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A Review of Thin Layer Drying of Foods: Theory,

Modeling, and Experimental ResultsZafer Erbay

a& Filiz Icier

b

aGraduate School of Natural and Applied Sciences, Food Engineering Branch, Ege Univers

35100, Izmir, Turkeyb

Department of Food Engineering, Faculty of Engineering, Ege University, 35100, Izmir,

Turkey

Version of record first published: 05 Apr 2010.

To cite this article: Zafer Erbay & Filiz Icier (2010): A Review of Thin Layer Drying of Foods: Theory, Modeling, andExperimental Results, Critical Reviews in Food Science and Nutrition, 50:5, 441-464

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Critical Reviews in Food Science and Nutrition, 50:441464 (2009)

Copyright C Taylor and Francis Group, LLC

ISSN: 1040-8398

DOI: 10.1080/10408390802437063

A Review of Thin Layer Drying

of Foods: Theory, Modeling,and Experimental Results

ZAFER ERBAY1 and FILIZ ICIER2

1Graduate School of Natural and Applied Sciences, Food Engineering Branch, Ege University, 35100 Izmir, Turkey2Department of Food Engineering, Faculty of Engineering, Ege University, 35100 Izmir, Turkey

Drying is a complicated process with simultaneous heat and mass transfer, and food drying is especially very complexbecause of the differential structure of products. In practice, a food dryer is considerably more complex than a device

that merely removes moisture, and effective models are necessary for process design, optimization, energy integration, and

control. Although modeling studies in food drying are important, there is no theoretical model which neither is practical nor

can it unify the calculations. Therefore the experimental studies prevent their importance in drying and thin layer drying

equations are important tools in mathematical modeling of food drying. They are practical and give sufficiently good results.

In this study first, the theory of drying was given briefly. Next, general modeling approaches for food drying were explained.

Then, commonly used or newly developed thin layer drying equations were shown, and determination of the appropriate

model was explained. Afterwards, effective moisture diffusivity and activation energy calculations were expressed. Finally,

experimental studies conducted in the last 10 years were reviewed, tabulated, and discussed. It is expected that this

comprehensive study will be beneficial to those involved or interested in modeling, design, optimization, and analysis of food

drying.

Keywords food drying, thin layer, mathematical modeling, diffusivity, activation energy

INTRODUCTION

Drying is traditionally defined as the unit operation that con-vertsa liquid, solid, or semi-solid feed materialinto a solid prod-uctof significantlylower moisture content. In most cases,dryinginvolves the application of thermal energy, which causes waterto evaporate into the vapor phase. Freeze-drying provides an ex-ception to this definition, since this process is carried out belowthe triple point, and water vapor is formed directly through the

sublimation of ice. The requirements of thermal energy, phasechange, and a solid final product distinguish drying from me-chanical dewatering, evaporation, extractive distillation, adsorp-tion, and osmotic dewatering (Keey, 1972; Mujumdar, 1997).

Drying is one of the oldest unit operation, and widespreadin various industries recently. It is used in the food, agricul-tural, ceramic, chemical, pharmaceutical, pulp and paper, min-eral, polymer, and textile industries to gain different utilities.

Address correspondence to: Zafer Erbay, Graduate School of Natural andApplied Sciences, Food Engineering Branch, Ege University, 35100 Izmir,Turkey. Tel:+90 232 388 4000 (ext.3010) Fax: +90 232 3427592. E-mail:[email protected]

The methods of drying are diversified with the purpose ofprocess. There are more than 200 types of dryers (Mujum1997). For every dryer, the process conditions, such as the ding chamber temperature, pressure, air velocity (if the cargas is air), relative humidity, and the product retention tihave to be determined according to feed, product, purpose, method. On the other hand, drying is an energy-intensive pcess and its energy consumption value is 1015% of the tenergy consumption in all industries in developed count

(Keey, 1972; Mujumdar, 1997). It is a very important procaccording to the main problems in the whole world such asdepletion of fossil fuels and environmental pollution. In brdrying is arguably the oldest, most common, most diverse, most energy-intensive unit operation and because of all thfeatures, the engineering in drying processes gains importan

In the food industry, foods are dried, starting from their ural form (vegetables, fruits, grains, spices, milk) or after hdling (e.g. instant coffee, soup mixes, whey). The producof a processed food may involve more than one drying procat different stages and in some cases, pre-treatment of foonecessary before drying. In the food industry, the main purp

441


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442 Z. ERBAY AND F. ICIER

of drying is to preserve and extend the shelf life of the product.In addition to this, in the food industry, drying is used to obtaina desired physical form (e.g. powder, flakes, granules); to obtainthe desired color, flavor, or texture; to reduce the volume or theweight for transportation; and to produce new products which

would not otherwise be feasible (Mujumdar, 1997).Drying is one of the most complex and least understoodprocesses at the microscopic level, because of the difficultiesand deficiencies in mathematical descriptions. It involves si-multaneous and often coupled and multiphase, heat, mass, andmomentum transfer phenomena (Kudra and Mujumdar, 2002;Yilbas et al., 2003). In addition, the drying of food materialsis further complicated by the fact that physical, chemical, andbiochemical transformations may occur during drying, some ofwhich may be desirable. Physical changes such as glass transi-tions or crystallization during drying can result in changes in themechanisms of mass transfer andrates of heat transfer withinthematerial, often in an unpredictable manner (Mujumdar, 1997).

The underlying chemistry and physics of food drying are highlycomplicated, so in practice, a dryer is considerably more com-plex than a device that merely removes moisture, and effectivemodels are necessary for process design, optimization, energyintegration, and control. Although many research studies havebeen done about mathematical modeling of drying, undoubt-edly, the observed progress has limited empiricism to a largeextent and there is no theoretical model that is practical and canunify the calculations (Marinos-Kouris and Maroulis, 1995).

Thin layer drying equations are important tools in mathemat-ical modeling of drying. They are practical and give sufficientlygood results. To use thin layer drying equations, the drying-ratecurves have to be known. However, the considerable volume

of work devoted to elucidate the better understanding of mois-ture transport in solids is not covered in depth, in practice,drying-rate curves have to be measured experimentally, ratherthan calculated from fundamentals (Baker, 1997). So the ex-perimental studies prevent their importance in drying. There isno review done about the experimental results of the thin layerdrying experiments of foods and mathematical models in thinlayer drying in open literature for more than 10 years. Jayas etal. (1991) have written the last review according to the authorsknowledge. In this study, the fundamentals of thin layer dryingwere explained, and commonly used or newly developed semi-theoretical and empirical models in the literature were shown.In addition, the experimental results gained in the last 10 yearsfor food materials were summarized and discussed.

THE THEORY AND MATHEMATICAL MODELING

OF FOOD DRYING

Mechanisms of Drying

The main mechanisms of drying are surface diffusion orliquid diffusion on the pore surfaces, liquid or vapor diffusiondue to moisture concentration differences, and capillary action

in granular and porous foods due to surface forces. In additionto these, thermal diffusion that is defined as water flow causedby the vaporization-condensation sequence, and hydrodynamicflow that is defined as water flow caused by the shrinkage andthe pressure gradient may also be seen in drying (Strumillo

and Kudra, 1986;Ozilgen and

Ozdemir, 2001). The dominantdiffusion mechanism is a function of the moisture content and

the structure of the food material and it determines the dryingrate. The dominant mechanism can change during the processand, the determination of the dominant mechanism of drying isimportant in modeling the process.

For hygroscopic products, generally the product dries in con-stant rate and subsequent falling rate periods and it stops whenan equilibrium is established. In the constant rate period of dry-ing, external conditions such as temperature, drying air velocity,direction of air flow, relative humidity of the medium, physicalform of product, the desirability of agitation, and the method ofsupporting the product during drying are essential and the dom-

inant diffusion mechanism is the surface diffusion. Toward theend of the constant rate period, moisture has to be transportedfrom the inside of the solid to the surface by capillary forcesand the drying rate may still be constant until the moisture con-tent has reached the critical moisture content and the surfacefilm of the moisture has been so reduced with the appearanceof dry spots on the surface. Then the first falling rate periodor unsaturated surface drying begins. Since, however, the rateis computed with respect to the overall solid surface area, thedrying rate falls even though the rate per unit wet solid sur-face area remains constant (Mujumdar and Menon, 1995). Inthis drying period, the dominant diffusion mechanism is liquiddiffusion due to moisture concentration difference and internal

conditions such as the moisture content, the temperature, andthe structureof theproduct are important. When the surface filmof the liquid is entirely evaporated, the subsequent falling rateperiod begins. In the second falling rate period of drying thedominant diffusion mechanism is vapor diffusion due to mois-ture concentration difference and internal conditions keep ontheir importance (Husain et al., 1972).

Although biological materials such as agricultural productshave a high moisture content, generally no constant rate periodis seen in the drying processes (Bakshi and Singh, 1980). Infact, some agricultural materials such as grains or nuts usuallydry in the second falling rate period (Parry, 1985). Althoughsometimes there is an overall constant rate period at the initialstages of drying, a statement such as the food materials drywithout a constant rate period is generally true.

Mathematical Modeling of Food Drying

Drying processes are modeled with two main models:

(i) Distributed modelsDistributed models consider simultaneous heat and masstransfer. They take into consideration both the internal and


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A REVIEW OF THIN LAYER DRYING OF FOODS

external heat and mass transfer, and predict the temperatureand the moisture gradient in the product better. Generally,these models depend on the Luikov equations that comefrom Ficks second law of diffusion shown as Eq. 1 or theirmodified forms (Luikov, 1975).

M

t= 2K11M+

2K12T+2K13P

T

t= 2K21M+

2K22T+2K23P

P

t= 2K31M+

2K32T+2K33P (1)

where, K11, K22, K33 are the phenomenological coeffi-cients, while K12, K13, K21, K23, K31, K32 are the couplingcoefficients (Brooker et al., 1974).

For most of the processes, the pressure effect can be ne-glected compared with the temperature and the moistureeffect, so the Luikov equations become as (Brooker et al.,1974):

M

t= 2K11M+

2K12T

T

t= 2K21M+

2K22T (2)

Nevertheless, the modified form of the Luikov equations(Eq. 2) may not be solved with analytical methods, be-

cause of the difficulties and complexities of real dryingmechanisms. On the other hand, this modified form canbe solved with the finite element method (Ozilgen andOzdemir, 2001).

(ii) Lumped parameter modelsLumped parameter models do not pay attention to the tem-perature gradient in the product and they assume a uniformtemperature distribution that equals to the drying air tem-perature in the product. With this assumption, the Luikovequations become as:

M

t= K11

2M (3)

T

t= K22

2T (4)

Phenomenological coefficient K11 is known as effectivemoisture diffusivity (Deff) and K22 is known as thermaldiffusivity (). Forconstantvalues ofDeff and , Equations3 and 4 can be rearranged as:

M

t= Deff

2M

x2+

a1

x

M

x

(5)

T

t=

2T

x2+

a1

x

T

x

where, parameter a1 = 0 for planar geometries, a1 =for cylindrical shapes and a1 = 2 for spherical sha

(Ekechukwu, 1999).

The assumptions resembling the uniform temperature dibution andtemperatureequivalent of theambientair andprodcause errors. This error occurs only at the beginning of the pcess and it may be reduced to acceptable values with reducthe thickness of the product (Henderson and Pabis, 1961). Wthis necessity, thin layer drying gains importance and thin laequations are derived.

Thin Layer Drying Equations

Thin layer drying generally means to dry as one layesample particles or slices (Akpinar, 2006a). Because of its structure, the temperature distribution can be easily assumas uniform and thin layer drying is very suitable for lumparameter models.

Recently thin layer drying equations have been found to hwide application due to their ease of use and requiring less dunlike in complex distributed models (such as phenomenolcal and coupling coefficients) (Madamba et al., 1996; Ozdeand Devres, 1999).

Thin layer equations may be theoretical, semi-theoretiandempirical models. Theformer takes into account only theternal resistance to moisture transfer (Henderson, 1974; Sua

et al., 1980; Bruce, 1985; Parti, 1993), while the others consonly the external resistance to moisture transfer betweenproduct and air (Whitaker et al., 1969; Fortes and Okos, 19Parti, 1993;Ozdemir and Devres, 1999). Theoretical modelsplain thedryingbehaviors of the product clearly and can be uat all process conditions, while they include many assumpticausing considerable errors. The most widely used theoretmodels are derived from Ficks second law of diffusion. Silarly, semi-theoretical models are generally derived from Ficsecondlawandmodificationsofitssimplifiedforms(othersemtheoretical models are derived by analogues with Newtons of cooling). They are easier and need fewer assumptions to using of some experimental data. On the other hand, t

are valid only within the process conditions applied (Fortes Okos, 1981; Parry, 1985). The empirical models have also silar characteristics with semi-theoretical models. They strondepend on the experimental conditions and give limited inmation about the drying behaviors of the product (Keey, 19

Theoretical Background

Isothermal conditions changing only with time may besumed to prevail within the product, because the heat tranrate within the product is two orders of magnitude greater ttherate of moisture transfer (Ozilgen and Ozdemir, 2001). It


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L

Nw

Me

Q

Mi

Ta

Q

Me

Nw

Figure 1 Schematic view of thin layer drying, if drying occurs from bothsides.

be assumed as only Eq. 5 describes the mass transfer (Whitakeret al., 1969; Young, 1969). Then Eq. 5 can be analyticallysolved

with the above assumptions, and the initial and boundary con-ditions are (Fig. 1):

t= 0, L x L, M= Mi (7)

t > 0, x = 0, d M/d x = 0 (8)

t > 0, x = L, M= Me (9)

t > 0, L x L, T = Ta (10)

Assumptions:

(i) the particle is homogenous and isotropic;(ii) the materialcharacteristics areconstant, and theshrinkage

is neglected;(iii) the pressure variations are neglected;(iv) evaporation occurs only at the surface;(v) initially moisture distribution is uniform (Eq. 7) and sym-

metrical during process (Eq. 8);(vi) surface diffusion is ended, so the moisture equilibrium

arises on the surface (Eq. 9);(vii) temperature distribution is uniform and equals to the am-

bient drying air temperature, namely the lumped system(Eq. 10);

(viii) theheat transfer is done by conduction within theproduct,and by convection outside of the product;(ix) effective moisture diffusivity is constant versus moisture

content during drying.

Then analytical solutions of Eq. 5 are given below for infiniteslab or sphere in Eq. 11, and for infinite cylinder in Eq. 12(Crank, 1975):

MR = A1

i=1

1

(2i 1)2exp

(2i 1)2 2Defft

A2

(11)

Table 1 Values of geometric constants according to the product geometry.

Product Geometry A1 A2

Infinite slab 8/ 2 4L2

Sphere 6/ 2 4r2

3-dimensional finite slab (8/ 2)3 1/(L21 +L22 + L

23)

L is the half thickness of the slice if drying occurs from both sides, or L is thethickness of the slice if drying occurs from only one side.

MR = A1

i=1

1

J20exp

J20 Defft

A2

(12)

where, Deffis the effective moisture diffusivity (m2/s), t is time

(s), MR is the fractional moisture ratio, J0 is the roots of theBessel function, and A1, A2 are geometric constants.

For multidimensional geometries such as 3-dimensional slab

the Newmans rule can be applied (Treybal, 1968). In brief, thevalues of geometric constants are shown in Table 1.MR can be determined according to the external conditions.

If the relative humidity of the drying air is constant during thedrying process, then the moisture equilibrium is constant too. Inthis respect,MR is determined as in Eq. 13. If therelative humid-ity of the drying air continuously fluctuates, then the moistureequilibrium continuously varies so MR is determined as in Eq.14 (Diamante and Munro, 1993);

MR =(Mt Me)

(Mi Me)(13)

MR = Mt

Mi(14)

where, Mi is the initial moisture content, Mt is the mean mois-ture content at time t, Me is the equilibrium moisture content,and all these values are in dry basis. If we accept that food ma-terials dry without a constant rate period, than Mi is equal tothe Mcr which is defined as the moisture content of a material atthe end of the constant rate period of drying, then Eq. 13 equalsto Eq. 15 and MR can be named as the characteristic moisturecontent ().

=(Mt Me)

(Mcr Me) (15)

Semi-Theoretical Models

Semi-theoretical models can be classified according to theirderivation as:

(i) Newtons law of cooling:These are the semi-theoretical models that are derived

by analogues with Newtons law of cooling. These modelscan be classified in sub groups as:


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a. Lewis modelb. Page model & modified forms

(ii) Ficks second law of diffusionThe models in this group are the semi-theoretical modelsthat are derived from Ficks second law of diffusion. These

models can be classified in sub groups as:a. Single term exponential model and modified formsb. Two term exponential model and modified formsc. Three term exponential model

The Models Derived From Newtons Law of Cooling.

a. Lewis (Newton) Model

This model is analogous with Newtons law of cooling somany investigators named this model as Newtons model.First, Lewis (1921) suggested that during the drying ofporous hygroscopic materials, the change of moisture con-

tent of material in the falling rate period is proportional tothe instantaneous difference between the moisture contentand the expected moisture content when it comes into equi-librium with drying air. So this concept assumed that thematerial is thin enough, or the air velocity is high, and thedrying air conditions such as the temperature and the relativehumidity are kept constant.

dM

dt= K (MMe) (16)

where, K is the drying constant (s1). In the thin layer dry-

ing concept, the drying constant is the combination of dry-ing transport properties such as moisture diffusivity, thermalconductivity, interface heat, and mass coefficients (Marinos-Kouris and Maroulis, 1995).IfK is independent from M,then Eq. 16 can be rewritten as:

MR =(Mt Me)

(Mi Me)= exp(kt) (17)

where, k is the drying constant (s1) that can be obtainedfrom the experimental data and Eq. 17 is known as the Lewis(Newton) model

b. Page ModelPage (1949) modified theLewis model to get a more accuratemodel by adding a dimensionless empirical constant (n) andapply to the mathematical modeling of drying of shelledcorns:

MR =(Mt Me)

(Mi Me)= exp(ktn) (18)

Generally, n is named as the model constant (dimensionless).c. Modified Page Models

Overhults et al. (1973) modified the Page model to describethe drying of soybeans. This modified form is generally

known as the Modified Page-I Model:

MR =(Mt Me)

(Mi Me)= exp(kt)n

In addition, White et al. (1978) used another modified foof the Page model to describe the drying of soybeans. Tform is generally known as the Modified Page-II Model

MR =(Mt Me)

(Mi Me)= exp (kt)n

Diamente and Munro (1993) used another modified foof the Page model to describe the drying of sweet potslices. This form is generally known as the Modified Pequation-II Model:

MR =(Mt Me)

(Mi Me)= expk t/ l2n

where, l is an empirical constant (dimensionless).

The Models Derived From Ficks Second Law of Diffusio

a. Henderson and Pabis (Single term) Model

Henderson and Pabis (1961) improved a model for dryby using Ficks second law of diffusion and applied the nmodel on drying of corns. As the derivation was shownthe previous section, they use Eq. 11. For sufficiently ldrying times, only the first term (i = 1) of the general sesolution of Eq. 11 can be used with small error. Accordto this assumption, Eq. 11 can be written as:

MR =(Mt Me)

(Mi Me)= A1 exp

2Deff

A2t

IfDeff is constant during drying, then Eq. 22 can be rranged by using the drying constantk as:

MR =(Mt Me)

(Mi Me)= a exp(kt)

where, a is defined as the indication of shape and genernamed as model constant (dimensionless). These constaare obtained from experimental data. Equation 23 is genally known as the Henderson and Pabis Model.

b. Logarithmic (Asymptotic) Model

Chandra and Singh (1995) proposed a new model includthe logarithmic form of Henderson and Pabis model withempirical term addition, and Yagcioglu et al. (1999) appthis model to the drying of laurel leaves.

MR =(Mt Me)

(Mi Me)= a exp (kt)+ c

where, c is an empirical constant (dimensionless).


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c. Midilli Model

Midilli et al. (2002) proposed a new model with the addi-tion of an extra empirical term that includes t to the Hen-derson and Pabis model. The new model was the com-bination of an exponential term and a linear term. They

applied this new model to the drying of pollen, mush-room, and shelled/unshelled pistachio for different dryingmethods.

MR =(Mt Me)

(Mi Me)= a exp(kt)+ bt (25)

where, b is an empirical constant (s1).d. Modified Midilli Model

Ghazanfari et al. (2006) emphasized that the indication ofshape term (a) of the Midilli model (Eq. 25) had to be 1.0 att= 0 and proposed a modification as:

MR =(Mt Me)(Mi Me)

= exp (kt)+ bt (26)

This model was not applied to a food material, but gave goodresults with flax fiber.

e. Demir et al. Model

Demir et al. (2007) proposed a new model that was similarto Henderson and Pabis, Modified Page-I, Logarithmic, andMidilli models:

MR =(Mt Me)

(Mi Me)= a exp [(kt)]n + b (27)

This model has been just proposed and applied to the dryingof green table olives and got good results.

f. Two-Term Model

Henderson (1974) proposed to use the first two term of thegeneral series solution of Ficks second law of diffusion (Eq.5) for correcting the shortcomings of the Henderson andPabis Model. Then, Glenn (1978) used this proposal in graindrying. With this argument, the new model derived as:

MR =(Mt Me)

(Mi Me)= a exp (k1t)+ b exp (k2t) (28)

where, a, b are defined as the indication of shape and gen-erally named as model constants (dimensionless), and k1, k2are the drying constants (s1). These constants are obtainedfrom experimental data and Eq. 28 is generally known as theTwo-Term Model.

g. Two-Term Exponential Model

Sharaf-Eldeen et al. (1980) modified the Two-Term modelby reducing the constant number and organizing the secondexponential terms indication of shape constant (b). Theyemphasized that b of the Two-Term model (Eq. 27) has to be(1 a) at t= 0 to get MR= 1 and proposed a modification

as:

MR=(Mt Me)

(Mi Me)=a exp (kt)+ (1 a) exp (kat) (29)

Equation 29 is generally known as the Two-Term Exponen-tial model.

h. Modified Two-Term Exponential Models

Verma et al. (1985) modified the second exponential termof the Two-Term Exponential model by adding an empiricalconstant and applied for the drying of rice.

MR =(MtMe)

(Mi Me)= a exp(kt)+ (1 a)exp(gt) (30)

This modified model (Eq. 30) is known as the Verma Model.Kaseem (1998) rearranged the Verma model by separatingthe drying constant term k from g and proposed the renewedform as:

MR=(Mt Me)

(Mi Me)=a exp (kt)+ (1 a) exp (kbt) (31)

This modified form (Eq. 31) is known as the Diffusion Ap-proach model. These two modified models were applied forsome products drying at the same time, and gave the sameresults as expected (Torul and Pehlivan, 2003; Akpinar et al.,

2003b; Gunhan et al., 2005; Akpinar, 2006a; Demir et al.,2007).

i. Modified Henderson and Pabis (Three Term Exponen-

tial) Model

Karathanos (1999) improved the Henderson and Pabis andTwo-Term models as adding the third term of the generalseries solution of Ficks second law of diffusion (Eq. 5)for correcting the shortcomings of the Henderson and Pabisand Two-Term models. Karathanos emphasized that the firstterm explains the latest part, the second term explains theintermediate part, and the third term explains the beginningpart of the drying curve (MR-t) as:

MR =(Mt Me)

(Mi Me)= a exp (kt)

+ b exp(gt)+ c exp(ht) (32)

where, a, b, and c are defined as the indication of shape andgenerally named as model constants (dimensionless), andk, g, and h are the drying constants (s1). These constantsare obtained from experimental data and Eq. 32 is generallyknown as the Modified Henderson and Pabis model.


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Empirical Models

a. Thompson ModelThompson et al. (1968) developed a model with the experi-mental results of drying of shelled corns in the temperaturerange 60150C.

t= a ln (MR)+ b [ln (MR)]2 (33)

r =NN

i=1 MRpre,iMRexp,i N

i=1 MRpre,iN

i=1 MRexp,iNN

i=1 MR2pre,i

Ni=1 MRpre,i

2NN

i=MR2exp,i

Ni=1 MRexp,i

2

where, a and b were dimensionless constants obtained fromexperimental data. This model was also used to describe thedrying characteristics of sorghum (Paulsen and Thompson,

1973).b. Wang and Singh ModelWang and Singh (1978) created a model for intermittentdrying of rough rice.

MR = 1+ bt+ at2 (34)

where, b (s1) and a (s2) were constants obtained fromexperimental data.

c. Kaleemullah Model

Kaleemullah(2002) createdan empirical model that includedMR, T, and t . They applied it to the drying of red chillies(Kaleemullah and Kailappan, 2006).

MR = expcT + bt(pT+n) (35)

where, constant c is in C1s1, constant b is in s1, p isin C1 and n is dimensionless.

Determination of Appropriate Model

Mathematical modeling of the drying of food products of-ten requires the statistical methods of regression and correlationanalysis. Linear and nonlinear regression analyses are importanttools to find the relationship between different variables, espe-cially, for which no established empirical relationship exists.

As mentioned above, thin layer drying equations require MRvariation versus t. Therefore, MR data plotted with t, and re-gression analysis was performed with the selected models todetermine the constant values that supply the best appropriate-ness of models. The validation of models can be checked withdifferent statistical methods. The most widely used method inliterature is performing correlation analysis, reduced chi-square( 2) test and root mean square error (RMSE) analysis, respec-tively. Generally, the correlation coefficient (r) is the primarycriterion for selecting the best equation to describe the dryingcurve equation and the highest r value is required (OCallaghanet al., 1971; Verma et al., 1985; Kassem, 1998; Yaldiz et al.,

2001; Midilli et al., 2002; Akpinar et al., 2003b; Wang et2007a). In addition to r , 2 and RMSE are used to determthe best fit. The highest r and the lowest 2 and RMSE valrequired to evaluate the goodness of fit (Sawhney et al., 199Yaldiz et al., 2001; Toruland Pehlivan, 2002; Midilli andKu

2003; Akpinar et al., 2003a; Lahsasni et al., 2004; Ertekin Yaldiz, 2004; Wanget al., 2007b). r, 2, andRMSE calculatcan be done by equations below:

2 =

ni=1 (MRexp,i MRpre,i)

2

N n

RMSE= 1

N

Ni=1

(MRpre,i MRexp,i)21/2

where, N is the number of observations, n is the numof constants, MRpre,i ith predicted moisture ratio valMRexp,i ith experimental moisture ratio values.

Finally, the effect of the variables on model constants be investigated by performing multiple regression analysis wmultiple combinations of different equations such as the simlinear, logarithmic, exponential, power, and the Arrhenius t(Guarte, 1996). These equation types arerelativelyeasy to usmultiple regression analysis, because they could be linearizThe other types of equations must be solved with nonlinear

gression techniques and it is too hard to find the solution to snonlinear equations if there are many parameters. After invegating the effect of experimental variables on model constathe final model has to be validated by the statistical meththat are mentioned above.

Effective Moisture Diffusivity Calculations

Diffusion in solids during drying is a complex process may involve molecular diffusion, capillary flow, Knudsen flhydrodynamic flow, or surface diffusion. With a lumped pareter model concept, all these phenomena are combined in term named as effective moisture diffusivity (Eq. 3). Equat

22 and 23 are derived for the constant values ofDeff(m2/s) for sufficiently long drying times. With a simple arrangemEq. 39 is obtained:

ln (MR) = ln (a) kt

and, k is defined as:

k = 2Deff

A2

where, A2 is the geometric constant that is shown in Table 1main geometries.


9/25


Equation 39 indicates that the variation of ln(MR) valuesversus t is linear and the slope is equal to drying constant(k). By revealing the drying, the constant effective moisturediffusivity can be calculated easily with different geometries(Eq. 40).

As a matter of fact, the drying curves have a concave formwhen the curves of ln(MR)-t are analyzed. The reason for thisis the assumption of the invariability of the effective moisturediffusion (independency ofDefffrom moisture content) duringdrying while deriving the equations (Bruin and Luyben, 1980).The concave form of drying curves is caused by variation ofthe moisture content and Deff during drying. Because of this,the slopes have to be derived from linear regression of ln(MR)-tdata.

Deffmainly varies with internal conditions such as the prod-ucts temperature, the moisture content, and the structure. Thisis harmonious with the assumptions of the thin layer concept.But all assumptions cause some errors and Deffis also affected

from external conditions. These effects are insignificant relativeto internal conditions while they cannot be disregarded in someranges. Dryingairvelocity is an example of this. Islam andFlink(1982) explained that the resistance of theexternal mass transferwas important in 2.5 m/s or lower velocities. Mulet et al. (1987)expressed that drying air velocity affected the diffusion coef-ficient at an interval of a certain flow velocity. Ece and Cihan(1993) used a temperature and air velocity dependent Arrheniustype diffusivity and Akpinar et al. (2003a) exposed a tempera-ture and air velocity dependent Arrhenius type diffusivity withexperimental data. So, for clarifying the drying characteristics,it is important to calculate Deff.

Activation Energy Calculations

As mentioned above, the factors affecting Deffare significantto clarify the drying characteristics of a foodproduct, meanwhilethe power of the effect is significant. The effect of temperatureon Deffgains importance at this point. Because temperature hastwo critical properties in this matter:

(i) temperature is one of the strongest factor affects on Deff,(ii) it is easily calculated or fixed during experiments.

As a consequence, many researchers studied the effect oftemperature on Deff, and this effect can generally be described

by an Arrhenius equation (Henderson, 1974; Mazza and LeMaguer, 1980; Suarez et al., 1980; Steffe and Singh, 1982;Pinaga et al., 1984; Carbonell et al., 1986; Crisp and Woods,1994; Madamba et al., 1996):

Deff= D0 exp

103

Ea

R (T + 273.15)

(41)

where, D0 is the Arrhenius factor that is generally defined asthe reference diffusion coefficient at infinitely high temperature(m2/s), Ea is the activation energy for diffusion (kJ/mol), R isthe universal gas constant (kJ/kmol.K). The value ofEa showsthe sensibility of the diffusivity against temperature. Namely,

26.8%

11.3%

9.9%

15.5%

8.5%

12.7%

4.2%

5.6%

4.2%

1.4%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

2007200620052004200320022001200019991998

Publishing years

Distributio

n(%)

Figure 2 Distribution of the studies according to the publishing years.

the greater value ofEa means more sensibility ofDeff to tem-

perature (Kaymak-Ertekin, 2002).To calculate Ea , Eq. 41 is arranged as:

ln(Deff) = ln(D0) 103 Ea

R

1

(T + 273.15)(42)

Equation 42 indicates that the variation of ln(Deff) versus

[1/(T+273.15)]is linearand the slope isequalto (103.Ea/R),so Ea is easily calculated with revealing the slope by derivingfrom linear regression of ln(Deff)-[1/(T + 273.15)].

If the coefficient of the determination value cannot be ashigh as required, other factors would affect the Deff and theyhave to be considered. At this condition, the most appropriate

methodis to reflectthesefactors to theD0 and perform nonlinearregression analysis to fit thedata. For microwavedrying, anotherform was developed to calculate the activation energy by Dadalet al. (2007b). They described the Deffas a function of productmass and microwave power level with an Arrhenius equation:

Deff= D0 exp

Ea m

Pm

(43)

where, m is the weight of the raw material (g), Pm is the mi-crowave output power (W), and Ea is the activation energy forthe microwave drying of the product (W/g).

In addition, Dadal et al. (2007a) used an exponential ex-

pression based on the Arrhenius equation for prediction of therelationship between drying rate constant and effective diffusiv-ity as:

k = k0 exp

Ea m

Pm

(44)

where, k is the drying rate constant predicted by the appropriatemodel and k0 is the pre-exponential constant (s1). The acti-vation energy values obtained from Eqs. 43 and 44 were quitesimilar and they showed the linear relationship between the dry-ing rate constant and effective diffusivity with Eqs. 43 and 44,


10/25

Table2

Studiesconductedonmathe

maticalmodelingofsundryingoffoodproducts

Product

Processconditions

#

Bestmodel

Effectsofprocessconditionsonmod

elconstants

Reference

Apricot

T=

2743C

(Untreated)

12

Diffusion

Approach

a=

116.304+

5615T71.40T2+

18567.2RH

TogrulandPehlivan,2004

b=

4.136+

0.1924T0.00259T2+

1.8054RH

k=

405

.219.6

T+

0.25T264RH

T=

2743C

(SO2-sulphu

red)

a=

1.3536

0.3392T+

0.00548T2+

13.64RH

b=

0.0210.00371T+

0.000098T2

0.00772RH

k=

0.00406+

0.0239T-0.000515T2

0.0498RH

T=

2743C

(NaHSO3-

sulphured)

Modified

Henderson&

Pabis

a=

31686.21537.26T+

18.52T2+

86.68RH

b=

206

32.67993.17T+

11.92T2

116.52RH

c=

9845.92

+

452.37T5.304T2+

689.51RH

k=

0.07830.00348T0.000041T2

0.01064RH

g=

3049.82149.57T+

1.81T2+

53.08RH

h=

214

0.31104.16T+

1.256T2

+14.65RH

Basil

12

ModifiedPage-II

Akpinar,2006b

Bitterleaves

8

Midilli

Sobukola

etal.,2007

Crain-crainleaves

Feverleaves

Figs

T=

2743C

(Untreated)

12

Diffusion

Approach

a=

17947.61

899.84T+

10.173T215206RH

18383.1RH

2+

689.56TRH


b=

696.75+

30.682T0.312T2+

667.47RH+

826.62RH2

24.75TRH

k=

144.51+

7.257T0.0821T2+

119.83RH+

152.98RH2

5.531TRH

Grape

T=

2743C

(pretreated)

12

Modified

Hendersonand

Pabis

a=

-10403.4

+

440.23T4.47T2-764.33RH+

10172.7RH

270.584TRH


b=

2625.76111.34T+

1.163T2+

301.24RH

1566.3

RH2

4.752TRH

c=

29575.3

+

1501.73T18.9

T250390.6RH

7998.7

RH2+

1192.85TRH

k=

181.426.875T0.0673T2138.64RH+

51.95RH2+

2.058TRH

g=

318.54

12.61T+

0.1305T2249.37RH+

320.2RH2+

2.368TRH

h=

16.690

.7479T+

0.000084T2+

3.566RH+

1.208RH2

0.091TRH

Mint

12

ModifiedPage-II

Akpinar,2006b

(Continuedonnextpage)


11/25

Table2


maticalmodelingofsundryingoffoodproducts.(

Continued)

Product

Processconditions

#

Bestmodel

Effectsofprocessconditionsonmod

elconstants

Reference

Mulberryfruits

(MorusalbaL.)

Untreated

2

Hendersonand

Pabis

Doymaz,2004b

Pretreated

Parsley

12

Verma

Akpinar,2006b

Peach

T=

2743C

(Untreated)

12

Verma

a=

4.873+

0.269T0.0000372T2+

0.252RH

k=

0.5742+

0.0317T0.000449T2

0.0956RH


g=

0.0479

0.0000262T+

0.0000361T2

0.0000128RH

Pistachio

T=

2432C

(shelled)

8

Midilli

a=

0.9975+

0.0007lnT

k=

0.1291+

0.0006lnT

Midilliet

al.,2002

n=

0.8828+

0.0008lnT

b

=0.0490+

0.0001lnT

T=

2432C

(unshelled)

a=

1.0030+

0.0003lnT

k=

0.1500+

0.0002lnT

n=

1.1044+

0.0005lnT

b

=0.0744+

0.0004lnT

Plum

T=

2743C

(pretreated)

12

Modified

Henderson&

Pabis

a=

3743.05424.11T+

7.65T2+

3849.9

RH

+

13477.76

RH2147.13TRH


b=

4354.1417.01T+

7.379T21464.73RH+

21426.01RH2109.47TRH

c=

7273.1-829T+

15.042T2+

7219.2

RH

+

30018.1R

H2314.25TRH

k=

-0.0628+

0.0000905T0.000175T2

0.1396RH

0.5232RH2+

0.000064TRH

g=

865.08

82.384T+

1.427T2164.32RH

+

3078.6R

H212.7

TRH

h=

758.05

72.23T+

1.251T2141.84RH+

2698.85RH

211.18TRH

450


12/25

Table3


maticalmodelingoffooddryingperformedwithconvectivetypebatchdryers

Product

Processconditions(oC;m/s;gwater/kgda;mm)#

Bestmodel

Effectsofprocessconditionsonmodelconstants

Reference

Apple(slice)

T=

6080

=

1.01.5

13

M

idilli

a=

1.0040840.000073T0.001

960+

3.944759

k=

0.006391+

0.000065T

+0.009775+

1.576723

Akpinar,2006a

=

8

8

1812.5

12.525

n=

1.187734+

0.002467T

0.128878202.536

b

=

0.0000820.000002T

0.000041+

0.041667

Apple(Golden)

T=

6080

=

1.03.0

14

M

idilli

a=

1.4678

0.0067Tk=

1.08350.1316n=

0.8867b

=0.0030

Mengesand

Ertekin,2006a

Applepomace

T=

75105

10

Log

arithmic

a=

271.158.91T+

0.097T23.52T3

k=

0.61+

0.02T0.0002T2+

0.0000008T3

Wangetal.,2007a

c=

267.45+

8.82T0.096T2+

0.0004T3

Apricot

T=

47.361

.74

=

0.7072.3

14

M

idilli

a=

1.0699310.001297T0.004

534+

0.005478RSC

Akpinaretal.,

2004

RSC=

02.2

5rpm

(SO2-sulphured)

k=

0.086272+

0.001775T+

0.035643+

0.009545RSC

n=

1.7058400.013076T0.167

507

0.020810RSC

b

=

0.0101220.000162T0.00

1439

0.000240RSC

T=

5080

=

0.21.5

(SO2-sulphured)

14

Log

arithmic

a=

1.13481exp(0.018352)

k=

0.001269+

0.000018T

x+

0.00105

To

gruland

Pehlivan,2003

c=

1.16416+

exp(1.6982/T)0.0138

Bagasse

T=

80120

=

0.52.0

12

Page

k=

0.49123557038+

0.0031094667H

0.0031183596869T0.0394750

7753+

0.113762212L

Vijayarajetal.,

2007

H=

924

L=

2060

n=

0.86990405+

0.238750462lo

gt

1.175456904k

Bayleaves

T=

4060

RH=

525%

15

Page

k=

exp(-4.4647+

0.07455T0.00714RH)n=

1.14325

Gunhanetal.,

2005

BlackTea

T=

80120

=

0.250.65

5

Lewis

k=

0.125631.15202exp(209.12341/Tabs)

Pa

nchariyaetal.,

2002

Carrot(slice)

T=

6090

=

0.51.5

4ModifiedPage-IIk=

42.660.3123(2L)0.8437exp(2386.6/T)

Er

enturkand

Erenturk,2007

L=

2.55

n=

5.480.0846(2L)0.1066exp(4

52.5/T)

CitrusaurantiumleavesT=

5060

RH=

4153%

13

M

idilli

a=

49.079+

1.838T0.0167T2

k=

13.604+

0.498T

0.004518T2

Mohamedetal.,

2005

. V= 0

.0277

0.0833m3/s

n=

37.4471.346T+

0.01231T2

b

=

0.451+

0.01576T

0.00014T2

Coconut(Young)

T=

5070(Osmotically

pre-dried)

L=

2.54

3

Page

k=

21.8exp(2136.9/Tabs)

Madamba,2003

n=

0.0980.082L

Dates

T=

7080(Sakievar.)

3

Page

k=

2.463+

0.0613T0.00035T

2

n=

1.228+

0.0524T

0.00032T2

Hassanand

Hobani,2000

T=

7080(Sukkarivar.)

k=

0.00000027T3.0511

n=

4.437+

0.1353T

0.00085T2

Echinaceaangustifolia

T=

1545

=

0.31.1

4ModifiedPage-IIk=

0.070.1793(2r)1.2349exp(-20.66/T)

Er

enturketal.,

2004



13/25

Table3

Studiesconductedonmathema

ticalmodelingoffooddryingperformedwithconvectivetypebatchdryers.(

Continued)

Product

Processconditions(C;m/s;gwater/kgda;mm)#

B

estmodel


Reference

r=

rootsize

(mm)

n=

0.960.0139(2r)0.0433exp(-1.73/T)

Eggplant

T=

3070

=

0.52.0

14

Midilli

a=

0.98979

0.08071lnk=

0.00160T1.55945n=

1.09877+

0.29745lnb

=

0.00062

Ertekinand

Yaldiz,2004

Figs(whole)

T=

46.160

=

1.05.0

7

Logarithmic

a=

1.12998+

0.0006324T-0.0368791-

0.00410299H

Xanthopouloset

al.,2007

H=

8.1413.32

k=

0.0898261+

0.00244127T+

0.004457210.0000864371H

c=

0.161594

0.000764116T+

0.0347936+

0.00720103H

Grape(Sultana)

T=

32.440.3

=

0.51.5

8

Two-term

a=

0.336-0.004T

k1=

7.7038.717ln

Yaldizetal.,2001

b=

0.8060.039

k2=

-0.141+

0.048lnT

Grape(Thompsonseedless)T=

5080

=

0.251.0

(pretreated)

3

Page

k=

2.91

1060.22exp(5749.05/T)

Sawhneyetal.,

1999a

n=

1.14

T=

5070

=

0.251.0

-

k=

37200000.19H0.13exp(-6032/Tabs)

Pangavhaneetal.,

2000

RH=

1323

%

n=

1.107

Greenbean

T=

5080

=

0.251.0

12

Page

k=

0.35600.1407

n=

0.7832+

0.0892ln

Yaldizand

Ertekin,2001

Greenchilli

T=

4065

RH=

1060%

2

Page

k=

0.0087590.00027T+

0.000000282T2+

0.00166

0.01058RH

+

0.009057RH2

HossainandBala,

2002

=

0.11.0

(Over/underflow)

n=

0.563021+

0.006435T+0

.088298+

0.63696RH

T=

4065

RH=

1060%

k=

0.02184+

0.000781T

0.0000068T2+

0.004522+

0.004437RH0.01335RH2

=

0.11.0

(Through

flow)

n=

0.580425+

0.00465T+1.7177

1.299121.2421RH+

1.38

45RH2

Greenpepper

T=

5080

=

0.251.0

12DiffusionApproacha=

1.6626+

1.7015

b=

0.58680.0172

Yaldizand

Ertekin,2001

k=

0.35490.1489

Hazelnut

T=

10016

0

8

T

hompson

a=

116.05+

0.656T

b=

19.89+

0.122T

Ozdemirand

Devres,1999

T=

10016

0

Mi=

12.3%

(moisturized)

3

Two-term

a=

0.535-0.00058T

k1=

0.465

Ozdemiretal.,

2000

b=

0.00058+

236248.7

T

k2=

4.52

T=

10016

0

Mi=

6.14%

(untreated)

Two-term

a=

0.434-0.00304T

k1=

0.566

b=

0.00304+

236248.7

T

k2=

5.29

T=

10016

0

Mi=

2.41%

(pre-dried)

Two-term

a=

0.714

0.00356T

k1=

0.286

b=

0.00356+

236248.7

T

k2=

2.89

452


14/25

Kale

T=

3060

L=

1050

4

Mod.P

age-I

k=

exp(8.04873836.1/Tabs)

n=

0.894653

Mw

ithigaand

O

lwal,2005

Kurut

T=

3565

11

Two-term

-

Karabulutetal.,

2

007

Onion

T=

5080

=

0.251.0

12

Two-term

a=

0.4866+

0.6424ln

k1=

0.1557+

0.1995ln

Yaldizand

E

rtekin,2001

b=

0.51430.6424ln

k2=

0.11170.0992ln

T=

5080

=

0.251.0

-Henderson

andPabisa=

1.01

Saw

hneyetal.,

1

999b

H=

6.510.5

(pretreated)

k=

122.340.31exp(-3020/Tabs)

Paddy(parboiled)T=

70150

=

0.52.0

-

Lew

is

k=

0.020.473L0.699

d

T0.478

Raoetal.,2007

Ld=

50200

Parsley

T=

5693

9

Page

k=

0.000012T0.706263

n=

0.293914T0.299815

Akpinaretal.,

2

006

Peachslice

T=

5565

6

Logari

thmic

-

Kin

gsleyetal.,

2

007

Blanchedwith%1

KMS

orAA

Pistachionuts

T=

2570

6

Page

k=

0.00209+

0.000208T+

0.005022

n=

0.844+

0.00262T0.106

Kashaninejad

e

tal.,2007

Pistachio

T=

4060

=

0.51.5

8

Mid

illi

a=

0.9968+

0.0007lnT

k=

0.1493+

0.0006lnT

Midillietal.,2002

RH=

520%(she

lled)

n=

0.9178+

0.0008lnT

b

=

0.0501+

0.0001lnT

T=

4060

=

0.51.5

a=

0.9968+

0.0003lnT

k=

0.1545+

0.0002lnT

RH=

520%(unshelled)

n=

0.9247+

0.0005lnT

b

=

0.0486+

0.0004lnT

Plum(Stanley)

T=

6080

=

1.03.0

(pretreated)

14

Mid

illi

a=

2.5729

0.3726lnT

k=

0.26430.3665

Me

ngesand

E

rtekin,2006b

n=

0.00011T2.1554

b

=

0.0044

T=

6080

=

1.03.0

(untreated)

a=

3.2180

0.5255lnT

k=

0.22880.2994

n=

0.000057T2.3144

b

=

0.0028

Pollen

T=

45

8

Mid

illi

a=

0.9987+

0.0003lnT

k=

0.2616+

0.0002lnT

Midillietal.,2002

n=

0.5869+

0.0005lnT

b

=

0.0609+

0.0004lnT

Potato(slice)

T=

6080=1.01.5

13

Mid

illi

a=

0.986173+

0.000069T+

0.005702+

0.098206k=

-0.015582+

0.000

156T+

0.013467+

0.266761

Akpinar,2006a

=

8

8

18

12.5

12.5

25

n=

1.218379+

0.000802T0.162776

138.528

b

=

0.0000085+

0.00000029T

0.00003930.0203022

PricklypearfruitT=

5060

8

Two-term

a=

2.9205+

0.1117T0.0011T2

k1=

1.16190.0439T+

0.0004T2

Lahsasnietal.,

2

004

b=

2.30990.0547T+

0.0005T2

k2=

-0.0764+

0.0027T

0.000021658T2



15/25

Table3

Studiesconductedonmath

ematicalmodelingoffooddryingperformedwithconvectivetypebatchdryers.(

Continued)

Product

Processcondition

s(C;m/s;gwater/kgda;mm)#

Bestm

odel


Reference

Pumpkin(slice)

T=

6080

=

1.01.5

13

Mid

illi

a=

0.966467+

0.000184T+

0.007

014

k=

0.005645-0.000095T

+0.003791

Akpinar,2006a

n=

0.572175+

0.009074T

0.064652

b

=

0.000050-0.000001T

0.000024

Redchillies

T=

5065

4

Kaleem

ullah

c=

0.0084766

b

=

-0.34775

Kaleemullahand

Kailappan,

2006

m=

0.00004934

n=

1.1912

T=

4065

=

0.121.02

2

Lew

is

k=

0.0034840.000222T+

0.00000366T2

0.007085RH+

0.00572RH0.00

2738

0.0012352

Hossainetal.,

2007

RH=

1060

Redpepper

T=

5570

11DiffusionApproacha=

1844.324493.320lnT

b=

1.033970exp(-12.2945/Tabs)Akpinaretal.,

2003c

k=

63319.52exp(-4973.88/Tabs)

Rice(rough)

T=

22.334.9RH

=

34.557.9%

Page

k=

-0.00209+

0.000208T+

0.005022n=

0.844+

0.00262T0.106

BasuniaandAbe,

2001

T=

535

=

0.752.5

4Henderson

andPabisa=

18.15781.49019-0.027191T

0.263827RH+0.00453363T+

0.000966809TRH+

0.00304256R

H

Igu

azetal.,2003

RH=

3070%

k=

0.003014140.000021593T+

0.0000000389067T2+

0.0000047

8

StuffedPepper

T=

5080

=

0.251.0

12

Two-term

a=

0.63150.2957

k1=

0.0224exp(4.7396)

Yaldizand

Ertekin,2001

b=

0.3679+

0.2962

k2=

0.06770.0117ln

Wheat(parboiled)T=

4060

6

Two-term

a=

0.03197T1.009

k1=

0.034

Mo

hapatraand

Rao,2005

b=

-0.032T+

1.9918

k2=

0.009

Yoghurt(strained)T=

4050=1

.02.0

9

Mid

illi

a=

1

k=

0.0005569+

0.00001205T+

0.0002047

Hayalogluetal.,

2007

n=

1.7

b

=

0.00003489-

0.00000038T0.00000542

454


16/25


Table 4 Studies conducted on mathematical modeling of food drying conducted by natural convection in a drying cupboard

Product Process conditions # Best model Effects of process conditions on model constants Reference

Mushroom T = 45C 8 Midilli a = 0.9937 + 0.0003 lnT k = 0.7039 + 0.0002 lnT Midilli et al., 2n = 0.8506 + 0.0005 lnT b = 0.0064 0.0004 lnT

Pollen a = 0.9975 + 0.0007 lnT k = 1.0638 + 0.0006 lnT

n = 0.5658 + 0.0008 lnT b = 0.0432 0.0001 lnT

and described as:

kth = Deffth(45)

where, kth is the theoretical value of drying rate constant ob-tained from Eq. 44 (s1), (Deff)th is the theoretical effective

diffusivity value obtained from Eq. 43 (m2/s) and is the em-pirical constant (m2).

STUDIES CONDUCTED ON MODELING OF FOOD

DRYING WITH THIN LAYER CONCEPT

The considerable volume of work devoted to elucidating abetter understanding of moisture transport in solids is not cov-ered in depth, and the reason for this is that, in practice, drying-rate curves have to be measured experimentally, rather than cal-culated from fundamentals (Baker, 1997). So the experimentalstudies prevent their importance in drying, especially for foodproducts, and there have been many studies done in the last 10years in literature. The distribution of the studies according tothepublishingyearswassummarizedinFig.2.Thisgraphshowsthe increasing interest to the thin layer drying investigations in

recent years.Process conditions, the product, and the drying method areimportant variables in thin layer drying modeling. The mainparameter in this article was chosen as the drying method forthe categorization of the reviewed studies.

The oldest method of drying is sun drying. Due to requiringextensive drying area and long drying time, microbial risks canappear in many products. On the contrary, it has been used

Vegetables;

21.8%

Fruits; 36.8%

Grains; 12.6%

Medical &

aromaticplants; 20.7%

Others; 8.0%

Figure 3 Distribution of the product types used in studies.

widely because of lowtechnology and energy requirementssthat modeling studies conducted on sun drying have preserits importance as shown in Table 2.

The most popular thin layer drying method in literature industrial applications is hot air drying using convection asmain heat transfer mechanism. Generally, heated air is bloto the product and the drying rate is increased with the helpthe forced convection. The mainmodeling studies executedwthis methodwithin the last 10 years were compiled and showTable3.Furthermore,themodelinginadryingcupboardwith

the effect of airflow, done for some products, was summariin Table 4.The improving effect of electrical heating methods on dry

processes, especially microwave and infrared, is strong. Thmethods canshorten thedrying time,and many modeling stufor these processes were performed with the thin layer conc(Table 5).

Furthermore, various pre-treatments are done to the raw fproducts to facilitate the drying and to improve the prodquality. These processes affect the drying kinetics directly many investigators used the thin layer concept to explain effects of various pre-treatments, especially in fruit drying. studies conducted on the effects of pre-treatments to the dry

kinetics are shown in Table 6.As mentioned above, the effective moisture diffusivit

a useful tool in explaining the drying kinetics, and activa

DC; 1

SD; 8.3%MD; 6.9%

ICD; 6.9%

ID; 4.2%

FBD; 1.4%

CBD; 70.

Figure 4 Distribution of the drying methods used in studies.


17/25

Table5

Studiesconductedonmathematicalmodelingoffooddryingwiththinlayerco

nceptandperformedbyelectricalmethods.

Product

DM

Processconditions

#

Bestmodel


Reference

Apple(slice)

ID

T=

5080C

10

ModifiedPageeq-II

k=

9.08244+

1.580765lnT

n=

11.495441.74016lnT

Togrul,2005

l=

0.628792+

0.574354lnT

ApplePomace

MD

Pm

=

150600W

Untreated

10

Page

k=

0.01783+

0.0001303Pm

n=

1.67470.00728Pm

Wangetal.,2007b

Pm

=

180900W

Hotairpre-dried

k=

0.02484+

0.000479Pm

n=

0.87040.00104Pm

ICD

T=

5575C

Untreated

10

Logarithmic

a=

20.71196+

0.72489T0.005

67T2

c=

21.800750.72728T+

0.00569T2

Sunetal.,2007

k=

0.169550.00485T+

0.000034

85T2

T=

5575C

Hotairpre-dried

Page

k=

0.112690.0034T+

0.0000261

5T2

n=

8.6026+

0.30111T

0.00221T2

Barley

ICD

I=

0.1670.5W

/cm2

=

0.30.7m/s

Page

k=

0.80495+

7.2839I2+

1.4943RH

1.66621.3368Mi

AfzalandAbe,

2000

RH=

3660%

Mi=

2540%

n=

0.97857+

0.7309I+

0.4604RH

0.41773

Carrot

ID

T=

5080C

5

Midilli

a=

64T0.716565

n=

0.117979exp(0.006983T)

Togrul,2006

k=

111T1.67037

b

=

0.000051exp(0.004993T)

Olivehusk

ICD

T=

80140C

Midilli

a=

0.96656exp(0.00032696T)

n=

1.876930.01393T+

0.00004891T2

Celmaetal.,2007

k=

0.00234+

0.00054676lnT

b

=

[564428.48+

9055.14T

37.28T2]1

Onion

ICD

I1=

0.51.0kW

/kg

=

0.10.35m/s

3

Page

k=

0.058exp(2.5681I1+

1.8410

.022L2

0.0608RH2

Wang,2002.

RH=

28.643.1%

L=

26mm

n=

1.3658

I=

2.654.42W

/cm2

T=

3545C

9

Logarithmic

a=

0.725+

0.0415I+

0.00331T+

0.054

k=

1.5730.357I0.0339T+0

.0555

JainandPathare,

2004

=

1.01.5m/s

c=

0.006510.00121I+

0.000223T

0.00584

456


18/25


Table 6 Studies conducted on the effect of pretreatment applications on the drying behaviors

Process Best DeffProduct DM conditions Pretreatments # model (m2/s) Reference

Banana CBD T = 50C = 3.1 m/s

Untreated 3 Two-term 4.3E-10 - 13.2E-10 Dandamrongrak e2002

BlanchedChilledFrozenBlanched & Frozen

Mulberry fruits(Morus alba L.)

CBD T = 50C = 1.0 m/s

Untreated 6 Logarithmic 2.23E-10 6.91E-10 Doymaz, 2004c

Dipped in HWDipped in AEEODipped in AA, then

AEEODipped in CA, then

AEEODipped in HW, then

AEEOMulberry fruits

(Morus alba

L.)

SD Untreated 2 Henderson and Pabis 4.26E-11 Doymaz, 2004b

Dipped in AEEO 4.69E-10

energy is important in describing the sensibility of Deff withtemperature. The values ofDeff and Ea calculated by the thinlayer concept were collected in Table 7. Furthermore, Ea val-ues for microwave drying calculated by the Dadal model wereshown in Table 8.

Approximately a hundred articles on the thin layer dryingmodeling have been published in the last 10 years. Replicatedstudies on the same product and method have not been reviewedin this article, only represented articles were chosen. The results

of the representing studies were interpreted and discussed toattain some general approaches in the thin layer drying of foods.Figure 3 shows the distribution of the product types used in

the studies. The most widely studied product types are fruits(36.8%) and vegetables (21.8%). But the intensity of medicaland aromatic plants is very interesting (20.7%) because they arevery suitable for thin layer drying.

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52

Number of Products

Deff(m2/s)

Figure 5 Distribution of effective moisture diffusivity values compiled fromstudies.

The distribution of the drying methods used in the studis shown in Fig. 4. This graph displays that the interest ofinvestigators to the convective type batch dryers in food dryprocesses. 70.8% of the studies reviewed have used convtive type batch dryers in their experiments. At the same tithis graph shows the increasing interest of the electrical drymethods, especially infrared drying. 18% of the reviewed sies conducted on electrical drying methods and 11.1% ofthe studies were used in various types of infrared dryers.

intensity of the infrared dryers can be explained as the harmof infrared theory and thin layer concept.Marinos-Kouris and Maroulis (1995) compiled the 37

ferent effective moisture diffusivity value intervals that wcalculated by the experiments. They expressed that the diffuities in foods had values in the range 1013 to 106 m2/s, most of them (82%) were accumulated in the region 101

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1

Number of Products

Deff(m2/s)

Figure 6 Distribution of effective moisture diffusivity values compiled studies in which the experiments were done with convective type batch dry


19/25


Table 7 Effective moisture diffusivity and activation energy values calculated by thin layer concept in literature

Product DM Process conditions Deff (m2/s) Ea (kJ/mol) Reference

Apple (slice) CBD T = 6080C = 1.01.5 m/s 8.41E-10 20.60E-10 Akpinar et al., 2003b = 8 8 1812.5 12.5 25 mm

Apple pomace CBD T = 75105C 2.03E-9 3.93E-9 24.51 Wang et al., 2007aMD Pm = 150600 W Untreated 1.05E-8 3.69E-8 Wang et al., 2007b

Pm = 180900 W Hot air pre-dried 2.99E-8 9.15E-8ICD T = 5575C Untreated 3.48E-9 6.48E-9 31.42 Sun et al., 2007

T = 5575C Hot air pre-dried 4.55E-9 8.81E-9 29.76Apricot CBD T = 5080C = 0.21.5 m/s

(SO2-sulphured)4.76E-98.32E-9 Togrul and Pehlivan,

2003Bagasse CBD T = 80120C = 0.52.0 m/s 1.63E-10 3.2E-10 19.47 Vijayaraj et al., 2007

H = 924 g/kg L = 2060 mmBasil SD 6.44E-12 Akpinar, 2006bBitter leaves SD 43.42E-10 Sobukola et al., 2007Black Tea CBD T = 80120C = 0.250.65 m/s 1.14E-11 2.98E-11 406.02 Panchariya et al.,

2002Carrot (slice) CBD T = 5070C = 0.51.0 m/s 7.76E-10 93.35E-10 28.36 Doymaz, 2004a

= 10 10 1020

20 20 mm(pretreated)

ID T = 5080C 7.30E-11 15.01E-11 22.43 Togrul, 2006Coconut (Young) CBD T = 5070C L = 2.5 4 mm 1.71E-10 5.51E-10 81.11 Madamba, 2003

(Osmoticallypre-dried)

Crain-crain leaves SD 52.91E10 Sobukola et al., 2007Fever leaves SD 48.72E10 Grape (Chasselas) CBD T = 5070C (1) 49 Azzouz et al., 2002Grape (Sultanin) CBD T = 5070C (2) 54Green bean CBD T = 5070C 2.64E-9 5.71E-9 35.43 Doymaz, 2005

FBD T = 3050C = 0.25 1.0m/s 29.57 39.47 Senadeera et al., 2003RH= 15% LD = 1:1, 2:1, 3:1

Hazelnut CBD T = 100160C 2.30E-7 11.76E-7 34.09 Ozdemir and Devres,1999

T = 100160

C Mi = 12.3 %(moisturized) 3.14E-7 30.95E-7 48.70Ozdemir et al., 2000

T = 100160C Mi = 6.14 %(untreated)

3.61E-7 21.10E-7 41.25

T = 100160C Mi = 2.41 %(pre-dried)

2.80E-7 15.65E-7 36.59

Kale CBD T = 3060C L = 1050 mm 1.49E-9 5.59E-9 36.12 Mwithiga and Olwal,2005

Kurut CBD T = 3565C 2.44E-9 3.60E-9 19.88 Karabulut et al., 2007Mint SD - 7.04E-12 - Akpinar, 2006b

CBD T = 3050C = 0.5 1.0m/s 9.28E-13 11.25E-13 61.91 82.93 Park et al., 2002T = 3560C = 4.1m/s 3.07E-9 19.41E-9 62.96 Doymaz, 2006

Mulberry fruits(Morus alba L.)

CBD T = 6080C = 1.2m/s 2.32E-10 27.60E-10 21.2 Maskan and Gou,1998

Okra MD Pm = 180900 W m = 25100 g 2.05E-9 11.91E-9 - Dadal et al., 2007bOlive cake CBD T = 50110C 3.38E-9 - 11.34E-9 17.97 Akgun and Doymaz,

2005Olive husk ICD T = 80140C 5.96E-9 15.89E-9 21.30 Celma et al., 2007Paddy (parboiled) CBD T = 70150C

= 0.52.0 m/sLd = 50200 mm

6.08E-11 - 34.40E-11(3)

21.90 - 23.88 Rao et al., 2007

Parsley SD - 4.53E-12 - Akpinar, 2006bPeach slice CBD T = 5565C

(Blanched with %1KMS or AA)

3.04E-10 4.41E-10 - Kingsley et al., 2007

Peas FBD T = 3050C = 0.251.0 m/s

RH= 15%

- 42.35 58.15 Senadeera et al., 2003

(Continued on next page)


20/25


Table 7 Effective moisture diffusivity and activation energy values calculated by thin layer concept in literature (Continued)

Product DM Process conditions Deff (m2/s) Ea (kJ/mol) Reference

Pestil SD L = 0.712.86 mm 1.93E-11 9.16E-11 - Maskan et al., 200CBD T = 5575C L = 0.712.86 mm 3.00E-11 37.6E-11 10.3 21.7

Pistachio nuts CBD T = 2570C 5.42E-11 92.9E-11 30.79 Kashaninejad et a

2007Plum (variety: Sutlej

purple)CBD T = 5565C (Untreated) 3.04E-10 4.41E-10 - Goyal et al., 2007

T = 5565C (Blanched)T = 5565C (Blanched with KMS)

Plum (Stanley) CBD T = 6080C = 1.0 3.0m/s(pretreated)

1.20E-7 4.55E-7 - Menges and Ertek2006b

T = 6080C = 1.0 3.0m/s(untreated)

1.18E-9 6.67E-9

T = 65C = 1.2m/s (Dippedin AEEO)

2.40E-10 - Doymaz, 2004d

T = 65C = 1.2m/s(untreated)

2.17E-10

Potato (slice) FBD T = 3050C = 0.25 1.0m/s - 12.32 24.27 Senadeera et al., 2RH= 15% AR = 1:1, 2:1, 3:1

Red chillies CBDT =

5065

C 3.78E-9 7.10E-9 37.76 Kaleemullah andKailappan, 200Rice (rough) CBD T = 535C

= 0.752.5 m/sRH= 3070%

5.79E-11 17.15E-11 18.50 21.04 Iguaz et al., 2003

Spinach MD Pm = 180900 Wm = 25100 g

7.6E-11 52.4E-11 - Dadali et al., 2007

Tarhana Dough ID T = 6080C L = 16 mmUntreated

4.1E-11 50.0E-11 41.6 49.5.Ibanoglu and Mask

2002T = 6080C L = 16 mm Cooked 7.7E-11 67.0E-11 20.5 24.9

Wheat (parboiled) CBD T = 4060C 1.23E-10 -2.86E-10 37.01 Mohapatra and R2005

Yoghurt (strained) CBD T = 4050C = 1.0 2.0m/s 9.5E-10 1.3E-9 26.07 Hayaloglu et al., 2

(1)Deff= D0exp(-Ea/RTabs )exp(-(dTabs + e)M) Deff= 0.0016exp(-Ea/RTabs )exp(-(0.0012Tabs+ 0.309)M)(2)D

eff

= D0exp(-Ea/RTabs )exp(-(dTabs + e)M) Deff

= 0.522exp(-Ea/RTabs )exp(-(0.0075Tabs+ 1.829)M)(3)Deff= (67.37+ 110.8 14.64Ld+ 0.5946T 4.706Ld+ 0.696L

2d 0.0369LdT)10

12

108 m2/s. In this study, 52 different diffusivity intervals werecompiled and shown in Fig. 5. The biggest Deff values were

between 105 and 106 (product number 23 to 26). The biggest4 values gained in hazelnut drying and the drying temperaturesof these experiments were between 100160C. These temper-ature values are too high for food drying, so these values werenot taken into consideration for creating general and appropriatestatistics. Except these values, the effective moisture diffusivityvalues in foods are in the range 1012 to 106 m2/s and this

range is more narrow than what Marinos-Kouris and Maroulis

Table 8 Activation energy values calculated by Dadal model

Product Process conditions Ea (W/g) Reference

Mint Pm = 180900 W 11.05(2) 12.28 (1) Ozbek and Dadali, 2007Okra m = 25100 g 5.54(1) Dadal et al., 2007a

5.70(2) Dadal et al., 2007bSpinach 9.62 (2) 10.84 (1) Dadali et al., 2007c

(1)k = k0exp(-Ea.m/Pm)(2)Deff= D0exp(-Ea .m/Pm)

expressed. The accumulation of the values is in the region 10to 108 m2/s (75%).

On the other hand, the distribution ofDeff values accordto the drying method was plotted. Figure 6 showed the distrtionofDeffvalues collectedfrom the studies reviewed, in whthe experiments were conducted with a convective type badryer. Disregarding the hazelnut values as mentioned above,accumulation of Deff values of the foods that were dried

convective type batch dryer is in the region 1010 to 108 m

(86,2%).Figure 7 is arranged according to the Deff values obtaiby electrical methods. All values of infrared drying withoutairflow were in the region 1010 to 109 m2/s (ID). Deffvafor infrared drying systems that contain airflow mechanis(ICD) appeared approximately in 108 m2/s level. This showthat the drying rate for ICD were faster as expected, becausthe enhancing effect of the airflow. In addition, the microwdryer (MD) values were higher than the convective type badryers, and this was harmonious with the theory.

During the sun drying experiments (Fig. 8), the ambient tperature in Nigeria increased up to 44C, while in Turkey


21/25


MD

MD

MD

MD

ICDICDICD

IDIDID

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1 2 3 4 5 6 7 8 9 10

Number of Products

Deff(m2/s)

Figure 7 Distribution of effective moisture diffusivity values compiled fromstudies in which the experiments were done by electrical methods.

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1 2 3 4 5 6 7 8 9

Number of Products

Deff(m2/s)

Figure 8 Distribution of effective moisture diffusivity values compiled fromstudies in which the experiments were done by sun drying.

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

0 7 14 21 28 35 42

Number of Products

Ea(kJ/mol)

Figure 9 Distribution of activation energy values compiled from studies.

maximum temperature value was measured as 36C. Because ofthe temperature difference, the values gained in Nigeria (prod-uct number 3, 4 and 5) were higher than the others, and thisshowed the critical effect of the temperature on Deff.

Finally, the activation energy values in literature were com-

piled and graphed in Fig. 9. In this graph, the black tea valuewas disregarded. Ea of black tea was 406.02 kJ/mol and thisvalue is too high according to others. As shown in Fig. 9, allother values (41 different products) are in the range of 12.32 to82.93 kJ/mol. The accumulation of the values was in the rangeof 18 to 49.5 kJ/mol (80.5%).

CONCLUSIONS

In this study, the most commonly used or newly developedthin layer drying models were shown, the determination meth-ods of the appropriate model were explained, Deff and Ea cal-

culations were expressed, and experimental studies performedwithin the last 10 years were reviewed and discussed.The main conclusions, which may be drawn from the results ofthe present study, were listed below:

a. Although there are lots of studies conducted on fruits, veg-etables, and grains, there is insufficient data in drying ofother types of foods, for example meat and fish drying.

b. The effective moisture diffusivity values in foods were inthe range of 1012 to 106 m2/s and the accumulation ofthe values was in the region 1010 to 108 m2/s (75%).In addition, 86.2% of Deff values of the foods dried in a

convective type batch dryer were in the region 10

10

to 10

8

m2/s.c. Thestudiesshowedthatelectricaldryingmethodswerefaster

than the others.d. The effect of temperature on Deffwas critical.e. The activation energy values of foods were in the range of

12.32 to 82.93 kJ/mol and 80.5% of the values were in theregion 18 to 49.5 kJ/mol.

ACKNOWLEDGEMENT

This study is a part of the MSc. Thesis titled The investiga-

tion of modeling, optimization, and exergetic analysis of dryingof olive leaves, and supported by Ege University ScientificResearch Project no. of 2007/MUH/30.

NOMENCLATURE

a empirical model constant (dimensionless)a empirical constant (s2)a1 geometric parameter in Eqs. 5, 6


22/25


A1, A2 geometric constantsAR aspect ratio (dimensionless)b empirical model constant (dimensionless)b empirical constant (s1)c empirical model constant (dimensionless)

c

empirical constant (o

C1

s1

)d empirical constant (K1)e empirical constant (dimensionless)Deff effective moisture diffusivity (m

2/s)(Deff)th theoretical value of effective moisture diffusiv-

ity (m2/s)D0 Arrhenius factor (m2/s)Ea activationenergy for diffusion (kJ/mol)or (W/g)

in Eqs. 43,44g drying constant obtained from experimental

data (s1)h drying constant obtained from experimental

data (s1)

H humidity (g water / kg dry air)i number of terms of the infinite seriesI radiation intensity (W/cm2)J0 roots of Bessel functionk, k1, k2 drying constants obtained from experimental

data (s1)k0 pre-exponential constant (s1)kth theoretical value of drying constant (s1)K drying constant (s1)K11, K22, K33 phenomenological coefficients in Eqs. 14K12, K13, K21, coupling coefficients in Eqs. 1, 2K23, K31, K32l empirical constant (dimensionless)L thickness of the diffusion path (m); slice thick-

ness (mm) in Tables 3,5,7L1, L2, L3 dimensions of finite slab (m)Ld grain depth (mm)LD length per diameter (dimensionless)m sample amount (g)M local moisture content (kg water/kg dry matter)

or (% dry basis)Mcr critical moisture content (% dry basis)Me equilibrium moisture content (% dry basis)Mi initial moisture content (% dry basis)Mt mean moisture content at time t (% dry basis)MR

fractional moisture ratio (dimensionless)MRexp,i ith experimental moisture ratio (dimensionless)MRpre,i ith predicted moisture ratio (dimensionless)n empirical model constant (dimensionless);

number of constants in Eq. 37N number of observationsNw drying rate (kg/m2s)p empirical constant (oC1)P pressure (kPa)Pm microwave output power (W)Q heat transfer rate (W)r correlation coefficient; radius (m) in Table 1

R universal gas constant (kJ/kmol.K)RH relative humidity (%)RMSE root mean square errorRSC rotary speed column (rpm)T temperature (oC)

Tabs absolute temperature (K)t time (s)x diffusion path (m) 2 reduced chi-square velocity (m/s).V volumetric flow rate (m3/s) dimensions (mm) thermal diffusivity (m2s) empirical constant defines relationship betw

Deffand Ea (m2)

characteristic moisture content (dimensionl# number of models tested

Abbreviations

AA ascorbic acid solutionAEEO alkali emulsion of ethyl oleateCA citric acid solutionCBD convective type batch dryerDC drying cupboardDM drying methodFBD fluid bed dryerHW hot waterICD infrared convective dryer (with airflow)ID infrared dryer (without airflow)

MD microwave dryerSD sun drying

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Akpinar, E.K. (2006a). Determination of suitable thin layer drying cmodel for some vegetables and fruits. Journal of Food Engineering. 7384.

Akpinar, E.K. (2006b).Mathematical modellingof thinlayer drying procesder open sun of some aromatic plants. Journal of Food Engineering. 77:870.

Akpinar, E., Midilli, A. and Bicer, Y. (2003a). Single layer drying behavof potato slices in a convective cyclone dryer and mathematical mode

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A Review of Thin Layer Drying of Foods Theory, Modeling, and Experimental Results.pdf