄) + 2.733 (33)

This equation validated to moisture contents from 0.5 to 9d.b.). We can conclude that:


′′ = (0.3202 × ln(X̄) + 0.2964) × ε′′

0 (34)

sted hot-air dryer.

According to foregoing discussion we can write:

Q̇ = (0.3202 × ln(X̄) + 0.2964) × Q̇0 (35)

Since the power densities measured by Eq. (32) adjusted asshowed in Eq. (35). Experiments to determine the kinetics ofthe convective microwave drying process were performed intriplicates and their averages used to validate the mathemati-cal model. The operational parameters are listed in Table 2.Relative humidity of ambient air was 35% which was keptconstant by means of a laboratory’s air conditioner.

4. Results and discussion

The total heat transfer coefficient during testing was calcu-lated using Eq. (12), as well known lumped parameter analysis


13 60 0.11314 60 0.000

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Fig. 3 – Aluminum objects used to estimate heat transfercoefficient.

Fig. 5 – Average moisture content of apple cubes duringdrying at microwave power densities of 0 W, 150 W(0.113 W/g) and 300 W (0.263 W/g), air temperature of 50 ◦Cand air velocity of 21 m/s.

apple cubes were used to determine the heat transfer coeffi-cient (Fig. 3).

The temperature at the center of the solid was mea-sured at different time intervals under all conditions.The time–temperature data were then used to plotLn[(T − Tair)/(T0 − Tair)] vs. t and the slope of the straightline was used to calculate the heat transfer coefficients forthe 10 mm diameter aluminum cube (K = 204 W/m ◦C andCp = 0.896 kJ/kg ◦C) according to Eq. (12). For example, whenthe air temperature was 50 ◦C and its relative humidity was35%, the total heat transfer coefficient was measured to beabout 131 W/m2 ◦C (Fig. 4).

The effect of microwave power density on the averagemoisture content of the drying samples is shown in Fig. 5. Itis clear that the microwave energy enhanced drying rate andreduced drying time. Drying times for samples dried by theapplication of microwave energy were decreased about 66%and 73% at 150 and 300 W (0.113 and 0.263 W/g), respectively.These results are in agreement with those obtained by other


researchers (Abbasi Souraki and Mowla, 2008).

Fig. 4 – Time–temperature (dimensionless) plot fordetermination of heat transfer coefficient of aluminumcubes (h = 131 W/m2 K) at an air velocity of 21 m/s. Thepresented data are the average of three replications.

Comparison of the experimental and predicted (by Eq.(23)) average moisture content was carried out at differ-ent drying times. When the air stream was directed toanother duct, weight measurement was made possible. Thismethod is more accurate than intermittent offline weigh-ing of the drying samples. An exponential decay of moisturecurve characterizes the falling rate period for the hygroscopicmaterials. The good agreement between the predicted aver-age moisture and experimental data may be related to thedependency of effective moisture diffusivities on moisturecontent and sample’s temperature which were used to solvethe mathematical model. The theoretical and experimen-tal temperature variations for the apple cubes dried withoutmicrowave energy at different temperatures are shown inFig. 6.

Temperature measurement could not be done at differ-ent points on the drying samples because of their small size.Only the temperature of the center and the surface of thesamples were measured using a probe type (Testo, Germany)thermometer to check the accuracy of the temperature pre-dicted by the mathematical model. These measurements werecarried out in the drying chamber during drying.

A flexible thermocouple (Fiso Technologies, Quebec,Canada) was placed at the center of each sample duringdrying. Special attention was paid to ensure that samplemovement in the drying chamber was similar to that of otherdrying samples on the fluidized bed. The surface temperaturewas measured using an emission-type thermometer (Ebro. TFI500, Germany) as the fluidized sample left the chamber usinga special device on the top of the chamber. The time requiredfor surface temperature measurement was about 2 seconds.As seen in Fig. 6, there was a significant difference betweenpredicted and measured temperature, especially at the initialstages of the drying process.

The temperature fall in the initial stage may be due to thefact that at the beginning of the process, the surface moisturedid not equal Xe, so the effect of evaporative cooling was moresignificant and the calculated temperature fell. This was lessevident when higher temperatures were used. However, therewas no good agreement between the estimated and measuredvalues. The assumption that the distribution of temperature


inside the sample is uniform is the source of this deviation. In

dx.doi.org/10.1016/j.fbp.2012.09.007



Fig. 6 – Predicted and measured temperature variation inapple cubes during warm air drying at (a) 50 ◦C and (b) 70 ◦Cwithout microwave energy.

ac

pavtswtgpsptae

aiadtstwec

Fig. 7 – Predicted temperature variation in apple cubesduring warm air drying at 50 ◦C with microwave powerdensities of (a) 150 (0.113 W/g) and (b) 300 W (0.263 W/g).
ddition, the surface temperature was lower than that at the
enter of the drying samples.Temperature variations in drying samples at 50 ◦C in the

resence of microwave heating at 0.113 and 0.263 W/g (150nd 300 W) power densities were different from those con-entional heating. Fig. 7 shows the temperature drops athe first stage of drying due to evaporative cooling duringurface evaporation. However, this is less evident comparedith those from conventional heating. It could be concluded

hat the temperature drop was compensated by internal heateneration. In addition, there was a dissimilar trend in tem-erature variation between the center and outer layer ofamples. Temperature rose more rapidly at the first stage,articularly in the center of the apple cubes. Unlike conven-ional heating, the temperature at the center of the dryingpples was evidently higher when microwave heating wasmployed.

As illustrated, the surface temperature was higher whenpple cubes were dried using conventional hot air drying, evenn a fluidized bed. On the other hand, there was no temper-ture variation at the surface and center of samples duringrying, as was observed for microwave heating. It is clear thathe temperature variation, which reached 51 ◦C at the initialtages when the air temperature was 50 ◦C, was the result ofhe use of microwave power. The temperature dissimilarityas more apparent at higher power densities (Fig. 7b). How-


ver, it was disappeared as moisture content decreased whichould be explained by the moisture dependency of microwave

heating. Similar results were observed during the drying ofcarrots (Sanga et al., 2002), corn (Jumah, 2005), potatoes andcarrots (Srikiatden and Roberts, 2006) and green peas (AbbasiSouraki and Mowla, 2008). These three different periods canbe observed in Fig. 7.

In the early minutes of drying, the higher moisture contentallowed efficient internal heat generation, causing an increasein sample temperature. Cooling from evaporation at the sam-ple surface may have compensated for this increase, sosample temperature did not change dramatically. During thesecond period, sample temperature increased to the tempera-ture of the drying air, surpassing it under some conditions.The dielectric properties of water depend on temperatureand enhanced heat generation at higher temperatures. Inthe third period, the moisture content of samples decreasedand microwave absorption decreased progressively therefore,samples’ temperature reached to the temperature of dryingair.

Finally, the over-estimation was observed in the laststage of drying, when higher power densities wereused. This may have been a result of over-estimation ofmicrowave heating when the sample moisture contentdecreased and, consequently, heat generation would bedecreased.


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5. Conclusion

Moisture distribution and temperature variation in applecubes in a microwave-assisted fluidized bed drier wasmodeled using the basic law of conservation of mass andheat. The predicted average moisture content showed a goodagreement with the experimental data. Microwave energyenhanced the drying rate and samples were dried in lowertimes. At the initial stages when the microwave power was notapplied, the center temperature was lower than surface andsurface temperature was lower than drying air temperature.With microwave heating at the beginning stages the temper-ature was rose quickly since microwave heating was moreefficient and leads to a different between center and surfacetemperature. Predicted temperature was placed between thecenter and surface temperatures. Center temperature showeda significant variation due to pulsed microwave heating. Thesevariations are not observed at the surface due to the coolingeffects of drying air and lower moisture content. It could beconcluded that some undesired phenomena such as charringand thermal deterioration of vitamins takes place in the cen-tral areas of microwave heated samples. At the lower moisturecontents, the effect of microwave heating on the so calledtemperature variation was weakened and classical dryingbehavior was observed. That is calculated in model solution.At these stages surface and center’s temperature were moreadapted predicted values even in higher microwave powers.

Nomenclature

A surface area (m2)aw water activityCp specific heat (J/kg ◦C)Deff effective moisture diffusivity (m2/s)h total heat transfer coefficient (W/m2 ◦C)M mass (kg)Ms mass of drying solid (kg)Nu Nusselt number (dimensionless)Pr Prandtl number (dimensionless)Re Reynolds number (dimensionless)Qmicrowave microwave heat generation (W)t time (s)T temperature (◦C)V volume (m3)X moisture content (kg water/kg dry solid)X̄ average moisture content (kg water/kg dry solid)x, y, z, l distance (m)

Subscripts0 initial valuea drying aire equilibrium

Greek letters� latent heat of vaporization (J/kg)�s density (kg/m3 dry solid)

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