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A Review of Thin Layer Drying of Foods: Theory,Modeling, and Experimental ResultsZafer Erbay a & Filiz Icier ba Graduate School of Natural and Applied Sciences, Food Engineering Branch, Ege University,35100, Izmir, Turkeyb Department of Food Engineering, Faculty of Engineering, Ege University, 35100, Izmir,TurkeyPublished online: 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, DOI: 10.1080/10408390802437063

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Critical Reviews in Food Science and Nutrition, 50:441–464 (2009)Copyright C©© Taylor and Francis Group, LLCISSN: 1040-8398DOI: 10.1080/10408390802437063

A Review of Thin Layer Dryingof 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 devicethat merely removes moisture, and effective models are necessary for process design, optimization, energy integration, andcontrol. Although modeling studies in food drying are important, there is no theoretical model which neither is practical norcan it unify the calculations. Therefore the experimental studies prevent their importance in drying and thin layer dryingequations 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 appropriatemodel 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 thiscomprehensive study will be beneficial to those involved or interested in modeling, design, optimization, and analysis of fooddrying.

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

INTRODUCTION

Drying is traditionally defined as the unit operation that con-verts a liquid, solid, or semi-solid feed material into a solid prod-uct of significantly lower 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 thesublimation 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:Zafererbay@yahoo.com

The methods of drying are diversified with the purpose of theprocess. There are more than 200 types of dryers (Mujumdar,1997). For every dryer, the process conditions, such as the dry-ing chamber temperature, pressure, air velocity (if the carriergas is air), relative humidity, and the product retention time,have to be determined according to feed, product, purpose, andmethod. On the other hand, drying is an energy-intensive pro-cess and its energy consumption value is 10–15% of the totalenergy consumption in all industries in developed countries(Keey, 1972; Mujumdar, 1997). It is a very important processaccording to the main problems in the whole world such as thedepletion of fossil fuels and environmental pollution. In brief,drying is arguably the oldest, most common, most diverse, andmost energy-intensive unit operation and because of all thesefeatures, the engineering in drying processes gains importance.

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

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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 whichwould 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 and rates of heat transfer within thematerial, 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 volumeof 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 authors’knowledge. 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 MODELINGOF 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 (Strumilloand Kudra, 1986; Ozilgen and Ozdemir, 2001). The dominantdiffusion mechanism is a function of the moisture content andthe 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 internalconditions such as the moisture content, the temperature, andthe structure of the product 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 443

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 Fick’s 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 (α). For constant values of Deff and α, Equations3 and 4 can be rearranged as:

∂M

∂t= Deff

[∂2M

∂x2+ a1

x

∂M

∂x

](5)

∂T

∂t= α

[∂2T

∂x2+ a1

x

∂T

∂x

](6)

where, parameter a1 = 0 for planar geometries, a1 = 1for cylindrical shapes and a1 = 2 for spherical shapes(Ekechukwu, 1999).

The assumptions resembling the uniform temperature distri-bution and temperature equivalent of the ambient air and productcause errors. This error occurs only at the beginning of the pro-cess and it may be reduced to acceptable values with reducingthe thickness of the product (Henderson and Pabis, 1961). Withthis necessity, thin layer drying gains importance and thin layerequations are derived.

Thin Layer Drying Equations

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

Recently thin layer drying equations have been found to havewide application due to their ease of use and requiring less dataunlike in complex distributed models (such as phenomenologi-cal and coupling coefficients) (Madamba et al., 1996; Ozdemirand Devres, 1999).

Thin layer equations may be theoretical, semi-theoretical,and empirical models. The former takes into account only the in-ternal resistance to moisture transfer (Henderson, 1974; Suarezet al., 1980; Bruce, 1985; Parti, 1993), while the others consideronly the external resistance to moisture transfer between theproduct and air (Whitaker et al., 1969; Fortes and Okos, 1981;Parti, 1993; Ozdemir and Devres, 1999). Theoretical models ex-plain the drying behaviors of the product clearly and can be usedat all process conditions, while they include many assumptionscausing considerable errors. The most widely used theoreticalmodels are derived from Fick’s second law of diffusion. Simi-larly, semi-theoretical models are generally derived from Fick’ssecond law and modifications of its simplified forms (other semi-theoretical models are derived by analogues with Newton’s lawof cooling). They are easier and need fewer assumptions dueto using of some experimental data. On the other hand, theyare valid only within the process conditions applied (Fortes andOkos, 1981; Parry, 1985). The empirical models have also sim-ilar characteristics with semi-theoretical models. They stronglydepend on the experimental conditions and give limited infor-mation about the drying behaviors of the product (Keey, 1972).

Theoretical Background

Isothermal conditions changing only with time may be as-sumed to prevail within the product, because the heat transferrate within the product is two orders of magnitude greater thanthe rate of moisture transfer (Ozilgen and Ozdemir, 2001). It can

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444 Z. ERBAY AND F. ICIER

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 analytically solvedwith 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, dM/dx = 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 material characteristics are constant, and the shrinkage

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) the heat transfer is done by conduction within the product,and by convection outside of the product;

(ix) effective moisture diffusivity is constant versus moisturecontent 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)2π2Defft

A2

](11)

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

Product Geometry A1 A∗2

Infinite slab 8/π2 4L2

Sphere 6/π2 4r2

3-dimensional finite slab (8/π2)3 1/(L21 + L2

2 + L23)

∗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

J 20

exp

[−

J 20 Defft

A2

](12)

where, Deff is 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 slabthe Newman’s 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 the relative 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 (φ).

φ = (Mt − Me)

(Mcr − Me)(15)

Semi-Theoretical Models

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

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

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

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A REVIEW OF THIN LAYER DRYING OF FOODS 445

a. Lewis modelb. Page model & modified forms

(ii) Fick’s second law of diffusionThe models in this group are the semi-theoretical modelsthat are derived from Fick’s second law of diffusion. Thesemodels 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 Newton’s Law of Cooling.

a. Lewis (Newton) ModelThis model is analogous with Newton’s law of cooling somany investigators named this model as Newton’s 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 (M − Me) (16)

where, K is the drying constant (s−1). 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).If K 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 (s−1) that can be obtainedfrom the experimental data and Eq. 17 is known as the Lewis(Newton) model

b. Page ModelPage (1949) modified the Lewis 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 (19)

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

MR = (Mt − Me)

(Mi − Me)= exp − (kt)n (20)

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

MR = (Mt − Me)

(Mi − Me)= exp −k

(t/ l2

)n(21)

where, l is an empirical constant (dimensionless).

The Models Derived From Fick’s Second Law of Diffusion.

a. Henderson and Pabis (Single term) ModelHenderson and Pabis (1961) improved a model for dryingby using Fick’s second law of diffusion and applied the newmodel on drying of corns. As the derivation was shown inthe previous section, they use Eq. 11. For sufficiently longdrying times, only the first term (i = 1) of the general seriessolution of Eq. 11 can be used with small error. Accordingto this assumption, Eq. 11 can be written as:

MR = (Mt − Me)

(Mi − Me)= A1 exp

(−

π2DeffA2

t

)(22)

If Deff is constant during drying, then Eq. 22 can be rear-ranged by using the drying constantk as:

MR = (Mt − Me)

(Mi − Me)= a exp (−kt) (23)

where, a is defined as the indication of shape and generallynamed as model constant (dimensionless). These constantsare obtained from experimental data. Equation 23 is gener-ally known as the Henderson and Pabis Model.

b. Logarithmic (Asymptotic) ModelChandra and Singh (1995) proposed a new model includingthe logarithmic form of Henderson and Pabis model with anempirical term addition, and Yagcioglu et al. (1999) appliedthis model to the drying of laurel leaves.

MR = (Mt − Me)

(Mi − Me)= a exp (−kt) + c (24)

where, c is an empirical constant (dimensionless).

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446 Z. ERBAY AND F. ICIER

c. Midilli ModelMidilli 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. Theyapplied 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) + b∗t (25)

where, b∗ is an empirical constant (s−1).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) + b∗t (26)

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

e. Demir et al. ModelDemir 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 ModelHenderson (1974) proposed to use the first two term of thegeneral series solution of Fick’s 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, k2

are the drying constants (s−1). These constants are obtainedfrom experimental data and Eq. 28 is generally known as theTwo-Term Model.

g. Two-Term Exponential ModelSharaf-Eldeen et al. (1980) modified the Two-Term modelby reducing the constant number and organizing the secondexponential term’s 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 ModelsVerma 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 = (Mt − Me)

(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) ModelKarathanos (1999) improved the Henderson and Pabis andTwo-Term models as adding the third term of the generalseries solution of Fick’s 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 (s−1). These constantsare obtained from experimental data and Eq. 32 is generallyknown as the Modified Henderson and Pabis model.

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A REVIEW OF THIN LAYER DRYING OF FOODS 447

Empirical Models

a. Thompson ModelThompson et al. (1968) developed a model with the experi-mental results of drying of shelled corns in the temperaturerange 60–150◦C.

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

r = N∑N

i=1 MRpre,iMRexp,i − ∑Ni=1 MRpre,i

∑Ni=1 MRexp,i√(

N∑N

i=1 MR2pre,i − (∑N

i=1 MRpre,i

)2)(N

∑Ni= MR2

exp,i − (∑Ni=1 MRexp,i

)2) (36)

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 + b∗t + a∗t2 (34)

where, b∗ (s−1) and a∗ (s−2) were constants obtained fromexperimental data.

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

MR = exp −c∗T + b∗t (pT +n) (35)

where, constant c∗ is in ◦C−1s−1, constant b∗ is in s−1, p isin ◦C−1 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(χ2) 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 (O’Callaghanet al., 1971; Verma et al., 1985; Kassem, 1998; Yaldiz et al.,

2001; Midilli et al., 2002; Akpinar et al., 2003b; Wang et al.,2007a). In addition to r , χ2 and RMSE are used to determinethe best fit. The highest r and the lowest χ2 and RMSE valuesrequired to evaluate the goodness of fit (Sawhney et al., 1999a;Yaldiz et al., 2001; Torul and Pehlivan, 2002; Midilli and Kucuk,2003; Akpinar et al., 2003a; Lahsasni et al., 2004; Ertekin andYaldiz, 2004; Wang et al., 2007b). r, χ2, and RMSE calculationscan be done by equations below:

χ2 =∑n

i=1 (MRexp,i − MRpre,i)2

N − n(37)

RMSE =[

1

N

N∑i=1

(MRpre,i − MRexp,i)2

]1/2

(38)

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

Finally, the effect of the variables on model constants canbe investigated by performing multiple regression analysis withmultiple combinations of different equations such as the simplelinear, logarithmic, exponential, power, and the Arrhenius type(Guarte, 1996). These equation types are relatively easy to use inmultiple regression analysis, because they could be linearized.The other types of equations must be solved with nonlinear re-gression techniques and it is too hard to find the solution to suchnonlinear equations if there are many parameters. After investi-gating the effect of experimental variables on model constants,the final model has to be validated by the statistical methodsthat are mentioned above.

Effective Moisture Diffusivity Calculations

Diffusion in solids during drying is a complex process thatmay involve molecular diffusion, capillary flow, Knudsen flow,hydrodynamic flow, or surface diffusion. With a lumped param-eter model concept, all these phenomena are combined in oneterm named as effective moisture diffusivity (Eq. 3). Equations22 and 23 are derived for the constant values of Deff (m2/s) andfor sufficiently long drying times. With a simple arrangement,Eq. 39 is obtained:

ln (MR) = ln (a) − kt (39)

and, k is defined as:

k = −π2Deff

A2(40)

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

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448 Z. ERBAY AND F. ICIER

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 of Deff from 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.

Deff mainly varies with internal conditions such as the prod-uct’s temperature, the moisture content, and the structure. Thisis harmonious with the assumptions of the thin layer concept.But all assumptions cause some errors and Deff is also affectedfrom external conditions. These effects are insignificant relativeto internal conditions while they cannot be disregarded in someranges. Drying air velocity is an example of this. Islam and Flink(1982) explained that the resistance of the external 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 Deff are significantto clarify the drying characteristics of a food product, meanwhilethe power of the effect is significant. The effect of temperatureon Deff gains 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 describedby 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 of Ea 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

Dis

trib

utio

n (%

)

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

the greater value of Ea means more sensibility of Deff 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 linear and the slope is equal to (−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 appropriatemethod is to reflect these factors to the D0 and perform nonlinearregression analysis to fit the data. For microwave drying, anotherform was developed to calculate the activation energy by Dadalıet al. (2007b). They described the Deff as a function of productmass and microwave power level with an Arrhenius equation:

Deff = D0 exp

(−Eam

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, Dadalı 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

(−Eam

Pm

)(44)

where, k is the drying rate constant predicted by the appropriatemodel and k0 is the pre-exponential constant (s−1). 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,

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embe

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13

Tabl

e2

Stud

ies

cond

ucte

don

mat

hem

atic

alm

odel

ing

ofsu

ndr

ying

offo

odpr

oduc

ts

Prod

uct

Proc

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cond

ition

s#

Bes

tmod

elE

ffec

tsof

proc

ess

cond

ition

son

mod

elco

nsta

nts

Ref

eren

ce

Apr

icot

T=

27–4

3◦C

(Unt

reat

ed)

12D

iffu

sion

App

roac

ha

=−1

16.3

04+

5615

T–

71.4

0T2+

1856

7.2R

HTo

grul

and

Pehl

ivan

,200

4

b=

−4.1

36+

0.19

24T

–0.

0025

9T2+

1.80

54R

Hk

=40

5.2

–19

.6T

+0.

25T

2–

64R

HT

=27

–43◦

C(S

O2-s

ulph

ured

)a

=−1

.353

6–

0.33

92T

+0.

0054

8T2+

13.6

4RH

b=

0.02

1–

0.00

371T

+0.

0000

98T

2

–0.

0077

2RH

k=

−0.0

0406

+0.

0239

T-

0.00

0515

T2

–0.

0498

RH

T=

27–4

3◦C

(NaH

SO3-

sulp

hure

d)

Mod

ified

Hen

ders

on&

Pabi

s

a=

3168

6.2

–15

37.2

6T+

18.5

2T2+

86.6

8RH

b=

2063

2.67

–99

3.17

T+

11.9

2T2

–11

6.52

RH

c=

−984

5.92

+45

2.37

T–

5.30

4T2+

689.

51R

Hk

=0.

0783

–0.

0034

8T–

0.00

0041

T2

–0.

0106

4RH

g=

3049

.82

–14

9.57

T+

1.81

T2+

53.0

8RH

h=

2140

.31

–10

4.16

T+

1.25

6T2

+14

.65R

HB

asil

—12

Mod

ified

Page

-II

—A

kpin

ar,2

006b

Bitt

erle

aves

—8

Mid

illi

—So

buko

laet

al.,

2007

Cra

in-c

rain

leav

esFe

ver

leav

esFi

gsT

=27

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C(U

ntre

ated

)12

Dif

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a=

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7.61

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2–

1520

6RH

–18

383.

1RH

2+

689.

56T

RH

Togr

ulan

dPe

hliv

an,2

004

b=

–696

.75

+30

.682

T–

0.31

2T2+

667.

47R

H+

826.

62R

H2

–24

.75T

RH

k=

–144

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+7.

257T

–0.

0821

T2+

119.

83R

H+

152.

98R

H2

–5.

531T

RH

Gra

peT

=27

–43◦

C(p

retr

eate

d)12

Mod

ified

Hen

ders

onan

dPa

bis

a=

-104

03.4

+44

0.23

T–

4.47

T2

-76

4.33

RH

+10

172.

7RH

2–

70.5

84T

RH

Togr

ulan

dPe

hliv

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004

b=

2625

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1.16

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RH

c=

–295

75.3

+15

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T2

–50

390.

6RH

–79

98.7

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2+

1192

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k=

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6.87

5T–

0.06

73T

2–

138.

64R

H+

51.9

5RH

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2.05

8TR

Hg

=31

8.54

–12

.61T

+0.

1305

T2

–24

9.37

RH

+32

0.2R

H2+

2.36

8TR

Hh

=16

.69

–0.

7479

T+

0.00

0084

T2+

3.56

6RH

+1.

208R

H2

–0.

091T

RH

Min

t—

12M

odifi

edPa

ge-I

I—

Akp

inar

,200

6b(C

onti

nued

onne

xtpa

ge)

449

Dow

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by [

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es ]

at 0

9:42

17

Sept

embe

r 20

13

Tabl

e2

Stud

ies

cond

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don

mat

hem

atic

alm

odel

ing

ofsu

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offo

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ts.(

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Proc

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cond

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s#

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tmod

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proc

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=–4

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269T

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0000

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2+

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k=

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+0.

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128R

HPi

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(she

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=0.

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lnT

k=

0.12

91+

0.00

06ln

TM

idill

ieta

l.,20

02

n=

0.88

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0.00

08ln

Tb

∗=

0.04

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0.00

01ln

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T=

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(uns

helle

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0030

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0003

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00+

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02ln

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0.00

05ln

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Plum

T=

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(pre

trea

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12M

odifi

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ende

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a=

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–42

4.11

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7.65

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3849

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7.76

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Togr

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b=

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379T

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c=

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829T

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7219

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4.25

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8+

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0090

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0175

T2

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1396

RH

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0.00

0064

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Hg

=86

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–82

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T+

1.42

7T2

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4.32

RH

+30

78.6

RH

2–

12.7

TR

Hh

=75

8.05

–72

.23T

+1.

251T

2–

141.

84R

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.85R

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450

Dow

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ded

by [

Was

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ton

Stat

e U

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rsity

Lib

rari

es ]

at 0

9:42

17

Sept

embe

r 20

13

Tabl

e3

Stud

ies

cond

ucte

don

mat

hem

atic

alm

odel

ing

offo

oddr

ying

perf

orm

edw

ithco

nvec

tive

type

batc

hdr

yers

Prod

uct

Proc

ess

cond

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s(o

C;m

/s;g

wat

er/k

gda

;mm

)#

Bes

tmod

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ffec

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proc

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cond

ition

son

mod

elco

nsta

nts

Ref

eren

ce

App

le(s

lice)

T=

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0υ

=1.

0–1.

513

Mid

illi

a=

1.00

4084

–0.

0000

73T

–0.

0019

60υ+

3.94

4759

ω

k=

–0.0

0639

1+

0.00

0065

T

+0.

0097

75υ+

1.57

6723

ω

Akp

inar

,200

6a

ω=

8×

8×

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12.5

×12

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25n

=1.

1877

34+

0.00

2467

T

–0.

1288

78υ

–20

2.53

6ωb

∗=

0.00

0082

–0.

0000

02T

–0.

0000

41υ+

0.04

1667

ω

App

le(G

olde

n)T

=60

–80

υ=

1.0–

3.0

14M

idill

ia

=1.

4678

−−0

.006

7Tk

=1.

0835

υ0.

1316

n=

0.88

67b

∗=

0.00

30M

enge

san

dE

rtek

in,2

006a

App

lepo

mac

eT

=75

–105

10L

ogar

ithm

ica

=27

1.15

–8.

91T

+0.

097T

2–

3.52

T3

k=

–0.6

1+

0.02

T–

0.00

02T

2+

0.00

0000

8T3

Wan

get

al.,

2007

a

c=

–267

.45

+8.

82T

–0.

096T

2+

0.00

04T

3

Apr

icot

T=

47.3

–61.

74υ

=0.

707–

2.3

14M

idill

ia

=1.

0699

31–

0.00

1297

T–

0.00

4534

υ+

0.00

5478

RSC

Akp

inar

etal

.,20

04R

SC=

0–2.

25rp

m(S

O2-s

ulph

ured

)k

=–0

.086

272

+0.

0017

75T

+0.

0356

43υ+

0.00

9545

RSC

n=

1.70

5840

–0.

0130

76T

–0.

1675

07υ

–0.

0208

10R

SCb

∗=

0.01

0122

–0.

0001

62T

–0.

0014

39υ

–0.

0002

40R

SCT

=50

–80

υ=

0.2–

1.5

(SO

2-s

ulph

ured

)14

Log

arith

mic

a=

1.13

481e

xp(0

.018

352υ

)k

=0.

0012

69+

0.00

0018

T

x+

0.00

105υ

Togr

ulan

dPe

hliv

an,2

003

c=

–1.1

6416

+ex

p(1.

6982

/T)

–0.

0138

υ

Bag

asse

T=

80–1

20υ

=0.

5–2.

012

Page

k=

0.49

1235

5703

8+

0.00

3109

4667

H–

0.00

3118

3596

869T

–0.

0394

7507

753υ

+0.

1137

6221

2L

Vija

yara

jeta

l.,20

07

H=

9–24

L=

20–6

0n

=–0

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9040

5+

0.23

8750

462l

ogt

–1.

1754

5690

4kB

ayle

aves

T=

40–6

0R

H=

5–25

%15

Page

k=

exp(

-4.4

647

+0.

0745

5T–

0.00

714R

H)

n=

1.14

325

Gun

han

etal

.,20

05B

lack

Tea

T=

80–1

20υ

=0.

25–0

.65

5L

ewis

k=

0.12

563υ

1.15

202ex

p(−2

09.1

2341

/Tabs)

Panc

hari

yaet

al.,

2002

Car

rot(

slic

e)T

=60

–90

υ=

0.5–

1.5

4M

odifi

edPa

ge-I

Ik

=42

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0.31

23(2

L)−

0.84

37ex

p(–2

386.

6/T

)E

rent

urk

and

Ere

ntur

k,20

07L

=2.

5–5

n=

5.48

υ−0

.084

6(2

L)−

0.10

66ex

p(–4

52.5

/T)

Cit

rus

aura

ntiu

mle

aves

T=

50–6

0R

H=

41–5

3%13

Mid

illi

a=

–49.

079

+1.

838T

–0.

0167

T2

k=

–13.

604

+0.

498T

–0.

0045

18T

2M

oham

edet

al.,

2005

. V= 0.

0277

−−0

.083

3m3/s

n=

37.4

47–

1.34

6T+

0.01

231T

2b

∗=

–0.4

51+

0.01

576T

–0.

0001

4T2

Coc

onut

(You

ng)

T=

50–7

0(O

smot

ical

lypr

e-dr

ied)

L=

2.5–

43

Page

k=

21.8

exp(

–213

6.9/

Tabs)

Mad

amba

,200

3

n=

0.09

8–

0.08

2LD

ates

T=

70–8

0(S

akie

var.)

3Pa

gek

=–2

.463

+0.

0613

T–

0.00

035T

2n

=–1

.228

+0.

0524

T–

0.00

032T

2H

assa

nan

dH

oban

i,20

00T

=70

–80

(Suk

kari

var.)

k=

0.00

0000

27T

3.05

11n

=–4

.437

+0.

1353

T–

0.00

085T

2

Ech

inac

eaan

gust

ifol

iaT

=15

–45

υ=

0.3–

1.1

4M

odifi

edPa

ge-I

Ik

=0.

07υ

0.17

93(2

r)−

1.23

49ex

p(-2

0.66

/T)

Ere

ntur

ket

al.,

2004

(Con

tinu

edon

next

page

)

451

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ded

by [

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at 0

9:42

17

Sept

embe

r 20

13

Tabl

e3

Stud

ies

cond

ucte

don

mat

hem

atic

alm

odel

ing

offo

oddr

ying

perf

orm

edw

ithco

nvec

tive

type

batc

hdr

yers

.(C

onti

nued

)

Prod

uct

Proc

ess

cond

ition

s(◦

C;m

/s;g

wat

er/k

gda

;mm

)#

Bes

tmod

elE

ffec

tsof

proc

ess

cond

ition

son

mod

elco

nsta

nts

Ref

eren

ce

r=

root

size

(mm

)n

=0.

96υ

−0.0

139(2

r)−

0.04

33ex

p(-1

.73/

T)

Egg

plan

tT

=30

–70

υ=

0.5–

2.0

14M

idill

ia

=0.

9897

9−

0.08

071

lnυk

=0.

0016

0T1.

5594

5n

=1.

0987

7+

0.29

745

lnυb

∗=

0.00

062

Ert

ekin

and

Yal

diz,

2004

Figs

(who

le)

T=

46.1

–60

υ=

1.0–

5.0

7L

ogar

ithm

ica

=1.

1299

8+

0.00

0632

4T-

0.03

6879

1υ-

0.00

4102

99H

Xan

thop

oulo

set

al.,

2007

H=

8.14

–13.

32k

=−0

.089

8261

+0.

0024

4127

T+

0.00

4457

21υ

−0.0

0008

6437

1Hc

=−0

.161

594

−0.

0007

6411

6T+

0.03

4793

6υ+

0.00

7201

03H

Gra

pe(S

ulta

na)

T=

32.4

–40.

3υ

=0.

5–1.

58

Two-

term

a=

0.33

6-

0.00

4Tk

1=

7.70

3–

8.71

7ln

υY

aldi

zet

al.,

2001

b=

0.80

6υ−0

.039

k2

=-0

.141

+0.

048

lnT

Gra

pe(T

hom

pson

seed

less

)T

=50

–80

υ=

0.25

–1.0

(pre

trea

ted)

3Pa

gek

=2.

91×

106υ

0.22

exp(

5749

.05/

T)

Saw

hney

etal

.,19

99a

n=

1.14

T=

50–7

0υ

=0.

25–1

.0-

k=

3720

000υ

0.19

H−0

.13ex

p(-6

032/

Tabs)

Pang

avha

neet

al.,

2000

RH

=13

–23%

n=

1.10

7G

reen

bean

T=

50–8

0υ

=0.

25–1

.012

Page

k=

0.35

60–

0.14

07υ

n=

0.78

32+

0.08

92ln

υY

aldi

zan

dE

rtek

in,2

001

Gre

ench

illi

T=

40–6

5R

H=

10–6

0%2

Page

k=

0.00

8759

–0.

0002

7T+

0.00

0000

282T

2+

0.00

166υ

–0.

0105

8RH

+0.

0090

57R

H2

Hos

sain

and

Bal

a,20

02

υ=

0.1–

1.0

(Ove

r/un

derfl

ow)

n=

0.56

3021

+0.

0064

35T

+0.

0882

98υ

+0.

6369

6RH

T=

40–6

5R

H=

10–6

0%k

=−0

.021

84+

0.00

0781

T–

0.00

0006

8T2+

0.00

4522

υ+

0.00

4437

RH

–0.

0133

5RH

2

υ=

0.1–

1.0

(Thr

ough

flow

)n

=0.

5804

25+

0.00

465T

+1.

7177

υ–

1.29

91υ

2–

1.24

21R

H+

1.38

45R

H2

Gre

enpe

pper

T=

50–8

0υ

=0.

25–1

.012

Dif

fusi

onA

ppro

ach

a=

−1.6

626

+1.

7015

υb

=0.

5868

–0.

0172

υY

aldi

zan

dE

rtek

in,2

001

k=

0.35

49–

0.14

89υ

Haz

elnu

tT

=10

0–16

08

Tho

mps

ona

=−1

16.0

5+

0.65

6Tb

=−1

9.89

+0.

122T

Ozd

emir

and

Dev

res,

1999

T=

100–

160

Mi=

12.3

%(m

oist

uriz

ed)

3Tw

o-te

rma

=0.

535

-0.

0005

8Tk

1=

0.46

5O

zdem

iret

al.,

2000

b=

0.00

058

+23

6248

.7T

k2

=4.

52T

=10

0–16

0M

i=

6.14

%(u

ntre

ated

)Tw

o-te

rma

=0.

434

-0.

0030

4Tk

1=

0.56

6

b=

0.00

304

+23

6248

.7T

k2

=5.

29T

=10

0–16

0M

i=

2.41

%(p

re-d

ried

)Tw

o-te

rma

=0.

714

−0.

0035

6Tk

1=

0.28

6

b=

0.00

356

+23

6248

.7T

k2

=2.

89

452

Dow

nloa

ded

by [

Was

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ton

Stat

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es ]

at 0

9:42

17

Sept

embe

r 20

13

Kal

eT

=30

–60

L=

10–5

04

Mod

.Pag

e-I

k=

exp(

8.04

87–

3836

.1/T

abs)

n=

0.89

4653

Mw

ithig

aan

dO

lwal

,200

5K

urut

T=

35–6

511

Two-

term

-K

arab

ulut

etal

.,20

07O

nion

T=

50–8

0υ

=0.

25–1

.012

Two-

term

a=

0.48

66+

0.64

24ln

υk

1=

0.15

57+

0.19

95ln

υY

aldi

zan

dE

rtek

in,2

001

b=

0.51

43–

0.64

24ln

υk

2=

0.11

17–

0.09

92ln

υ

T=

50–8

0υ

=0.

25–1

.0-

Hen

ders

onan

dPa

bis

a=

1.01

Saw

hney

etal

.,19

99b

H=

6.5–

10.5

(pre

trea

ted)

k=

122.

34υ

0.31

exp(

-302

0/T

abs)

Padd

y(p

arbo

iled)

T=

70–1

50υ

=0.

5–2.

0-

Lew

isk

=0.

02υ

0.47

3L

−0.6

99d

T0.

478

Rao

etal

.,20

07L

d=

50—

200

Pars

ley

T=

56–9

39

Page

k=

0.00

0012

T0.

7062

63n

=0.

2939

14T

0.29

9815

Akp

inar

etal

.,20

06Pe

ach

slic

eT

=55

–65

6L

ogar

ithm

ic-

Kin

gsle

yet

al.,

2007

Bla

nche

dw

ith%

1K

MS

orA

APi

stac

hio

nuts

T=

25–7

06

Page

k=

−0.0

0209

+0.

0002

08T

+0.

0050

2υ2

n=

0.84

4+

0.00

262T

–0.

106υ

Kas

hani

neja

det

al.,

2007

Pist

achi

oT

=40

–60

υ=

0.5–

1.5

8M

idill

ia

=0.

9968

+0.

0007

lnT

k=

0.14

93+

0.00

06ln

TM

idill

ieta

l.,20

02R

H=

5–20

%(s

helle

d)n

=0.

9178

+0.

0008

lnT

b∗

=0.

0501

+0.

0001

lnT

T=

40–6

0υ

=0.

5–1.

5a

=0.

9968

+0.

0003

lnT

k=

0.15

45+

0.00

02ln

T

RH

=5–

20%

(uns

helle

d)n

=0.

9247

+0.

0005

lnT

b∗

=0.

0486

+0.

0004

lnT

Plum

(Sta

nley

)T

=60

–80

υ=

1.0–

3.0

(pre

trea

ted)

14M

idill

ia

=2.

5729

−0.

3726

lnT

k=

0.26

43υ

0.36

65M

enge

san

dE

rtek

in,2

006b

n=

0.00

011T

2.15

54b

∗=

−0.0

044

T=

60–8

0υ

=1.

0–3.

0(u

ntre

ated

)a

=3.

2180

−0.

5255

lnT

k=

0.22

88υ

0.29

94

n=

0.00

0057

T2.

3144

b∗

=−0

.002

8Po

llen

T=

458

Mid

illi

a=

0.99

87+

0.00

03ln

Tk

=0.

2616

+0.

0002

lnT

Mid

illie

tal.,

2002

n=

0.58

69+

0.00

05ln

Tb

∗=

0.06

09+

0.00

04ln

T

Pota

to(s

lice)

T=

60–8

0υ

=1.

0–1.

513

Mid

illi

a=

0.98

6173

+0.

0000

69T

+0.

0057

02υ+

0.09

8206

ωk

=-0

.015

582

+0.

0001

56T

+0.

0134

67υ+

0.26

6761

ω

Akp

inar

,200

6a

ω=

8×

8×

18−

12.5

×12

.5×

25n

=1.

2183

79+

0.00

0802

T–

0.16

2776

υ–

138.

528ω

b∗

=0.

0000

085

+0.

0000

0029

T–

0.00

0039

3υ–

0.02

0302

2ωPr

ickl

ype

arfr

uit

T=

50–6

08

Two-

term

a=

−2.9

205

+0.

1117

T–

0.00

11T

2k

1=

1.16

19–

0.04

39T

+0.

0004

T2

Lah

sasn

ieta

l.,20

04b

=2.

3099

–0.

0547

T+

0.00

05T

2k

2=

-0.0

764

+0.

0027

T

–0.

0000

2165

8T2

(Con

tinu

edon

next

page

)

453

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at 0

9:42

17

Sept

embe

r 20

13

Tabl

e3

Stud

ies

cond

ucte

don

mat

hem

atic

alm

odel

ing

offo

oddr

ying

perf

orm

edw

ithco

nvec

tive

type

batc

hdr

yers

.(C

onti

nued

)

Prod

uct

Proc

ess

cond

ition

s(◦

C;m

/s;g

wat

er/k

gda

;mm

)#

Bes

tmod

elE

ffec

tsof

proc

ess

cond

ition

son

mod

elco

nsta

nts

Ref

eren

ce

Pum

pkin

(slic

e)T

=60

–80

υ=

1.0–

1.5

13M

idill

ia

=0.

9664

67+

0.00

0184

T+

0.00

7014

υk

=0.

0056

45-

0.00

0095

T

+0.

0037

91υ

Akp

inar

,200

6a

n=

0.57

2175

+0.

0090

74T

–0.

0646

52υ

b∗

=0.

0000

50-

0.00

0001

T–

0.00

0024

υ

Red

chill

ies

T=

50–6

54

Kal

eem

ulla

hc∗

=0.

0084

766

b∗

=-0

.347

75K

alee

mul

lah

and

Kai

lapp

an,

2006

m=

0.00

0049

34n

=1.

1912

T=

40–6

5υ

=0.

12–1

.02

2L

ewis

k=

0.00

3484

–0.

0002

22T

+0.

0000

0366

T2

–0.

0070

85R

H+

0.00

572R

H0.

0027

38υ

–0.

0012

35υ

2

Hos

sain

etal

.,20

07

RH

=10

–60

Red

pepp

erT

=55

–70

11D

iffu

sion

App

roac

ha

=18

44.3

24–

493.

320

lnT

b=

1.03

3970

exp(

-12.

2945

/Tabs)

Akp

inar

etal

.,20

03c

k=

6331

9.52

exp(

-497

3.88

/Tabs)

Ric

e(r

ough

)T

=22

.3–3

4.9

RH

=34

.5–5

7.9%

—Pa

gek

=-0

.002

09+

0.00

0208

T+

0.00

502υ

2n

=0.

844

+0.

0026

2T–

0.10

6υB

asun

iaan

dA

be,

2001

T=

5–35

υ=

0.75

–2.5

4H

ende

rson

and

Pabi

sa

=18

.157

8–

1.49

019υ

-0.0

2719

1T–

0.26

3827

RH

+0.0

0453

363T

υ+

0.00

0966

809T

RH

+0.

0030

4256

RH

υ

Igua

zet

al.,

2003

RH

=30

–70%

k=

0.00

3014

14–

0.00

0021

593T

+0.

0000

0003

8906

7T2+

0.00

0004

78υ

Stuf

fed

Pepp

erT

=50

–80

υ=

0.25

–1.0

12Tw

o-te

rma

=0.

6315

–0.

2957

υk

1=

0.02

24ex

p(4.

7396

υ)

Yal

diz

and

Ert

ekin

,200

1b

=0.

3679

+0.

2962

υk

2=

0.06

77–

0.01

17ln

υ

Whe

at(p

arbo

iled)

T=

40–6

06

Two-

term

a=

0.03

197T

–1.

009

k1

=−0

.034

Moh

apat

raan

dR

ao,2

005

b=

-0.0

32T

+1.

9918

k2

=−0

.009

Yog

hurt

(str

aine

d)T

=40

–50

υ=

1.0–

2.0

9M

idill

ia

=1

k=

−0.0

0055

69+

0.00

0012

05T

+0.

0002

047υ

Hay

alog

luet

al.,

2007

n=

1.7

b∗

=−0

.000

0348

9-

0.00

0000

38T

–0.

0000

0542

υ

454

Dow

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ded

by [

Was

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at 0

9:42

17

Sept

embe

r 20

13

A REVIEW OF THIN LAYER DRYING OF FOODS 455

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 = 45◦C 8 Midilli a = 0.9937 + 0.0003 lnT k = 0.7039 + 0.0002 lnT Midilli et al., 2002n = 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 = λDeffth (45)

where, kth is the theoretical value of drying rate constant ob-tained from Eq. 44 (s−1), (Deff)th is the theoretical effective

diffusivity value obtained from Eq. 43 (m2/s) and λ is the em-pirical constant (m−2).

STUDIES CONDUCTED ON MODELING OF FOODDRYING 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 tothe publishing years was summarized in Fig. 2. This graph showsthe increasing interest to the thin layer drying investigations inrecent 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 & aromatic

plants; 20.7%

Others; 8.0%

Figure 3 Distribution of the product types used in studies.

widely because of low technology and energy requirements suchthat modeling studies conducted on sun drying have preservedits importance as shown in Table 2.

The most popular thin layer drying method in literature andindustrial applications is hot air drying using convection as themain heat transfer mechanism. Generally, heated air is blownto the product and the drying rate is increased with the help ofthe forced convection. The main modeling studies executed withthis method within the last 10 years were compiled and shown inTable 3. Furthermore, the modeling in a drying cupboard withoutthe effect of airflow, done for some products, was summarizedin Table 4.

The improving effect of electrical heating methods on dryingprocesses, especially microwave and infrared, is strong. Thesemethods can shorten the drying time, and many modeling studiesfor these processes were performed with the thin layer concept(Table 5).

Furthermore, various pre-treatments are done to the raw foodproducts to facilitate the drying and to improve the productquality. These processes affect the drying kinetics directly andmany investigators used the thin layer concept to explain theeffects of various pre-treatments, especially in fruit drying. Thestudies conducted on the effects of pre-treatments to the dryingkinetics are shown in Table 6.

As mentioned above, the effective moisture diffusivity isa useful tool in explaining the drying kinetics, and activation

DC; 1.4%

SD; 8.3%MD; 6.9%

ICD; 6.9%

ID; 4.2%

FBD; 1.4%

CBD; 70.8%

Figure 4 Distribution of the drying methods used in studies.

Dow

nloa

ded

by [

Was

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at 0

9:42

17

Sept

embe

r 20

13

Tabl

e5

Stud

ies

cond

ucte

don

mat

hem

atic

alm

odel

ing

offo

oddr

ying

with

thin

laye

rco

ncep

tand

perf

orm

edby

elec

tric

alm

etho

ds.

Prod

uct

DM

Proc

ess

cond

ition

s#

Bes

tmod

elE

ffec

tsof

proc

ess

cond

ition

son

mod

elco

nsta

nts

Ref

eren

ce

App

le(s

lice)

IDT

=50

–80◦

C10

Mod

ified

Page

eq-I

Ik

=–9

.082

44+

1.58

0765

lnT

n=

11.4

9544

–1.

7401

6ln

TTo

grul

,200

5l=

–0.6

2879

2+

0.57

4354

lnT

App

lePo

mac

eM

DP

m=

150–

600

WU

ntre

ated

10Pa

gek

=–0

.017

83+

0.00

0130

3Pm

n=

1.67

47–

0.00

728P

mW

ang

etal

.,20

07b

Pm

=18

0–90

0W

Hot

air

pre-

drie

dk

=0.

0248

4+

0.00

0479

Pm

n=

0.87

04–

0.00

104P

m

ICD

T=

55–7

5◦C

Unt

reat

ed10

Log

arith

mic

a=

–20.

7119

6+

0.72

489T

–0.

0056

7T2

c=

21.8

0075

–0.

7272

8T+

0.00

569T

2Su

net

al.,

2007

k=

0.16

955

–0.

0048

5T+

0.00

0034

85T

2

T=

55–7

5◦C

Hot

air

pre-

drie

dPa

gek

=0.

1126

9–

0.00

34T

+0.

0000

2615

T2

n=

–8.6

026

+0.

3011

1T–

0.00

221T

2

Bar

ley

ICD

I=

0.16

7–0.

5W

/cm

2υ

=0.

3–0.

7m

/s—

Page

k=

0.80

495

+7.

2839

I2+

1.49

43R

H–

1.66

62υ

–1.

3368

Mi

Afz

alan

dA

be,

2000

RH

=36

–60%

Mi=

25–4

0%n

=0.

9785

7+

0.73

09I+

0.46

04R

H–

0.41

773υ

Car

rot

IDT

=50

–80◦

C5

Mid

illi

a=

64T

−0.7

1656

5n

=0.

1179

79ex

p(0.

0069

83T

)To

grul

,200

6k

=11

1T−1

.670

37b

∗=

–0.0

0005

1exp

(0.0

0499

3T)

Oliv

ehu

skIC

DT

=80

–140

◦ C—

Mid

illi

a=

0.96

656e

xp(0

.000

3269

6T)

n=

1.87

693

–0.

0139

3T+

0.00

0048

91T

2C

elm

aet

al.,

2007

k=

–0.0

0234

+0.

0005

4676

lnT

b∗

=[–

5644

28.4

8+

9055

.14T

–37

.28T

2]−

1

Oni

onIC

DI 1

=0.

5–1.

0kW

/kg

υ=

0.1–

0.35

m/s

3Pa

gek

=0.

058e

xp(2

.568

1I1+

1.84

1υ–

0.02

2L2

–0.

0608

RH

2W

ang,

2002

.

RH

=28

.6–4

3.1%

L=

2–6

mm

n=

1.36

58I

=2.

65–4

.42

W/c

m2

T=

35–4

5◦C

9L

ogar

ithm

ica

=0.

725

+0.

0415

I+

0.00

331T

+0.

054υ

k=

1.57

3–

0.35

7I–

0.03

39T

+0.

0555

υ

Jain

and

Path

are,

2004

υ=

1.0–

1.5

m/s

c=

0.00

651

–0.

0012

1I+

0.00

0223

T–

0.00

584υ

456

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A REVIEW OF THIN LAYER DRYING OF FOODS 457

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

Process Best Deff

Product DM conditions Pretreatments # model (m2/s) Reference

Banana CBD T = 50◦Cυ = 3.1 m/s

Untreated 3 Two-term 4.3E-10 - 13.2E-10 Dandamrongrak et al.,2002

BlanchedChilledFrozenBlanched & Frozen

Mulberry fruits(Morus alba L.)

CBD T = 50◦Cυ = 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 of Deff and Ea calculated by the thinlayer concept were collected in Table 7. Furthermore, Ea val-ues for microwave drying calculated by the Dadalı 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 resultsof 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 inthe 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-051 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52

Number of Products

Def

f (m

2/s)

Figure 5 Distribution of effective moisture diffusivity values compiled fromstudies.

The distribution of the drying methods used in the studiesis shown in Fig. 4. This graph displays that the interest of theinvestigators to the convective type batch dryers in food dryingprocesses. 70.8% of the studies reviewed have used convec-tive type batch dryers in their experiments. At the same time,this graph shows the increasing interest of the electrical dryingmethods, especially infrared drying. 18% of the reviewed stud-ies conducted on electrical drying methods and 11.1% of allthe studies were used in various types of infrared dryers. Theintensity of the infrared dryers can be explained as the harmonyof infrared theory and thin layer concept.

Marinos-Kouris and Maroulis (1995) compiled the 37 dif-ferent effective moisture diffusivity value intervals that werecalculated by the experiments. They expressed that the diffusiv-ities in foods had values in the range 10−13 to 10−6 m2/s, andmost of them (82%) were accumulated in the region 10−11 to

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-051 29

Number of Products

Def

f (m

2/s)

Figure 6 Distribution of effective moisture diffusivity values compiled fromstudies in which the experiments were done with convective type batch dryer.

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458 Z. ERBAY AND F. ICIER

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 = 60–80◦C υ = 1.0–1.5 m/s 8.41E-10 – 20.60E-10 — Akpinar et al., 2003bω = 8 × 8 × 18–12.5

× 12.5 × 25 mmApple pomace CBD T = 75–105◦C 2.03E-9 – 3.93E-9 24.51 Wang et al., 2007a

MD Pm = 150–600 W Untreated 1.05E-8 – 3.69E-8 — Wang et al., 2007bPm = 180–900 W Hot air pre-dried 2.99E-8 – 9.15E-8

ICD T = 55–75◦C Untreated 3.48E-9 – 6.48E-9 31.42 Sun et al., 2007T = 55–75◦C Hot air pre-dried 4.55E-9 – 8.81E-9 29.76

Apricot CBD T = 50–80◦C υ = 0.2–1.5 m/s(SO2-sulphured)

4.76E-9–8.32E-9 — Togrul and Pehlivan,2003

Bagasse CBD T = 80–120◦C υ = 0.5–2.0 m/s 1.63E-10 – 3.2E-10 19.47 Vijayaraj et al., 2007H = 9–24 g/kg L = 20–60 mm

Basil SD — 6.44E-12 — Akpinar, 2006bBitter leaves SD — 43.42E-10 — Sobukola et al., 2007Black Tea CBD T = 80–120◦C υ = 0.25–0.65 m/s 1.14E-11 – 2.98E-11 406.02 Panchariya et al.,

2002Carrot (slice) CBD T = 50–70◦C υ = 0.5–1.0 m/s 7.76E-10 – 93.35E-10 28.36 Doymaz, 2004a

ω = 10 × 10 × 10–20× 20 × 20 mm(pretreated)

ID T = 50–80◦C 7.30E-11 – 15.01E-11 22.43 Togrul, 2006Coconut (Young) CBD T = 50–70◦C L = 2.5 – 4 mm 1.71E-10 – 5.51E-10 81.11 Madamba, 2003

(Osmoticallypre-dried)

Crain-crain leaves SD — 52.91E–10 — Sobukola et al., 2007Fever leaves SD — 48.72E–10 —Grape (Chasselas) CBD T = 50–70◦C (1) 49 Azzouz et al., 2002Grape (Sultanin) CBD T = 50–70◦C (2) 54Green bean CBD T = 50–70◦C 2.64E-9 – 5.71E-9 35.43 Doymaz, 2005

FBD T = 30–50◦C υ = 0.25 − 1.0m/s — 29.57 – 39.47 Senadeera et al., 2003RH = 15% LD = 1:1, 2:1, 3:1

Hazelnut CBD T = 100–160◦C 2.30E-7 – 11.76E-7 34.09 Ozdemir and Devres,1999

T = 100–160◦C Mi = 12.3 %(moisturized)

3.14E-7 – 30.95E-7 48.70 Ozdemir et al., 2000

T = 100–160◦C Mi = 6.14 %(untreated)

3.61E-7 – 21.10E-7 41.25

T = 100–160◦C Mi = 2.41 %(pre-dried)

2.80E-7 – 15.65E-7 36.59

Kale CBD T = 30–60◦C L = 10–50 mm 1.49E-9 – 5.59E-9 36.12 Mwithiga and Olwal,2005

Kurut CBD T = 35–65◦C 2.44E-9 – 3.60E-9 19.88 Karabulut et al., 2007Mint SD - 7.04E-12 - Akpinar, 2006b

CBD T = 30–50◦C υ = 0.5 − 1.0m/s 9.28E-13 – 11.25E-13 61.91 – 82.93 Park et al., 2002T = 35–60◦C υ = 4.1m/s 3.07E-9 – 19.41E-9 62.96 Doymaz, 2006

Mulberry fruits(Morus alba L.)

CBD T = 60–80◦C υ = 1.2m/s 2.32E-10 – 27.60E-10 21.2 Maskan and Gouþ,1998

Okra MD Pm = 180–900 W m = 25–100 g 2.05E-9 – 11.91E-9 - Dadalı et al., 2007bOlive cake CBD T = 50–110◦C 3.38E-9 - 11.34E-9 17.97 Akgun and Doymaz,

2005Olive husk ICD T = 80–140◦C 5.96E-9 – 15.89E-9 21.30 Celma et al., 2007Paddy (parboiled) CBD T = 70–150◦C

υ = 0.5–2.0 m/sLd = 50–200 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 = 55–65◦C

(Blanched with %1KMS or AA)

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

Peas FBD T = 30–50◦Cυ = 0.25–1.0 m/sRH = 15%

- 42.35 – 58.15 Senadeera et al., 2003

(Continued on next page)

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A REVIEW OF THIN LAYER DRYING OF FOODS 459

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 = 0.71–2.86 mm 1.93E-11 – 9.16E-11 - Maskan et al., 2002CBD T = 55–75◦C L = 0.71–2.86 mm 3.00E-11 – 37.6E-11 10.3 – 21.7

Pistachio nuts CBD T = 25–70◦C 5.42E-11 – 92.9E-11 30.79 Kashaninejad et al.,2007

Plum (variety: Sutlejpurple)

CBD T = 55–65◦C (Untreated) 3.04E-10 – 4.41E-10 - Goyal et al., 2007

T = 55–65◦C (Blanched)T = 55–65◦C (Blanched with KMS)

Plum (Stanley) CBD T = 60–80◦C υ = 1.0 − 3.0m/s(pretreated)

1.20E-7 – 4.55E-7 - Menges and Ertekin,2006b

T = 60–80◦C υ = 1.0 − 3.0m/s(untreated)

1.18E-9 – 6.67E-9

T = 65◦C υ = 1.2m/s (Dippedin AEEO)

2.40E-10 - Doymaz, 2004d

T = 65◦C υ = 1.2m/s(untreated)

2.17E-10

Potato (slice) FBD T = 30–50◦C υ = 0.25 − 1.0m/s - 12.32 – 24.27 Senadeera et al., 2003RH = 15% AR = 1:1, 2:1, 3:1

Red chillies CBD T = 50–65◦C 3.78E-9 – 7.10E-9 37.76 Kaleemullah andKailappan, 2006

Rice (rough) CBD T = 5–35◦Cυ = 0.75–2.5 m/sRH = 30–70%

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

Spinach MD Pm = 180–900 Wm = 25–100 g

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

Tarhana Dough ID T = 60–80◦C L = 1–6 mmUntreated

4.1E-11 – 50.0E-11 41.6 – 49.5.Ibanoglu and Maskan,

2002T = 60–80◦C L = 1–6 mm Cooked 7.7E-11 – 67.0E-11 20.5 – 24.9

Wheat (parboiled) CBD T = 40–60◦C 1.23E-10 -2.86E-10 37.01 Mohapatra and Rao,2005

Yoghurt (strained) CBD T = 40–50◦C υ = 1.0 − 2.0m/s 9.5E-10 – 1.3E-9 26.07 Hayaloglu et al., 2007

(1)Deff = D0exp(-Ea /RTabs )exp(-(dTabs + e)M) Deff = 0.0016exp(-Ea /RTabs )exp(-(0.0012Tabs+ 0.309)M)(2)Deff = D0exp(-Ea /RTabs )exp(-(dTabs + e)M) Deff = 0.522exp(-Ea /RTabs )exp(-(0.0075Tabs+ 1.829)M)(3)Deff = (67.37 + 110.8υ – 14.64Ld+ 0.5946T – 4.706υLd+ 0.696L2

d – 0.0369LdT )×10–12

10−8 m2/s. In this study, 52 different diffusivity intervals werecompiled and shown in Fig. 5. The biggest Deff values were

between 10−5 and 10−6 (product number 23 to 26). The biggest4 values gained in hazelnut drying and the drying temperaturesof these experiments were between 100–160◦C. 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 10−12 to 10−6 m2/s and thisrange is more narrow than what Marinos-Kouris and Maroulis

Table 8 Activation energy values calculated by Dadalı model

Product Process conditions Ea (W/g) Reference

Mint Pm = 180–900 W 11.05(2) – 12.28 (1) Ozbek and Dadali, 2007Okra m = 25–100 g 5.54(1) Dadalı et al., 2007a

5.70(2) Dadalı 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 10−10

to 10−8 m2/s (75%).On the other hand, the distribution of Deff values according

to the drying method was plotted. Figure 6 showed the distribu-tion of Deff values collected from the studies reviewed, in whichthe experiments were conducted with a convective type batchdryer. Disregarding the hazelnut values as mentioned above, theaccumulation of Deff values of the foods that were dried in a

convective type batch dryer is in the region 10−10 to 10−8 m2/s(86,2%).

Figure 7 is arranged according to the Deff values obtainedby electrical methods. All values of infrared drying without theairflow were in the region 10−10 to 10−9 m2/s (ID). Deff valuesfor infrared drying systems that contain airflow mechanisms(ICD) appeared approximately in 10−8 m2/s level. This showedthat the drying rate for ICD were faster as expected, because ofthe enhancing effect of the airflow. In addition, the microwavedryer (MD) values were higher than the convective type batchdryers, and this was harmonious with the theory.

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

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460 Z. ERBAY AND F. ICIER

MDMD

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-051 2 3 4 5 6 7 8 9 10

Number of Products

Def

f (m

2/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-051 2 3 4 5 6 7 8 9

Number of Products

Def

f (m

2/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/

mo

l)

Figure 9 Distribution of activation energy values compiled from studies.

maximum temperature value was measured as 36◦C. 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 10−12 to 10−6 m2/s and the accumulation ofthe values was in the region 10−10 to 10−8 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. The studies showed that electrical drying methods were faster

than the others.d. The effect of temperature on Deff was 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 (s−2)a1 geometric parameter in Eqs. 5, 6

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A REVIEW OF THIN LAYER DRYING OF FOODS 461

A1, A2 geometric constantsAR aspect ratio (dimensionless)b empirical model constant (dimensionless)b∗ empirical constant (s−1)c empirical model constant (dimensionless)c∗ empirical constant (oC−1s−1)d empirical constant (K−1)e empirical constant (dimensionless)Deff effective moisture diffusivity (m2/s)(Deff)th theoretical value of effective moisture diffusiv-

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

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

data (s−1)h drying constant obtained from experimental

data (s−1)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 (s−1)k0 pre-exponential constant (s−1)kth theoretical value of drying constant (s−1)K drying constant (s−1)K11, K22, K33 phenomenological coefficients in Eqs. 1–4K12, K13, K21, coupling coefficients in Eqs. 1, 2K23, K31, K32

l 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 (oC−1)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)χ2 reduced chi-squareυ velocity (m/s).V volumetric flow rate (m3/s)ω dimensions (mm)α thermal diffusivity (m2s)λ empirical constant defines relationship between

Deff and Ea (m−2)φ characteristic moisture content (dimensionless)# 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

REFERENCES

Afzal, T.M. and Abe, T. (2000). Simulation of moisture changes in barley dur-ing far infrared radiation drying. Computers and Electronics in Agriculture.26:137–145.

Akgun, N.A. and Doymaz, I. (2005). Modelling of olive cake thin-layer dryingprocess. Journal of Food Engineering. 68:455–461.

Akpinar, E.K. (2006a). Determination of suitable thin layer drying curvemodel for some vegetables and fruits. Journal of Food Engineering. 73:75–84.

Akpinar, E.K. (2006b). Mathematical modelling of thin layer drying process un-der open sun of some aromatic plants. Journal of Food Engineering. 77:864–870.

Akpinar, E., Midilli, A. and Bicer, Y. (2003a). Single layer drying behaviourof potato slices in a convective cyclone dryer and mathematical modeling.Energy Conversion and Management. 44:1689–1705.

Akpinar, E.K., Bicer, Y., and Midilli, A. (2003b). Modeling and experimentalstudy on drying of apple slices in a convective cyclone dryer. Journal of FoodProcess Engineering. 26:515–541.

Akpinar, E.K., Bicer, Y. and Yildiz, C. (2003c). Research note: Thin layer dryingof red pepper. Journal of Food Engineering. 59:99–104.

Akpinar, E.K., Sarsilmaz, C., and Yildiz, C. (2004). Mathematical modelling ofa thin layer drying of apricots in a solar energized rotary dryer. InternationalJournal of Energy Research. 28:739–752.

Dow

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rsity

Lib

rari

es ]

at 0

9:42

17

Sept

embe

r 20

13

462 Z. ERBAY AND F. ICIER

Akpinar, E.K., Bicer, Y., and Cetinkaya, F. (2006). Modelling of thin layerdrying of parsley leaves in a convective dryer and under open sun. Journal ofFood Engineering. 75:308–315.

Azzouz, S., Guizani, A., Jomaa, W., and Belghith, A. (2002). Moisture diffu-sivity and drying kinetic equation of convective drying of grapes. Journal ofFood Engineering. 55:323–330.

Baker, C.G.J. (1997). Preface. In: Industrial Drying of Foods. Baker, C.G.J.Eds., Chapman & Hall, London.

Bakshi, A.S., and Singh, R.P. (1980). Drying Characteristics of parboiled rice.In: Drying’80, Mujumdar, A.S. Eds., Hemisphere Publishing Company,Washington DC.

Basunia, M.A., and Abe, T. (2001). Thin-layer solar drying characteristics ofrough rice under natural convection. Journal of Food Engineering. 47:295–301.

Brooker, D.B., Bakker-Arkema, F.W., and Hall, C.W. (1974). Drying CerealGrains. The AVI Publishing Company Inc., Westport, Connecticut.

Bruce, D.M. (1985). Exposed-layer barley drying, three models fitted to newdata up to 150◦C. Journal of Agricultural Engineering Research. 32:337–347.

Bruin, S., and Luyben, K. (1980). Drying of Food Materials. In: Advances inDrying. pp. 155–215, Mujumdar, A.S. Eds., McGraw-Hill Book Co., NewYork.

Carbonell, J.V., Pinaga, F., Yusa, V., and Pena, J.L. (1986). Dehydration ofpaprika and kinetics of color degradation. Journal of Food Engineering.5:179–193.

Celma, A.R., Rojas, S., and Lopez-Rodriguez, F. (2007). Mathematical mod-elling of thin-layer infrared drying of wet olive husk. Chemical Engineeringand Processing. (article in press).

Chandra, P.K. and Singh, R.P. (1995). Applied Numerical Methods for Foodand Agricultural Engineers. pp. 163–167. CRC Press, Boca Raton, FL.

Crank, J. (1975). The Mathematics of Diffusion. 2nd Edition, Oxford UniversityPress, England.

Crisp, J. and Woods, J.L. (1994). The drying properties of rapeseed. Journal ofAgricultural Engineering Research. 57:89–97.

Dadalı, G., Kılıc, D., and Ozbek, B. (2007a). Microwave drying kinetics ofokra. Drying Technology. 25:917–924.

Dadalı, G., Kılıc Apar, D., and Ozbek, B. (2007b). Estimation of effective mois-ture diffusivity of okra for microwave drying. Drying Technology. 25:1445–1450.

Dadali, G., Demirhan, E., and Ozbek, B. (2007c). Microwave heat treatment ofspinach: drying kinetics and effective moisture diffusivity. Drying Technol-ogy. 25:1703–1712.

Dandamrongrak, R., Young, G., and Mason, R. (2002). Evaluation of variouspre-treatments for the dehydration of banana and selection of suitable dryingmodels. Journal of Food Engineering. 55:139–146.

Demir, V., Gunhan, T. and Yagcioglu, A.K. (2007). Mathematical modellingof convection drying of green table olives. Biosystems Engineering. 98:47–53.

Diamante, L.M., and Munro, P.A. (1993). Mathematical modelling of the thinlayer solar drying of sweet potato slices. Solar Energy. 51:271–276.

Doymaz,.I. (2004a). Convective air drying characteristics of thin layer carrots.

Journal of Food Engineering. 61:359–364.Doymaz,

.I. (2004b). Pretreatment effect on sun drying of mulberry fruits (Morus

alba L.). Journal of Food Engineering. 65:205–209.Doymaz,

.I. (2004c). Drying kinetics of white mulberry. Journal of Food Engi-

neering. 61:341–346.Doymaz,

.I. (2004d). Effect of dipping treatment on air drying of plums. Journal

of Food Engineering. 64:465–470.Doymaz,

.I. (2005). Drying behaviour of green beans. Journal of Food Engi-

neering. 69:161–165.Doymaz,

.I. (2006). Thin-layer drying behaviour of mint leaves. Journal of Food

Engineering. 74:370–375.Ece M.C. and Cihan A. (1993). A liquid diffusion model for drying rough rice.

Trans. ASAE. 36:837–840.Ekechukwu, O.V. (1999). Review of solar-energy drying systems I: an overview

of drying principles and theory. Energy Conversion & Management. 40:593–613.

Erenturk, S., and Erenturk, K. (2007). Comparison of genetic algorithm andneural network approaches for the drying process of carrot. Journal of FoodEngineering. 78:905–912.

Erenturk, K., Erenturk, S. and Tabil, L.G. (2004). A comparative study for theestimation of dynamical drying behavior of Echinacea angustifolia: regres-sion analysis and neural network. Computers and Electronics in Agriculture.45:71–90.

Ertekin, C., and Yaldiz, O. (2004). Drying of eggplant and selection of asuitable thin layer drying model. Journal of Food Engineering. 63:349–359.

Fortes, M., and Okos, M.R. (1981). Non-equilibrium thermodynamics approachto heat and mass transfer in corn kernels. Trans. ASAE. 22:761–769.

Ghazanfari, A., Emami, S., Tabil, L.G., and Panigrahi, S. (2006). Thin-layerdrying of flax fiber: II.Modeling drying process using semi-theoretical andempirical models. Drying Technology. 24:1637–1642.

Glenn, T.L. (1978). Dynamic analysis of grain drying system. Ph.D. Thesis,Ohio State University, Ann Arbor, MI (unpublished).

Goyal, R.K., Kingsly, A.R.P., Manikantan, M.R., and Ilyas, S.M. (2007). Math-ematical modelling of thin layer drying kinetics of plum in a tunnel dryer.Journal of Food Engineering. 79:176–180.

Guarte, R.C. (1996). Modelling the drying behaviour of copra and developmentof a natural convection dryer for production of high quality copra in thePhilippines. Ph.D.Dissertation, 287, Hohenheim University, Stuttgart, Ger-many.

Gunhan, T., Demir, V., Hancioglu, E., and Hepbasli, A. (2005). Mathematicalmodelling of drying of bay leaves. Energy Conversion and Management.46:1667–1679.

Hassan, B.H., and Hobani, A.I. (2000). Thin-layer drying of dates. Journal ofFood Process Engineering. 23:177–189.

Hayaloglu, A.A., Karabulut, I., Alpaslan, M., and Kelbaliyev, G. (2007). Mathe-matical modeling of drying characteristics of strained yoghurt in a convectivetype tray-dryer. Journal of Food Engineering. 78:109–117.

Henderson, S.M., and Pabis, S. (1961). Grain drying theory I: Temperatureeffect on drying coefficient. Journal of Agricultural Engineering Research.6:169–174.

Henderson, S.M. (1974). Progress in developing the thin layer drying equation.Trans. ASAE. 17:1167–1172.

Hossain, M.A., and Bala, B.K. (2002). Thin-layer drying characteristics forgreen chilli. Drying Technology. 20:489–502.

Hossain, M.A., Woods, J.L., and Bala, B.K. (2007). Single-layer drying char-acteristics and colour kinetics of red chilli. International Journal of FoodScience and Technology. 42:1367–1375.

Husain, A., Chen, C.S., Clayton, J.T., and Whitney, L.F. (1972). Mathematicalsimulation of mass and heat transfer in high moisture foods. Trans. ASAE.15:732–736.

Iguaz, A., San Martin, M.B., Mate, J.I., Fernandez, T., and Virseda, P. (2003).Modelling effective moisture diffusivity of rough rice (Lido cultivar) at lowdrying temperatures. Journal of Food Engineering. 59:253–258.

Islam M.N. and Flink J.M. (1982). Dehydration of potato: I.Air and solar dryingat low air velocities. J.Food Technol. 17:373–385.

Ýbanolu, Þ., and Maskan, M. (2002). Effect of cooking on the drying behaviourof tarhana dough, a wheat flour-yoghurt mixture. Journal of Food Engineer-ing. 54:119–123.

Jain, D., and Pathare, B. (2004). Selection and evaluation of thin layer dryingmodels for infrared radiative and convective drying of onion slices. BiosystemsEngineering. 89:289–296.

Jayas, D.S. Cenkowski, S., Pabis, S., and Muir, W.E. (1991). Review of thin-layer drying and wetting equations. Drying Technology. 9:551–588.

Kaleemullah, S. (2002). Studies on engineering properties and drying kineticsof chillies. Ph.D.Thesis, Department of Agricultural Processing, Tamil NaduAgricultural University: Coimbatore, India.

Kaleemullah, S., and Kailappan, R. (2006). Modelling of thin-layer dryingkinetics of red chillies. Journal of Food Engineering. 76:531–537.

Karabulut, I., Hayaloglu, A.A., and Yildirim, H. (2007). Thin-layer drying char-acteristics of kurut, a Turkish dried dairy by-product. International Journalof Food Science and Technology. 42:1080–1086.

Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

9:42

17

Sept

embe

r 20

13

A REVIEW OF THIN LAYER DRYING OF FOODS 463

Karathanos, V.T. (1999). Determination of water content of dried fruits by dryingkinetics. Journal of Food Engineering. 39:337–344.

Kashaninejad, M., Mortazavi, A., Safekordi, A., and Tabil, L.G. (2007). Thin-layer drying characteristics and modeling of pistachio nuts. Journal of FoodEngineering. 78:98–108.

Kaseem, A.S. (1998). Comparative studies on thin layer drying models forwheat. In 13th International Congress on Agricultural Engineering, Vol. 6:2–6. February, Morocco.

Kaymak-Ertekin, F. (2002). Drying and rehydrating kinetics of green and redpeppers. Journal of Food Science. 67:168–175.

Keey, R.B. (1972). Introduction. In: Drying Principles and Practice. pp. 1–18.Keey, R.B. Eds., Pergamon Press, Oxford.

Kingsley, R.P., Goyal, R.K., Manikantan, M.R., and Ilyas, S.M. (2007). Effectsof pretreatments and drying air temperature on drying behaviour of peachslice. International Journal of Food Science and Technology. 42:65–69.

Kudra, T., and Mujumdar, A.S. (2002). Part I. General Discussion: Conventionaland Novel Drying Concepts. In: Advanced Drying Technologies. pp. 1–26.Kudra, T., and Mujumdar, A.S. Eds., Marcel Dekker Inc., New York.

Lahsasni, S., Kouhila, M., Mahrouz, M., and Jaouhari, J.T. (2004). Dryingkinetics of prickly pear fruit. Journal of Food Engineering. 61:173–179.

Lewis, W.K. (1921). The rate of drying of solid materials. I&EC-Symposium ofDrying, 3(5):42.

Luikov, A.V. (1975). Systems of differential equations of heat and mass transferin capillary-porous bodies (review). International Journal of Heat and MassTransfer. 18:1–14.

Madamba, P.S. (2003). Thin layer drying models for osmotically pre-driedyoung coconut. Drying Technology. 21:1759–1780.

Madamba, P.S., Driscoll, R.H., and Buckle, K.A. (1996). Thin-layer dryingcharacteristics of garlic slices. Journal of Food Engineering. 29:75–97.

Marinos-Kouris, D., and Maroulis, Z.B. (1995). Transport Properties in theDrying of Solids. In: Handbook of Industrial Drying. pp. 113–160. Mujumdar,A.S. Eds., 2nd Edition, Marcel Dekker Inc., New York.

Maskan, M., and Gouþ, F. (1998). Sorption isotherms and drying characteristicsof mulberry (Morus alba). Journal of Food Engineering. 37:437–449.

Maskan, A., Kaya, S., and Maskan, M. (2002). Hot air and sun drying of grapeleather (pestil). Journal of Food Engineering. 54:81–88.

Mazza, G., and Le Maguer, M. (1980). Dehydration of onion: Some theoreticaland practical considerations. Journal of Food Technology. 15:181–194.

Menges, H.O., and Ertekin, C. (2006a). Mathematical modeling of thin layerdrying of Golden apples. Journal of Food Engineering. 77:119–125.

Menges, H.O., and Ertekin, C. (2006b). Thin layer drying model for treated anduntreated Stanley plums. Energy Conversion and Management. 47:2337–2348.

Midilli, A., and Kucuk, H. (2003). Mathematical modelling of thin layer dryingof pistachio by using solar energy. Energy Conversion and Management.44:1111–1122.

Midilli, A., Kucuk, H., and Yapar, Z. (2002). A new model for single-layerdrying. Drying Technology. 20:1503–1513.

Mohamed, L.A., Kouhila, M., Jamali, A., Lahsasni, S., Kechaou, N., andMahrouz, M. (2005). Single layer solar drying behaviour of Citrus auran-tium leaves under forced convection. Energy Conversion and Management.46:1473–1483.

Mohapatra, D. and Rao, P.S. (2005). A thin layer drying model of parboiledwheat. Journal of Food Engineering. 66:513–518.

Mujumdar, A.S. (1997). Drying Fundamentals. In: Industrial Drying of Foods.pp. 7–30. Baker, C.G.J. Eds., Chapman & Hall, London.

Mujumdar, A.S., and Menon, A.S. (1995). Drying of Solids: Principles, Clas-sification, and Selection of Dryers. In: Handbook of Industrial Drying. pp.1–40. Mujumdar, A.S. Eds., 2nd Edition, Marcel Dekker Inc., New York.

Mulet, A., Berna, A., Borras, M., and Pinaga, F. (1987). Effect of air flow rateon carrot drying. Drying Technology, 5(2):245–258.

Mwithiga, G., and Olwal, J.O. (2005). The drying kinetics of kale (Brassicaoleracea) in a convective hot air dryer. Journal of Food Engineering. 71:373–378.

O’Callaghan, J.R., Menzies, D.J., and Bailey, P.H. (1971). Digital simulation ofagricultural dryer performance. Journal of Agricultural Engineering Researh.16:223–244.

Overhults, D.G., White, G.M., Hamilton, H.E., and Ross, I.J. (1973). Dryingsoybeans with heated air. Trans. ASAE. 16:112–113.

Ozbek, B., and Dadali, G. (2007). Thin-layer drying characteristics and mod-elling of mint leaves undergoing microwave treatment. Journal of Food En-gineering. 83:541–549.

Ozdemir, M., and Devres, Y.O. (1999). The thin layer drying characteristics ofhazelnuts during roasting. Journal of Food Engineering. 42:225–233.

Ozdemir, M., Seyhan, F.G., Bodur, A.O., and Devres, O. (2000). Effect of initialmoisture content on the thin layer drying characteristics of hazelnuts duringroasting. Drying Technology. 18:1465–1479.

Ozilgen, M., and Ozdemir, M. (2001). A review on grain and nut deteriorationand design of the dryers for safe storage with special reference to Turkishhazelnuts. Critical Reviews in Food Science and Nutrition. 41:95–132.

Page, G.E. (1949). Factors ınfluencing the maximum rate of air drying shelledcorn in thin-layers. M.S.Thesis, Purdue University, West Lafayette, Indiana.

Panchariya, P.C., Popovic, D., and Sharma, A.L. (2002). Thin-layer modellingof black tea drying process. Journal of Food Engineering. 52:349–357.

Pangavhane, D.R., Sawhney, R.L., and Sarsavadia, P.N. (2000). Drying kineticstudies on single layer Thompson seedless grapes under controlled heated airconditions. Journal of Food Processing and Preservation. 24:335–352.

Park, K.J., Vohnikova, Z., and Brod, F.P.R. (2002). Evaluation of drying pa-rameters and desorption isotherms of garden mint leaves (Mentha crispa L.).Journal of Food Engineering. 51:193–199.

Parry, J.L. (1985). Mathematical modeling and computer simulation of heat andmass transfer in agricultural grain drying. Journal of Agricultural EngineeringResearch. 54:339–352.

Parti, M. (1993). Selection of mathematical models for drying in thin layers.Journal of Agricultural Engineering Research. 54:339–352.

Paulsen, M.R., and Thompson, T.L. (1973). Drying endysus of grain sorghum.Trans.ASAE. 16:537–540.

Pinaga, F., Carbonell, J.V., Pena J.L., and Miguel, I.J. (1984). Experimentalsimulation of solar drying of garlic slices using adsorbent energy storage bed.Journal of Food Engineering. 3:187–203.

Rao, P.S., Bal, S., and Goswami, T.K. (2007). Modelling and optimization ofdrying variables in thin layer drying of parboiled paddy. Journal of FoodEngineering. 78:480–487.

Sawhney, R.L., Pangavhane, D.R., and Sarsavadia, P.N. (1999a). Drying kineticsof single layer Thompson seedless grapes under heated ambient air conditions.Drying Technology. 17:215–236.

Sawhney, R.L., Sarsavadia, P.N., Pangavhane, D.R., and Singh, S.P. (1999b).Determination of drying constants and their dependence on drying air param-eters for thin layer onion drying. Drying Technology. 17:299–315.

Senadeera, W., Bhandari, B.R., Young, G., and Wijesinghe, B. (2003). Influenceof shapes of selected vegetable materials on drying kinetics during fluidizedbed drying. Journal of Food Engineering. 58:277–283.

Sharaf-Eldeen, Y. I., Blaisdell, J.L., and Hamdy, M.Y. (1980). A model for earcorn drying. Transaction of the ASAE. 23:1261–1271.

Sobukola, O.P., Dairo, O.U., Sanni, L.O., Odunewu, A.V. and Fafiolu, B.O.(2007). Thin layer drying process of some leafy vegetables under open sun.Food Science and Technology International. 13:35–40.

Steffe, J.F., and Singh, R.P. (1982). Diffusion coefficients for predicting ricedrying behavior. Journal of Agricultural Engineering Research. 27:189–193.

Strumillo, C., and Kudra, T. (1986). Heat and Mass Transfer in Drying Processes.In: Drying: Principles, Applications and Design. Gordon and Breach SciencePublishers, Montreux.

Suarez, C., Viollaz, P., and Chirife, J. (1980). Kinetics of Soybean Drying.In: Drying’80. pp. 251–255. Mujumdar, A.S. Eds. Hemisphere PublishingCompany, Washington DC.

Sun, J., Hu, X., Zhao, G., Wu, J., Wang, Z., Chen, F., and Liao, X. (2007).Characteristics of thin-layer infrared drying of apple pomace with and withouthot air pre-drying. Food Sci Tech Int. 13:91–97.

Thompson, T.L., Peart, P.M., and Foster, G.H. (1968). Mathematical simulationof corn drying: A new model. Trans. ASAE. 11:582–586.

Togrul, H. (2005). Simple modeling of infrared drying of fresh apple slices.Journal of Food Engineering. 71:311–323.

Togrul, H. (2006). Suitable drying model for infrared drying of carrot. Journalof Food Engineering. 77:610–619.

Dow

nloa

ded

by [

Was

hing

ton

Stat

e U

nive

rsity

Lib

rari

es ]

at 0

9:42

17

Sept

embe

r 20

13

464 Z. ERBAY AND F. ICIER

Togrul, Ý.T., and Pehivan, D. (2002). Modelling of drying kinetics of singleapricot. Journal of Food Engineering. 58:23–32.

Togrul, Ý.T., and Pehlivan, D. (2003). Modelling of drying kinetics of singleapricot. Journal of Food Engineering. 58:23–32.

Togrul, Ý.T., and Pehlivan, D. (2004). Modelling of thin layer drying kinetics ofsome fruits under open-air sun drying process. Journal of Food Engineering.65:413–425.

Treybal, R.E. (1968). Mass Transfer Operations, 2nd Edition, McGraw Hill,New York.

Verma, L.R., Bucklin, R.A, Ednan, J.B., and Wratten, F.T. (1985). Effects of dry-ing air parameters on rice drying models. Transaction of the ASAE. 28:296–301.

Vijayaraj, B., Saravanan, R., and Renganarayanan, S. (2007). Studies on thinlayer drying of bagasse. International Journal of Energy Research. 31:422–437.

Wang, J. (2002). A single-layer model for far-infrared radiation drying of onionslices. Drying Technology. 20:1941–1953.

Wang, C.Y., and Singh, R.P. (1978). A single layer drying equation for roughrice. ASAE Paper No. 3001.

Wang, Z., Sun, J., Liao, X., Chen, F., Zhao, G., Wu, J., and Hu, X. (2007a).Mathematical modeling on hot air drying of thin layer apple pomace. FoodResearch International. 40:39–46.

Wang, Z., Sun, J., Chan, F., Liao, X., and Hu, X. (2007b). Mathemat-ical modelling on thin layer microwave drying of apple pomace with

and without hot air pre-drying. Journal of Food Engineering. 80:536–544.

Whitaker, T., Barre, H.J., and Hamdy, M.Y. (1969). Theoretical and experimentalstudies of diffusion in spherical bodies with variable diffusion coefficient.Trans. ASAE. 11:668–672.

White, G.M., Bridges, T.C., Loewer, O.J., and Ross, I.J. (1978). Seed coatdamage in thin layer drying of soybeans as affected by drying conditions.ASAE paper no. 3052.

Xanthopoulos, G., Oikonomou, N., and Lambrinos, G. (2007). Applicability ofa single-layer drying model to predict the drying rate of whole figs. Journalof Food Engineering. 81:553–559.

Yagcioglu, A., Degirmencioglu, A., and Cagatay, F. (1999). Drying charac-teristics of laurel leaves under different conditions. Proceedings of the 7thinternational congress on agricultural mechanization and energy, ICAME’99,pp. 565–569, Adana, Turkey.

Yaldiz, O., and Ertekin, C. (2001). Thin layer solar drying of some vegetables.Drying Technology. 19:583–597.

Yaldız, O., Ertekin, C., and Uzun, H.I. (2001). Mathematical modelling of thinlayer solar drying of sultana grapes. Energy. 26:457–465.

Yilbas, B.S., Hussain, M.M., and Dincer, I. (2003). Heat and moisture diffusionin slab products to convective boundary conditions. Heat and Mass Transfer.39:471–476.

Young, J.H. (1969). Simultaneous heat and mass transfer in a porous solidhygroscopic solids. Trans. ASAE. 11:720–725.

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